Composites Part Bvbirman/papers/Review2018.pdf · 2017. 11. 15. · civil and marine structures. The core of aerospace structures is often aluminum or Nomex honeycomb. In civil engineering

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Composites Part B

journal homepage: www.elsevier.com/locate/compositesb

Review of current trends in research and applications of sandwich structures

Victor Birmana,∗, George A. Kardomateasb

aMissouri S&T Global-St. Louis, Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, 12837 Flushing Meadows Drive,Suite 210, St. Louis, MO 63131, USAb School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150, USA

A R T I C L E I N F O

Keywords:Sandwich structuresAnalytical modellingStrengthDesign

A B S T R A C T

The review outlines modern trends in theoretical developments, novel designs and modern applications ofsandwich structures. The most recent work published at the time of writing of this review is considered, oldersources are listed only on as-needed basis. The review begins with the discussion on the analytical models andmethods of analysis of sandwich structures as well as representative problems utilizing or comparing thesemodels. Novel designs of sandwich structures is further elucidated concentrating on miscellaneous cores, in-troduction of nanotubes and smart materials in the elements of a sandwich structure as well as using functionallygraded designs. Examples of problems experienced by developers and designers of sandwich structures, in-cluding typical damage, response under miscellaneous loads, environmental effects and fire are considered.Sample applications of sandwich structures included in the review concentrate on aerospace, civil and marineengineering, electronics and biomedical areas. Finally, the authors suggest a list of areas where they envision apressing need in further research.

1. Introduction

Sandwich structures can be defined as a subset of multilayeredcomposite structures, optimized for the anticipated lifetime loadingconditions. A typical sandwich structure consists of the outer facingsand the core embedded between them. See for example, Fig. 1 belowwhere two facings are clearly identified. While in this figure, thesandwich structure has a tetrahedral truss core, numerous alternativecore designs have been employed, including foam, honeycomb, corru-gated core, various bio-inspired cores, etc. (see section 3.1 for details onthe latest core design developments). The facings are built of stiff andstrong materials and they are much thinner than the light and relativelycompliant core. Accordingly, a typical sandwich structure is somewhatsimilar to an I-beam where the flanges carry the lion share of bendingand in-plane loads, while the web sustains transverse shear, redis-tributes concentrated normal to the surface forces and maintains theintegrity of the structure. The thickness of the facings found in typicalstructural applications seldom exceeds several millimeters, while thecore may be over 50mm thick, although usually it is thinner. Excep-tions to the dimensions referred to here can be found, but they seldomnecessitate a development of an alternative theory for the analysis.

Neither the facings nor the core of a sandwich structure have to behomogeneous. While the facings can consist of a single metallic layer,laminated or woven composite materials are also broadly employed.

The core designs are even more diverse, including honeycomb, cellular,lattice and truss designs or web-reinforced options. The facing-coreinterface is often the most vulnerable part of the sandwich structure.This interface is often bonded (e.g., graphite epoxy facings joined to analuminum honeycomb core). Alternatively, the facing-core interfacecan be blended or functionally graded as is sometimes suggested forceramic-metal sandwich structures.

The choice of sandwich materials depends on the function of thestructure, lifetime loading, availability and cost. Graphite-epoxy andcarbon-epoxy multilayered facings are typical in aerospace applica-tions, while glass-epoxy or glass-vinyl ester are used in the facings ofcivil and marine structures. The core of aerospace structures is oftenaluminum or Nomex honeycomb. In civil engineering the core is often aclosed-cell or open-cell foam, while balsa of various density is a typicalchoice in ship sandwich structures.

Even though this review is concerned with the most recent devel-opments in sandwich structures, the major steps outlining the theoryand analysis methodologies are listed to present a comprehensive pic-ture. Those include the books by Plantema [1], Allen [2], Zenkert [3]and Vinson [4]. A comprehensive review of the studies of sandwichstructures covering the early developments was published by Noor,Burton and Bert [5]. Chai and Zhu reviewed research on low-velocityimpact of sandwich structures [6]. Non-destructive testing of thickcomposite and sandwich structures was reviewed by Ibrahim [7] and

https://doi.org/10.1016/j.compositesb.2018.01.027Received 15 November 2017; Received in revised form 6 January 2018; Accepted 27 January 2018

∗ Corresponding author.E-mail addresses: [email protected] (V. Birman), [email protected] (G.A. Kardomateas).

Composites Part B 142 (2018) 221–240

Available online 31 January 20181359-8368/ © 2018 Elsevier Ltd. All rights reserved.

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Hsu [8]. The features and methods of control of sandwich structuresusing magnetorheological and electrorheological fluids in the core werereviewed in Ref. [9]. The analyses of bending, buckling and free vi-brations of sandwich beams using equivalent single layer theories,layerwise theories, zig-zag theories and exact elasticity were outlined inRef. [10]. Abrate and Di Sciuva presented a review of equivalent singlelayer theories, including the classical, first, second and third orderformulations, polynomial and non-polynomial displacement methods[11]. Langdon et al. reviewed experimental and numerical studies ofsandwich structures subject to air blast [12]. Asymptotic methods of thehomogenization of composite and sandwich structures evaluating theireffective properties were considered by Kalamkarov et al. [13].Acoustic response of sandwich panels was reviewed in Ref. [14]. Therecent book of Carlsson and Kardomateas provides an insight in themodern methods of analysis and testing of sandwich structures [15].

The present review concentrates on the latest work on sandwichstructures. Earlier work is referenced only on as-needed basis. The re-view of such extensive field as sandwich structures ought to be limitedto selected subjects due to its multidisciplinary aspect and diverse rangeof involved problems. In this review, we concentrate on the theoreticalmodels and new designs and applications of such structures and onobservations of their behavior under a multitude of loads. Such essen-tial topics as manufacture or lifetime inspection are outside the scope ofthe review.

2. Analytical methods and representative verification studies

The studies of sandwich structures rely on a multitude of theoriesthat monitor the behavior of such structures undergoing mechanicaland/or environmental loading. These theories invariably begin with aformulation of kinematic relations that represent displacementsthroughout the structure as functions of in-plane (beams or plates) orin-surface (shells) coordinates and the thickness coordinate. The core ofa sandwich structure is usually light and its shear stiffness is low.Accordingly, neglecting transverse shear as is the case in technicaltheories of beams, plates and shells becomes unacceptable for most ofsandwich structures. Furthermore, the theories may rely on the samekinematics throughout the thickness of the structure or apply differentkinematic formulations for different layers of the structure as is de-scribed below.

The core of a sandwich structure being lighter and more compliantthan the facings, its modelling often defines the theory employed in theanalysis. In-plane stiffness of the core is often neglected, so in thepioneering research of sandwich structures, the core was sometimesmodelled as a medium with zero in-plane stiffness, finite transverseshear stiffness and incompressible in the thickness direction. Such ap-proach has been employed in the first-order and higher-order de-formation theories (FSDT and HSDT, respectively) representing the in-

plane displacements in the core as polynomial (or other analytical)functions of the thickness coordinate, while the through-the-thicknessdisplacement was assumed constant throughout the depth of thestructure:

∑= =u x x x f x x g x i( , , ) ( , ) ( ), 1,2,3ij

j ij1 2 3 1 2 3(1)

where x1 and x2 are in-plane (plate) or in-surface (shell) coordinates, x3is the thickness coordinate perpendicular to the middle plane or middlesurface and f x x g x( , ), ( )j ij1 2 3 are functions chosen according to a par-ticular theory. These functions must satisfy the requirement of zero in-plane shear and zero normal stresses on the free surfaces of the struc-ture, if the structure is treated by the equivalent single layer (ESL)approach, i.e. a unique kinematics is applied throughout the thickness.The stretching in the thickness direction is neglected if is neglected if

=g x( ) 1j3 3 .The models employed to characterize sandwich structures were

summarized in detail in the work of Carrera that is sometimes referredto as “Carrera unified formulation” or CUF [16] [17], and [18]. Thesearticles also contain an excellent review of various methodologies andvariations of these theories that had been applied to the analysis ofmultilayered and sandwich structures. The analytical approach can bereduced to the equivalent single layer model (ESL) that refers kine-matics of the structure to that of the middle surface and the layer-wiseapproach (LW) that acknowledges the presence of several distinct layersin the structure, applies kinematic and constitutive conditions to eachlayer and subsequently, fulfills the equilibrium conditions for the entirestructure as well as the continuity conditions at the interfaces betweenthe layers. The latter approach includes the zigzag theory referred tobelow. In the LW methods, equation (1) are applied to every layer,kinematics being specified by enforcing the continuity inter-layer con-ditions on displacements, their slopes or interfacial shear stresses. Forexample, the zigzag theory enforces the continuity of the shear stressesat the interfaces, while violating the continuity of the gradient of dis-placements across the interface. The majority of solutions obtained bysuch popular and well-known theories as FSDT and HSDT are in therealm of ESL since they represent the displacements throughout theentire thickness using one system of kinematic relationships. FSDT andHSDT modelling is often used for structures with honeycomb cores thatpossess high stiffness in the sandwich depth direction. Other cores havealso been modelled using these theories. Examples of recent papersemploying FSDT and HSDT in various aspects of sandwich structuresare found in Refs. [19], [20]. Extensions of conventional HSDT ac-counting for the in-plane and transverse flexibilities of the core havebeen actively pursued (e.g. [21,22]).

A possible generalization of the unified formulation was suggestedby Demasi [23,24] who considered the approach where different vari-ables can be described by different theories (ESL or LW). In particular,this research included the solution where some of the variables could becharacterized by a zigzag ESL description, while others were modelledusing an ESL model. The previous study of the same author combined13 HSDT, 13 zigzag and 13 LW theories into a single FEA model [25]. Asublaminate formulation [26] subdivides the structure through thethickness into sublaminates, such that each of them can be character-ized by either ESL or LW approach. A mixed LW/ESL approach wassuggested in Ref. [27] where the transverse stresses were characterizedby LW but the displacements were introduced via ESL in the facings and

Nomenclature

CFRP carbon fiber reinforced plasticCUF Carrera unified formulationEHSAPT extended high-order sandwich panel theoryESL equivalent single layer model

FEA finite element analysisFGM functionally graded materialFSDT first-order shear deformation theoryHSDT high-order shear deformation theoryLW layer-wise approach

Fig. 1. Composite sandwich panel with a tetrahedral truss core. From Ref. [87]. Re-produced with permission from Elsevier.

V. Birman, G.A. Kardomateas Composites Part B 142 (2018) 221–240

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via LW at the sandwich scale. A refinement of layer-wise sandwich platemodels was considered in Ref. [28].

In the zigzag theory referred to above, the choice of the displace-ment field through the thickness is dictated by the requirement of thecontinuity of displacements and transverse shear stresses at the inter-face between the layers of the structure, while accepting the slopediscontinuities at the interfaces. The refined zigzag theory where thedisplacement determined in each layer by FSDT is supplemented byadditional functions accounting for deformations of the cross section toachieve a higher accuracy was introduced and employed in a number ofinvestigations (e.g. [29–33]).

Both ESL and LW approaches simplify the problem for a sandwichstructure as refers to its three-dimensional nature. However, due to thecomplexity of the three-dimensional solution, even in the linear elasticformulation, the number of relevant papers is limited. Representativeelasticity solutions that were also employed as a benchmark for thecomparison with advanced high-order shear deformation theory(HSDT) have been published by Kardomateas et al. (e.g. [34–36]).Brischetto has recently published exact solutions for multilayeredsimply supported shells, including sandwich structures, that are sub-jected to a harmonic load [37]. The exact elasticity solution for freevibrations of spherical sandwich shells with a functionally graded ma-terial (FGM) core that can be reduced to the cases of cylindrical shellsor flat plates was also developed in Ref. [38]. Giunto et al. [39] in-vestigated the accuracy of several models considering indentationfailure of sandwich plates subject to loading applied over a limitedsurface area and demonstrated that only LW models yield the resultsthat are in a good agreement with the benchmark Pagano exact elas-ticity solution. The authors attributed this deduction to prevalenttransverse shear and normal through-the-thickness stresses.

The model referred to as EHSAPT (the extended high-order sand-wich panel theory) is particularly useful in the case where a finite in-plane core rigidity should be considered, such as medium to heavy massdensity foam or wood or if the response of the panel is of the localnature. It represents an extension of the HSDT model and employs theclosed-form polynomial displacement field distributions through thedepth of the core. The transverse and in-plane displacements in the coreare represented by second-order and third-order polynomials of thethickness coordinate, respectively. As a result, displacements at themiddle plane of the core are characterized by three generalized co-ordinates, including in-plane and transverse displacements as well asthe rotation of the core centroid. This theory has been applied to anumber of problems. In particular, Frostig [22] applied EHSAPT to theanalysis of in-plane loads through core, Phan et al. successfully com-pared the theory to the benchmark elasticity solutions and studiedbuckling of sandwich panels [40,41] and Phan et al. considered freevibrations [42]. Further examples of the application of EHSAPT tomiscellaneous mechanical problems of sandwich beams are found inRefs. [43] and [44].

The theory of homogenization of the material is also relevant toheterogeneous sandwich structures, replacing heterogeneous solidswith an equivalent homogeneous counterpart.

The method of asymptotic homogenization [45] was successfullyapplied to evaluate the properties of sandwich shells with cellular coresof various geometry as well as smart sandwich shells. The study [46]presents an asymptotic homogenization approach suitable for the ana-lysis of hexagonal honeycomb sandwich plates. The model results in aunit cell problem that can be applied to the determination of closed-form expressions for the effective elastic coefficients of the periodic cell.An extension to piezoelectric and piezomagnetic structures is alsoconsidered.

The following papers are listed as representative examples of therecent application of analytical and numerical models of sandwichstructures, including the benchmark elasticity solutions, ESL and LWtheories, higher-order theories and finite element method. In particular,free vibrations of sandwich panels with compressible and

incompressible cores were considered by a variety of theories andcompared to benchmark elasticity and finite element solutions in Refs.[42,47]. The comparison with benchmark solutions was favorable forlower vibration modes by all theories. The Levy problem for free vi-brations of sandwich shells and plates was considered by Dozio usingHSDT [48]. A LW analysis of free vibrations of sandwich beams withdamping using the classical lamination theory for the cross-ply facingsand FSDT for the core was employed to both evaluate natural frequencyand specify the modal loss factors [49]. Vibrations and damping ofcylindrical sandwich panels containing a viscoelastic flexible core wereanalyzed using HSDT and validated through a comparison with a LWapproach solution [50]. This paper can be considered in conjunction ofthe static analysis of cylindrical sandwich shells conducted by the sameauthors [51,52]. The effectiveness of cork layers as a damping treat-ment for sandwich structures was demonstrated both numerically (FEA)and experimentally in Ref. [53]. This study concentrated on sandwichplates with aluminum facings and cork compound cores. Impact ana-lysis of cylindrical sandwich shells subjected to impact was conductedby HSDT and successfully compared to experimental data [54]. Thesolution was obtained by assumption that the in-surface stiffness of thecore was negligible. Accordingly, the facings were modelled by theclassical theory, while the displacements and stresses in the core werefound from the theory of elasticity. This approach has also been appliedto other mechanical loading cases [55].

The layer-wise analysis of a geometrically nonlinear behavior of asandwich beam with viscoelastic core and elastic facings using FSDTtheory for each layer was published in Ref. [56]. Guided wave propa-gation in composite and sandwich strips was considered using a LWapproach [57]. The waves were generated by a piezoelectric actuator,their monitoring is potentially important in health monitoring appli-cations. Static and dynamic problems of sandwich plates were analyzedand favorably compared to the three-dimensional elasticity benchmarksolutions and FEA results using the refined zigzag theory [58], [59].Brischetto employed a LW approach to study free vibrations of cross-plysandwich shells and plates [60]. The LW third-order shear deformationtheory was employed in Ref. [61] to analyze delamination in sandwichpanels subject to slamming loads.

Frostig compared the shear buckling solutions for sandwich panelsby FSDT and two HSDT theories accounting for compressibility of thecore, one of the latter theories also accounting for in-plane rigidity ofthe core [62]. While all theories accurately predicted the critical loads,the eigenmodes were more accurately predicted by the higher-ordertheories.

A comparison between several theories employed for the free vi-bration analysis of isotropic, composite and sandwich cylindrical andspherical shell was presented in Ref. [63]. The compared solutionmethods included two-dimensional and three-dimensional finite ele-ment formulations, classical and refined 2D generalized differentialquadrature methods and an exact three-dimensional solution em-ploying the LW approach, the integration of elastic dynamic equili-brium equations and enforcing interlayer continuity conditions. Aparametric analysis revealed some of the trends affecting a differencebetween the solutions generated by different methods. A comparisonbetween various ESL and LW sandwich shell models is also presented inRefs. [64] and [65] where several theories are formulated based on thegeneral unified formulation by Carrera (CUF). Low velocity impact ofcurved sandwich beams was investigated using LW and ESL HSDTtheories that were in a close agreement in Ref. [66]. High local radialstresses in the impact area confirm the presence of a 3-D state in thevicinity to concentrated load points in a sandwich structure.

Using a finite element analysis for the investigation of sandwichstructures is always a potential alternative to first-order and higher-order theories. As an example, Caliri et al. introduced a four-node plateelement based on Caliri's generalization of the Carrera unified for-mulation (CUF) to accurately trace the stresses throughout the thick-ness of the sandwich plate [67]. A meshless formulation for sandwich


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plates using layer-wise HSDT and enforcing the continuity of in-planedisplacements and transverse shear stresses at the layer interfaces wassuggested in Ref. [68]. Finite element solutions based on Carrera'sunified formulation were considered for transverse bending of sand-wich plate and for both bending and vibrations of sandwich beams andplates using a LW approach in Refs. [69,70] and [71]. Both static anddynamic problems of sandwich plates with a multilayered core wereanalyzed by a finite element method [72]. Liu et al. [73] analyzedfunctionally graded sandwich double-curvature shells using a LW ap-proach and a differential quadrature finite element method (DQFEM). ALW FEA of static and dynamic problems for sandwich plates using alayerwise/solid-element method where the facing were representedusing the four-node quadrilateral elements and the core was discretizedusing a LW approach and eight-node solid elements was conducted inRef. [74]. Dynamic response of sandwich beams employing variousversions of HSDT to model the core leading to a kriging-based finiteelements solution was considered in Ref. [75]. An application of the so-called “proper generalized decomposition” displacement fields in a LWFEA formulation was pursued in Ref. [76]. A LW FEA analysis ofsandwich plates with a viscoelastic core was conducted by Ferreiraet al. [77]. A solid-shell eight-node hexahedral finite element capable ofaccounting for geometric and physical nonlinearity of the sandwichstructure was developed and experimentally verified in Ref. [78].

Reducing the number of degrees of freedom in a FEA formulationwas considered in Ref. [27] where transverse stresses in composite fa-cings were analyzed by the LW theory, displacements in the facingswere represented by the ESL approach, but the LW formulation wasapplied at the sandwich, facing-core level. The effect of damping on thedynamic behavior of sandwich beams with an aluminum foam core wasconsidered using ABAQUS in Ref. [79]. The analysis of sandwich platessubject to thermomechanical loading was conducted using FEA basedon the Reissner mixed variational formulation with continuousthrough-the-thickness transverse stresses and zigzag displacement fields[80].

In conclusion of this section, modern developments in the modellingof sandwich structures provide a reliable and proven foundation for theanalysis of particular problems as well as design applications. Themodels vary in complexity and accuracy, including a variety of ESLmethods, LW formulations and the extended higher-order theory thatmay be considered a variant of LW methods. As new designs of sand-wich structures, some of them discussed below, become available,certain modifications of existing theories may be needed as well as anenhancement of homogenization techniques. Nevertheless, the theoryof sandwich structures is definitely a mature and comprehensive toolavailable to researchers and engineers.

3. Novel designs and developments in sandwich structures

Examples of novel designs and latest developments in sandwichstructures discussed below include new and nontraditional core con-cepts, incorporation of nanotubes and smart materials in sandwichstructures and functionally graded sandwich applications.

3.1. Developments in non-traditional core concepts for sandwich structures

Truss-core and lattice-core sandwich research includes the study ofthe response of a carbon-fiber truss-core structure with the rods or-iented perpendicular to the facings in the broad temperature range [81]where both the strength and stiffness were found deficient at hightemperature due to softening of the polymeric matrix, while the prop-erties at cryogenic temperatures were fully retained and improvedcompared to those at room temperature. Different truss-core designswith pyramidal carbon-fiber truss cores have also been investigated. Inparticular, the study of residual compressive strength after the exposureto an elevated temperature revealed a reduction in the strength thatwas attributed to a degradation of the matrix and fiber-matrix interface

as well as formation of pores and development of cracks under hightemperature [82]. Torsional behavior of sandwich panels with pyr-amidal truss core was also studied [83]. A performance of pyramidalcore sandwich panels subject to aerodynamic heating was compared tothat of corrugated core counterparts [84]. Both the insulation and thestrength of the former panels were found superior to those with acorrugated core. An integrated thermal protection system analyzed inRef. [85] employs a lightweight C/SiC pyramidal core lattice withalumina fibers filling in the core and may be potentially employed inhypersonic vehicles. The effect of manufacturing-induced random da-mage in metallic sandwich plates with a pyramidal truss core on itsdynamic behavior was studied both by FEA as well as experimentally[86].

Panels with a tetrahedral core were manufactured using a novel hot-press molding method [87], Fig. 1, and their compressive and shearresponse experimentally investigated. The effect of the angle of thelattice struts on the crashworthiness of the core was experimentallystudied [88]. Hollow tetrahedral truss cores manufactured from nano-crystalline nickel were successfully compared to Nomex® honeycombcore counterparts [89].

Sandwich structures containing cores comprising of body centeredcubic lattice cells were tested to failure under three point bending. Twooptimized functionally-graded core designs were proposed based onlattice beam diameter tailoring and lattice cell spatial tailoring, re-spectively. Both stiffness and strength of the optimized cores weresignificantly increased compared to the uniform benchmark core. Asexpected, the greatest improvement in stiffness and strength was seenin the spatially graded lattice core due to the greater number of designvariables available for optimization [90]. The optimum design of alu-minum tetrahedral cores that is also applicable to other types of trusscore (pyramidal, Kagome) and to any other periodic core, such ascorrugated core, was considered by Dragoni [91].

Kagome core sandwich structures have also been investigated fol-lowing the pioneering paper by Wicks and Hutchinson [92]. Failuremaps and performance of metallic sandwich panels with four differenttypes of core were considered in Ref. [93], including pyramidal, tet-rahedral, Kagome and X-type configurations (Fig. 2). It was found basedon the analysis of global buckling, face sheet buckling, face sheetyielding, core member buckling and core member yielding that thelatter two core classes (Kagome and X-type) outperformed the pyr-amidal and tetrahedral counterparts. Superior performance of Kagometruss sandwich core structures has also been confirmed in Refs.[94–96]. An example demonstrating superior energy absorption inKagome truss sandwich structures is presented in the Ashby plot inFig. 3. The analytical approach to the homogenization of a wire-wovenKagome core was suggested and compared to numerical and experi-mental results [97]. An experimental comparison between lattice-trusscore and isogrid core sandwich cylinders demonstrated an advantage ofthe former in terms of compressive strength as well as a higher fun-damental frequency [98].

The interest in sandwich decks in bridge engineering generated aneed in robust core designs with significant strength, energy absorptionand damage tolerance. A new type of sandwich deck panels that hasrecently been considered employs truss cores filled with a polyurethanefoam [99–103]. Three core configurations were compared yielding theoptimum design (Fig. 4). The optimum core guarantees high strengthand stiffness as well as damage tolerance and energy absorption of thesandwich structure.

Ceramic “corrugated core” sandwich structures that are a class oftruss-core designs and can be employed in high temperature applica-tions have been manufactured, tested and analyzed [104]. Sandwichpanels with a corrugated steel core used for bridge decks were alsoconsidered in Ref. [105].

A comparison between the response of paper sandwich panels withthree types of a corrugated core, i.e. arctangent, wavy trapezoidal andhemispherical cores, was presented using nonlinear FEA and


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experiments [106]. The panels with a hemispherical core exhibit abetter response under both crush compression and shear loads. Theother study of mechanics of corrugated core panels was concerned withthe formation of wrinkles under compression [107]. In this study, acontinuum damage model was used to trace the onset of damage andthe development of strains in the wrinkled regions of the panel. Globaland local buckling of corrugated core sandwich panels was investigatedaccounting for nonlinear effects in Ref. [108]. The study of torsionalstiffness and twist response of sandwich corrugated core single anddouble walled plates was conducted by FSDT and FEA [109], the formertheory found sufficiently accurate for the characterization of suchstructures.

Considering other classes of core design, the behavior of grid-scoredsandwich panels where the core material is cut in small blocks that areattached to a career fabric to fit a complicated structure geometrymodelling innovative wind turbine blades was presented in Refs.[110,111]. In particular, a criterion for the onset of failure in the resingrid was suggested and found in a good agreement with experiments.

Various mechanical, thermal and fatigue problems were consideredfor sandwich structures with ceramic tile core sections (Fig. 5) revealingthe mode of damage associated with debonds at the gaps between tiles[112–114]. The sandwich beam with the core consisting of discrete tilesand subject to three-point bending was analyzed both numerically usinga LW approach and a customary FEA as well as by a standard FEA

[115]. Predictably, the gaps between the solid blocks of the tile corecaused a stress concentration in the facings and high stresses in theadhesive layers between the facings and core that could be somewhatreduced by filling the gaps. Local effects around the junction betweenthe sections of different core materials, e.g. polymer foams of differentmass density, and the associated fracture and fatigue damage were in-vestigated in Ref. [116].

Energy absorption of coconut mesocarp core sandwich structureswith glass/epoxy and carbon/epoxy facings was experimentally studiedin Ref. [117] utilizing the high energy absorption in the grain direction.Using a mesocarp core serves as an example of a bioinspired material inengineering.

Besides conventional foam and honeycomb core sandwich struc-tures, developments utilizing auxetic cores with a negative Poissonratio have been investigated due to the potential for higher stiffness andtoughness. In particular, morphing origami sandwich structures haverecently been suggested [118]. Fisher developed an aluminum foldedcore resembling origami configurations [119]. Rapidly deployableshelters, which can be packaged small but offer a high volume expan-sion ratio, are a critical asset for the military forward operating basesand can also be effective for the disaster relief. Origami-inspired de-ployable light-weight shelters utilizing easy packaging of foldable or-igami cores were suggested in Ref. [120].

Kirigami sandwich structures with the graded origami core con-sisting of fold and valleys as well as ply cuts have been investigated forsandwich applications [121] and demonstrated a potential for a sig-nificant impact energy absorption. Doubly curved configurations, such

Fig. 2. Schematics of four sandwich panels with truss core (SPTC) configurations. FromRef. [93]. Reproduced with permission from Elsevier.

Fig. 3. Gravimetric energy absorption in compression (top) and shear (bottom). FromRef. [94]. Reproduced with permission from Elsevier.


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as deployable domes and folded cores aircraft applications, wereidentified as potential application areas of this class of structures [122].Four different Kirigami sandwich cores were compared in Ref. [123]where it was shown that two of them, diamond strip and cube strip,offer a high energy absorption capacity and out-of-plane crushingstrength. The application of these Kirigami patterns to space frame andto hierarchical folded sandwich structures with the extended range offolded geometric envelopes was suggested [124].

Graded honeycomb Kirigami cores considered in Ref. [125] con-sisted of a conventional hexagonal section and a re-entrant butterfly-type Kirigami section that possessed a negative Poisson ratio. Experi-ments including flatwise and edgewise compression, and edgewiseimpact were conducted demonstrating advantages offered by suchgraded core. Zero Poisson ratio Kirigami honeycomb sandwich PEEKstructures were also manufactured using thermoforming technique andtested [126].

The advantages of Kirigami and origami core sandwich structures

do not come without certain vulnerabilities. For example, a recent ex-perimental and FEA study of origami core sandwich structures de-monstrated their vulnerability at the folded edges (creases lines) [127].

A comparative study of in-plane uniaxial compression response ofregular honeycomb, re-entrant auxetic honeycomb with a negativePoisson ratio, locally reinforced auxetic-strut structure and a hybridstructure combining regular honeycomb and auxetic-strut structure(Fig. 6) was performed [128] demonstrating the advantage of the latterdesign. The compressive strength was increased three-fold as comparedto that of the honeycomb sandwich panel and by 65% compared to theauxetic counterpart. A comparison between crashworthiness of sand-wich panels with four different cores including expanded poly-propylene foam, aluminum honeycomb, rubber foam balls and plastichollow balls was conducted in Ref. [129]. The energy absorption wasfound notably different for static compression and dynamic low-velo-city impact. While aluminum honeycomb core ensured a desirable re-sponse in both static and dynamic cases, the core filled with plastic ballswas also efficient in the former case, but foam filled core appeared more

Fig. 4. Three cores compared in Refs. [99–103] included(a): high density polyurethane foam, (b): trapezoidal lowdensity polyurethane foam with mat reinforcement and (c):web-core foam with mat reinforcement (top figure). Themost efficient design was (b), the specimen prepared fortesting are shown in the bottom picture. From Refs. [103]and [100]. Reproduced with permission from Elsevier.

Fig. 5. Sandwich panel with discrete tile core (top figure) and schematics of three-pointbending test. From Ref. [115]. Reproduced with permission from Elsevier.

Fig. 6. Cell designs: (a) Honeycomb, (b) Re-entrant honeycomb, (c) Auxetic-strut, (d) and(e) Auxetic honeycomb designs. From Ref. [128]. Reproduced with permission fromElsevier.


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competitive in the latter case.The effect of filling aluminum honeycomb core with expanded

polypropylene (EPP) foam on crashworthiness of sandwich panels inout-of-plane and in-plane compression tests was considered in Ref.[130]. It was shown that filling the core with foam significantly in-creases the peak strength, mean crushing strength and energy absorp-tion. However, the effect of foam density on the specific energy ab-sorption was negligible.

In a recent paper [131] impact resistance of sandwich panels withauxetic lattice core was investigated modelling the response of thematerial at high strain rates by the Johnson-Cook model.

An interest to lattice core sandwich structures operating in a high-temperature environment motivated a development of lattices with atailorable coefficient of thermal expansion [132,133]. In particular, itwas demonstrated in the latter paper on the example of six planar lat-tices of multi-fold rotational symmetry that it is possible to design theproduct possessing both high specific stiffness as well as zero or nega-tive coefficients of thermal expansion.

Pyramidal lattice core sandwich panel fabricated from ceramicmatrix C/SiC composite were developed and capable of withstandingvery high temperatures, up to 1600 °C [85,134–136]. Among inter-esting findings reported in this papers, the specific strength and specificstiffness of C/SiC sandwich panels were found superior to of the ZrO2

counterpart. A combination of high temperature resistance, lightweightcharacteristic and robust mechanical properties of C/SiC lattice coresandwich panels reported in the papers lead to the conclusion that theyare very attractive candidates for aerospace applications, such asthermal protection systems.

Among other studies, the changes in the thickness of web-coresandwich plates subject to compression were experimentally in-vestigated in Ref. [137] and found significant in the post-bucklingphase. Out-of-plane tensile performance of sandwich structures withperforated and stitched core was found superior to counterparts withconventional cores [138]. The stiffness of sandwich panels with Kraftpaper honeycomb core and medium density fireboard facings was nu-merically studied in Ref. [139] where it was found that a decrease inthe ratio of the thickness of the core to the thickness of a facing in-creased the bending and shear stiffness.

“Composite” cores combining honeycomb and a regular grid re-present an interesting development with a potential of increasingstrength, stiffness and toughness of sandwich structures. Mentionedhere is the recent paper [140] where a cellular aluminum honeycombwas combined with aluminum flat bars forming a grid. Experimentaland numerical analyses demonstrated that the sandwich panel withsuch composite core had a superior in-plane compressive stiffness andenergy absorption compared to counterparts with either grid or hon-eycomb cores.

Bio-inspired sandwich structures have recently been studieddrawing on the examples in biology, such as turtle shell and beetle

forewings, to develop efficient engineering designs. For example,crashworthiness of aluminum honeycomb carbon fiber reinforcedplastic (CFRP) facing sandwich panels was experimentally and nu-merically investigated [141] demonstrating superior energy absorptionas compared to bare CFRP panels. A double-sine bi-directionally cor-rugated sandwich panel (Fig. 7) exhibited excellent crashworthinessand a significantly reduced peak force under out-of-plane quasi-staticcompression as compared to convention al triangular and sinusoidalcorrugated core counterparts [142]. The source of bio-inspired coreshown in Fig. 7 is evident from the CT scan of the thick pitch-gradedlayer of in the dactyl of a peacock mantis shrimp (right part of Fig. 7)that provides a superb strength and energy absorption capacity. Low-velocity impact response of woodpecker's head-inspired sandwich beamwith CFRP facings and rubber and aluminum honeycomb cores (rubberlayer over the aluminum honeycomb layer) was considered in Ref.[143] where the proposed design resulted in a several-fold improve-ment compared to conventional counterparts.

Square tubes with a filler represent an energy absorbing structurethat expands the sandwich concept to dampers. The principal functionof a compliant filler is to facilitate the absorption of energy. This con-cept was investigated under quasi-static axial crushing, lateral planarcrush and lateral bending for carbon fiber reinforced plastic tubes filledwith aluminum honeycomb in Refs. [144] and [145]. In particular,under axial crushing, the peak load and absorbed energy of the filledtubes were increased by over 10% compared to otherwise identicalhollow tubes. The energy absorbed and specific energy absorption ofthe filled tubes experiencing lateral crushing could be increased byfactors of 6.56 and 4.0, respectively, compared to the correspondingcharacteristics in the hollow tubes without fillings. The improvementsin specific energy absorption were smaller in case of lateral bending,though the energy absorption still showed a 32% increase in filledspecimens.

In general, recent research on novel core designs of sandwichstructures has demonstrated a potential for new and innovative coresthat can be advantageous compared to more conventional designs (e.g.,honeycomb or cellular cores) in numerous applications. While the easeof manufacture and accurate modelling of structures incorporating newcores may present a problem, the latest publications have reflectedsignificant progress fully justifying further research on such innovativedesigns and their eventual introduction in practical engineering appli-cations.

3.2. Nanoinclusions in sandwich structures (nanotubes and nanoparticles)

A considerable interest in using nanotubes and nanoinclusions toenhance the properties of structures yielded thousands of papers, someof them concerned with sandwich structures. In this section we re-ference recent static and dynamic studies of these structures, reflectingon a broad variety of addressed problems.

Fig. 7. Bio-inspired bi-directionally corrugated sandwichpanel (left) and a CT scanning of a dactyl club section(right). From Ref. [142]. Reproduced by permission ofElsevier.


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Brischetto and Carrera considered the effect of nanoscale re-inforcements on the static response of sandwich plates and shells sub-ject to pressure [146,147]. Two classes of reinforcements consideredincluded clay platelets and carbon nanotubes. The solutions by theclassical lamination theory, FSDT and the advance mixed-modelmethod where the displacements can be modelled using either an ESLor LW approach, while transverse stresses are evaluated using a LWapproach demonstrated the advantages of the latter method as well asthe effectiveness of nanoscale reinforcements.

The effect of adding SiC nanoparticles to polyurethane foam core ofsandwich structures was experimentally studied in Ref. [148]. Whilemechanical properties of the core were enhanced by adding nano-particles, the fracture toughness of the foam core was reduced. At SiCparticle concentrations the interface crack propagated in the core, butthe path changed at a lower concentration, so that the crack remainedin the vicinity to the facing-core interface.

A three-layer sandwich structure consisting of polymer multi-walledcarbon nanotube reinforced composites was proposed and experimen-tally investigated in Ref. [149] demonstrating both a satisfactory me-chanical performance and a high electromagnetic interference shieldingeffectiveness. Sandwich microwave absorbers were considered in Ref.[150] combining nanocomposite and honeycomb layers and producinga broad-wave absorber. A sandwich structure designed for a maximumradar absorption and consisting of a carbon nanotube composite facing,polymethacrylimide foam core and a carbon-epoxy composite reflectorfacing was designed, produced and assessed in Ref. [151].

An axisymmetric problem of buckling of a variable thickness cir-cular sandwich plate with functionally graded multi-walled nanotubereinforced facings and a polymer core subjected to radial compressionwas analyzed using FSDT in Ref. [152]. Interfacial fracture toughness ofsandwich glass/fiber facing, polyvinyl-chloride foam core compositeswas markedly improved by adding multi-walled carbon nanotubesdispersed in the epoxy resin using a sonicator [153]. In particular, theincreases in the peak load-carrying capacity and in fracture toughnessachieved by adding 1.5% weight fraction of nanotubes were 14.4% and34%, respectively.

The effectiveness of the impregnation of the polyurethane foam coreof sandwich plates with nanoparticles was considered in Ref. [154]. TheMori-Tanaka and self-consistent methods were employed to evaluatethe gain in stiffness associated with the introduction of nanoparticles,while the potentially detrimental effect on the strength was studiedusing the Goodier solution for dilute and the Mori-Tanaka theory for thefinite particle concentrations.

Free vibrations of sandwich plates with functionally graded nano-tube reinforcements subject to an elevated temperature were analyzedutilizing HSDT in Refs. [155] [156], and [157]. Both free vibrations aswell as buckling of sandwich beams with functionally graded nanotubereinforced facings were considered by FSDT in Ref. [158]. Vibrations ofa sandwich plate with carbon nanotube reinforced facings and a com-pliant core subjected to a combination of a magnetic field and tem-perature were analyzed [159] using a HSDT and accounting for theeffect of temperature on the material properties. The study of free vi-brations of carbon nanoparticle reinforced functionally graded sand-wich beams, including the micromechanical analysis that employed theMori-Tanaka method was presented in Ref. [160]. Both free vibrationsand static bending of sandwich plates with carbon nanotube reinforcedfacings were numerically studied by FEA utilizing HSDT [161]. Geo-metrically nonlinear vibration and bending problems of sandwichplates with nanotube reinforced facings subjected to an elevated tem-perature and supported by a Pasternak elastic foundation were con-sidered using HSDT in Ref. [162].

Nonlinear vibrations of doubly curved sandwich shells with carbon/epoxy facings where the carbon fibers are reinforced with nanotubesgrown on their surface were considered in Ref. [163]. In addition tonanotubes, vibrations were controlled through an active constrainedlayer representing a constrained viscoelastic layer sandwiched between

the host structure and the constraining piezoelectric fibers.Kolahchi et al. considered wave propagation in a sandwich plate

with polymeric nanotube-reinforced core and piezoelectric facingsemployed as an actuator and a sensor using a zigzag theory [164].Multi-walled nanotubes embedded in the facings of sandwich platessubject to a low-velocity impact improved the energy absorption anddamage tolerance both in the experimental work [165] and in theanalytical HSDT study [166]. Using nanoparticles for alleviation of theeffect of a low-velocity impact in sandwich panels was experimentallyinvestigated in Ref. [167] adding an acrylate triblock copolymer na-noinclusions to the epoxy matrix. Nanotubes have also been shownbeneficial reinforcing brittle resin epoxy cores in sandwich panels un-dergoing explosive blast [168].

Dynamic transient behavior of sandwich beams with carbon nano-tube reinforced facings and a soft core was considered extending thehigh order sandwich panel theory (EHSAPT) to the case of a dynamicloading [169]. Dynamic buckling of sandwich spherical caps withcarbon nanotube reinforced facings undergoing a suddenly appliedaxisymmetric load and dynamic instability of such caps subject to anaperiodic load were investigated by FEA in Refs. [170] and [171], re-spectively. Snap-through of a sandwich beam with functionally gradedor uniformly distributed nanotube reinforced facings undergoing acombination of pressure and thermal loading were considered by FSDT[172] accounting for geometric nonlinearity. Nonlocal piezo-magneto-elastic formulation for sandwich nanoplates containing a nanocore andintegrated piezo-magnetic facings was developed and applied to thedynamic analysis in Ref. [173].

A supersonic flutter of doubly curved sandwich panels with nano-tube reinforced facings was numerically investigated using FEA basedon a zigzag HSDT approach [174]. The other practical application ofnanotubes in aerospace sandwich structures is tail buffeting. In parti-cular, the effectiveness of nanotubes preventing tail buffeting of asandwich rudder of a business jet built of carbon/epoxy nanotube re-inforced facings and a honeycomb core was demonstrated in Ref. [175].

The list of publications on nanoinclusion and nanotube applicationsin sandwich structures can be expanded, the references listed abovebeing the latest in this area at the time of writing this review. Almost allaspects of mechanical and thermomechanical response of a sandwichstructure can be enhanced through the introduction of nanoreinforce-ments. Even though a mismatch in the properties of nanotubes and coreor facing materials may in theory cause microcracking during themanufacturing process or during lifetime, apparently such damage doesnot significantly affect the performance of structures.

3.3. Application of smart materials in sandwich structures

While the definition of so-called smart materials is rather vague, areasonable reference to these materials is that they exhibit a type ofbehavior that is not found in conventionally used isotropic and com-posite counterparts. The areas of practical or suggested applications ofsmart materials are diverse. Examples of such materials include pie-zoelectrics, shape memory alloys, electrorheological and magne-torheological fluids, etc. The use of piezoelectric, shape memory alloyand other smart materials has been actively pursued since the end of theeighties. Nowadays, such materials are included in the models ofsandwich structures to achieve passive or active control or with thepurpose of sensing.

The analysis of sandwich plates with a metallic core and outermetal-ceramic functionally graded or piezoelectric layers using B-splinefinite strip element models and based on first-order and higher-ordershear deformation theories was presented [176]. The homogenizationadopted in this paper employed the Mori-Tanaka scheme that is ac-ceptable if the volume fraction of inclusions remains below about 35%.An improved version of the zigzag theory was applied to monitor theresponse of cylindrical sandwich shells including piezoelectric layers tothermal and electrical loading [177] and using the heat conduction


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solution to model a distribution of temperature through the thickness ofthe shell.

A FEA formulation applied to forced and free vibrations of sandwichbeams with piezoelectric layers accounting for both electric transversestrains and transverse flexibility effects was presented in Refs.[178,179]. Using an active constraining layer employing oblique orvertical 1–3 piezoelectric fibers to control vibrations of functionallygraded sandwich plates was analyzed in Ref. [180]. Using patches of aconstraining layer with 1–3 piezoelectric material for active damping ofvibrations of sandwich beams was also studied [181].

A three-dimensional piezoelastic formulation was employed tocharacterize a viscoacoustic response of a hollow radially polarizedspherical shell in an ideal compressible fluid [182]. The solution wasapplied to a sandwich shell with piezoelectric facings and steel core.

A potential detrimental effect of embedding piezoelectric sensors inthe facings of a sandwich structure that is due to a mismatch in theproperties of piezoelectric and facing materials was considered in Ref.[183]. In the experiments, it was found that while the fatigue life islittle affected by the presence of sensors, there was a reduction in thestrength limited to several percentage points. The use of embeddedpiezoelectric sensors for health monitoring of laminated and sandwichstructures was also reported in Ref. [184] where the incorporation ofsensors resulted in a small degradation in mechanical properties.

A nonlinear dynamic analysis of sandwich plates with shapememory alloy wires embedded in the facings that were modelled by theBrinson constitutive method was considered using Carrera's unifiedformulation and a mixed LW/ESL approach [185], [186]. Free vibra-tions and buckling problems in cylindrical sandwich panels with amagnetorheological fluid layer were studied employing HSDT [187].

Active-passive controlled structures are often included in the familyof smart structures. Optimization of modal loss factors of active-passivesandwich plates with active elastic constrained damping layers and aviscoelastic core using the thickness and laminate layer orientationangles as design variables was conducted using a LW finite elementmodel in Ref. [188]. The study aimed at determining the location of aprescribed number of sensors and actuators necessary to maximize theloss factor. The previous optimization work [189] also concerned withsandwich plates with a viscoelastic core was confined to optimization ofpassive damping using a HSDT for the core and FSDT for the facings inthe framework of a LW FEA formulation.

3.4. Functionally graded sandwich structures

Functionally graded materials have been actively investigated inalmost all areas of structural analysis and design. In sandwich struc-tures, grading is usually employed in the core as well as at the facing-core interface.

Historically, one of the first studies of the three-layered sandwichsystem with the FGM core was proposed by Pitakthapanaphong andBusso [190]. Both thermoelastic as well as thermoplastic behavior wereconsidered in this paper. Following this study, stability, vibrations andbuckling of sandwich conical and cylindrical shells with functionallygraded core and coatings were considered by Sofiyev et al. [191–196].(see, Sofiyev et al. [2–6] and Deniz [7]). The latest studies of stabilityand dynamics of shear-deformable functionally graded conical shells bythe Sofiyev and his colleagues include [197–204]. A pioneering re-search of dynamic instability of sandwich cylindrical shells with a FGMcore was performed by Sofiyev and Kuruoglu [205]. In this study,Ambartsumian's first order shear deformation theory (FSDT) wasmodified for a sandwich cylindrical shell with a FGM core. Subse-quently, Sofiyev, Hui and their colleagues addressed the problems ofstability, free and parametric vibrations of sandwich cylindrical shellscontaining the FGM core and coatings in the framework of FSDT indifferent environments [206–208].

The effectiveness of functional grading of the core of a taperedsandwich beam in the axial direction was considered using a FSDT

geometrically nonlinear approach in Ref. [209]. The effect of elasticedge restraint on axisymmetric static bending of annular sandwichplates with a FGM core was studied in Ref. [210].

The beneficial effect of a functionally graded core preventingwrinkling in sandwich structures was considered for both a layer-wisecore analyzed using the theory of elasticity approach and for a corewith a continuous through the thickness grading by a modified Hoffmethod [211]. A significant increase in the wrinkling load was achievedby concentrating stiffer core adjacent to the loaded facing, without anappreciative detrimental effect on the weight of the structure. While anelevated temperature caused a decrease in the wrinkling stresses, thebenefits of functional grading was preserved. The subsequent studydemonstrated that even though the wrinkling load is reduced in case ofa biaxial compression and, to a lesser degree, in-plane shear, func-tionally graded plates retain the advantages over equal-weight coun-terparts with a homogeneous core [212].

Thermal buckling of a FGM sandwich panel was considered by bothfirst-order and higher-order shear deformation theories using the rule ofmixtures to specify the local material properties dependent on the vo-lume fractions of constituent materials [213]. Thermomechanical pro-blems of FGM sandwich microplates were considered in Ref. [214].

Free vibrations of cylindrical sandwich shells that were functionallygraded in the thickness direction were studied in Ref. [215]. Theproperties of the core were represented by power functions of the radialcoordinate. The shell was subdivided into thin layers of constantproperties enabling the exact solution by the theory of elasticity. A LWfinite element formulation accounting for the through-the-thicknessdeformations in the core of a sandwich panel was developed and ap-plied to both static and dynamic analyses [216]. Both bending and freevibrations of a sandwich plate with FGM core were considered em-ploying a finite element analysis in Ref. [217]. The analytical solutionfor free vibrations of sandwich plates with functionally graded coreswas suggested in Ref. [218] using a modified Ritz analysis and re-presenting displacements in series of Chebyshev polynomials. In thispaper, the rule of mixtures was employed to determine the properties ofthe FGM core.

Free vibrations of spherical and cylindrical sandwich shells withFGM cores were considered in Ref. [219] using a generalized differ-ential quadrature method. Blast response of sandwich plates with FGMceramic-metal facings was considered using HSDT in Ref. [220]. Blastdamage in sandwich structures with a layerwise density graded corewas experimentally investigated and the advantages of grading de-monstrated [221].

Miscellaneous problems of static and dynamic behavior of func-tionally graded sandwich plates resting on an elastic foundation wereanalyzed in Refs. [222–224]. Experimental work conducted on E-glassfacing, layer-wise graded PVC foam core flat and curved panels de-monstrated potential advantages of grading in preventing impact da-mage [225].

Neves et al. [226] presented explicit governing equations for staticsand dynamics of FGM sandwich plates using a higher-order shear de-formation theory where in-plane and through-the-thickness displace-ments were represented by cubic and quadratic polynomials of thethickness coordinate, respectively. The solutions utilizing Carrera'sUnified Formulation were shown for both static as well as free vibrationproblems, including buckling. Brischetto presented an elasticity solu-tion for natural frequencies of various classes of sandwich structuresrepresenting them by a number of layers, each layer having constantproperties, resulting in constant coefficients in the correspondingequations of motion [227].

While functional grading of sandwich structures is usually con-sidered in the framework of through-the-thickness variations of theconstituent material concentration, the variations of geometry usingstepped-wise facings changing from the center to the edges was alsostudied [228,229].

Introducing a chopped fiber mat between the core and facings may


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also be considered as a form of functional grading. Such modification ofthe facing-core interface can significantly enhance the impact tough-ness, flexural strength and energy absorption of the structure [230].

4. Sample problems in analysis and design of sandwich structures

4.1. Damage in sandwich structures

Extensive studies are conducted on damage in sandwich structures,including the conditions for damage onset, detection, propagation andmitigation. Modes I and II strain energy release rate at the facing-coreinterface in sandwich structures employed in wind turbines was ex-perimentally investigated [231]. Different core VaRTM (vacuum as-sisted resin transfer molding) machining patterns were compared tomaximize the interfacial facing-core fracture toughness [232]. High-sped infrared thermography was considered for monitoring the inter-facial fracture toughness in sandwich structures by monitoring tem-perature variations at the front of the crack [233]. The mode of fracturein sandwich structures depends on the stiffness of the core. This wasdemonstrated in the paper [234] where the mixed-mode fracture crackpropagated in a relatively compliant core (Divinycell H45), but dela-mination cracking occurred between the facing and the adjacent resin-rich layer of the core in the structure with a stiffer core (DivinycellH45). Mode III delamination fracture in sandwich plates was studiedexperimentally and by FEA in Ref. [235].

A methodology for the detection of interfacial cracks in sandwichstructures using high speed infrared thermography to trace the changesin temperature during the crack growth was proposed and verified onthe specimens with E-glass/epoxy facings and a PVC foam core in Ref.[233]. Using sandwich double cantilever beams for the characterizationof fracture in the foam has also been reported (e.g. [236]). Three dif-ferent U-shape “peel-stoppers” that could be effective arresting fractureand fatigue damage were discussed and successfully tested [237].

An efficient method of fatigue testing of sandwich structures using acomputer software to control the testing apparatus and called G-controlmethod since it enables keeping constant energy release rate was dis-cussed in recent papers [238,239]. Fatigue of sandwich beams withcarbon fiber polymer matrix facings and Nomex core was also experi-mentally investigated using accelerated testing techniques [240]. Atransition of the fatigue failure mode in sandwich beams from the coreshear to the facing tensile failure dependent on the amplitude of theload were experimentally observed [241]. Fatigue cracks in specimenswith Divinycell H45 core grew along the facing-core interface, while inthe specimens with a much stiffer H100 core the crack deviated into thecore or in the facing dependent on the mode mixity at the tip [242].Fatigue in damaged honeycomb core sandwich panels was consideredin Ref. [243] where it was demonstrated that in sandwich panels withBrinell or drilling holes, the lifetime of the specimens loaded in the Lconfiguration is longer than that for the counterparts loaded in the Wdirection (here L and W directions refer to the directions defined for ahexagonal core, as shown in the article).

Among the studies on the manufacturing damage, significant effectof wrinkles acquired during the manufacture process on fatigue ofglass/epoxy facing balsa core sandwich beams was found in experi-ments [244]. In particular, a wrinkle could reduce fatigue life of aspecimen by two thirds as compared to the counterparts without suchmode of damage. The effect of manufacture-acquired wrinkles on sta-tically compressed sandwich panels was also studied [245].

Frostig and Thomsen [22] investigated a thermomechanical re-sponse of a delaminated curved sandwich panel with a delaminationcrack at one of the facing-core interfaces. The response was promi-nently nonlinear, exhibiting a limit point and significant stress con-centrations at the tips of the delamination and near the supports. Theenergy release rate and the mode mixity in a sandwich beam withdissimilar facings and a facing-core debond were derived in a closedform [246] extending the known solutions for a delamination in a

homogeneous composite and an interfacial crack between two solids.Debonding between the facings and core under mixed-mode loadingwas experimentally studied in Ref. [247] where Mode II loading wasfound to enhance the fracture toughness of the interface.

Using z-pins can improve the load capacity and energy absorption ofthe sandwich structure. In particular, it was demonstrated that thecompressive strength of a sandwich composite can be increased by upto 700% using z-pins perpendicular to the surface of the component toalleviate the core crushing [248]. In the same paper, using z-pins theabsorbed compressive strain energy was increased by more than 600%.Impact damage and residual compressive strength and stiffness of z-pinned sandwich composites were considered in the subsequent study[249]. The absorbed energy of z-pinned specimens increased by260–300% compared to otherwise identical specimens without z-pins,but the extent of local damage in the impacted region was not affected.There was no significant improvement in the residual strength andstiffness of the structure. Using of z-pins to alleviate fracture in sand-wich composite T-joints was considered in Ref. [250] reinforcing cleatsconnecting the vertical and horizontal structural elements. Both thefracture load as well as the fracture energy were increased since z-pinsresisted crack propagation along the cleat-facing and facing-core in-terfaces. A composite wing with z-pin reinforced core sandwich panelswas considered in Ref. [251].

Stitching or tufting are techniques that can improve the damageresistance and load capacity of sandwich structures. Sandwich C/SiCpanels with a stitched lattice core possess high out-of-plane compres-sive strength and stiffness [252]. Improvement in mechanical proper-ties using core perforation and stitching were investigated in Refs.[138,253]. The interfacial fracture toughness of stitched sandwichspecimen was improved compared to unstitched counterparts [254].Tufting using through-the thickness aramid fibers was found effective inimproving the in-plane impact crushing response of sandwich structuresthrough the better facing-to-core adhesion [255]. In experiments re-ported in this paper, tufting nearly doubled the specific energy ab-sorption.

Damage detection in sandwich structures is paramount for theirapplication in industry. For example, a 10MHz ultrasonic 128 elementsphased array transducer was successfully used to detect and size defectsin sandwich honeycomb composite structures [256]. Random defects inthe facing-to-core welds were found surprisingly detrimental to thestrength of hexagonal cell aluminum honeycomb sandwich panels[257]: even defects in 1% of the weld length reduced the out-of-planetensile failure strain by more than 50%.

4.2. Miscellaneous loading conditions

Static and dynamic response of sandwich structures has been in-vestigated in hundreds of recent papers, considering both miscellaneousdesign issues as well as employing various sandwich model theories.Accordingly, only sample problems and solutions are outlined in thissection, aiming to reflect the broad spectrum of modern studies. Forexample, both static and dynamic response of sandwich beams wasstudied, accounting for the strain-rate effect [258]. Both quasi-staticand dynamic compressive response of sandwich structures with a cor-rugated core was experimentally investigated [259]. Crushing of tuftedsandwich coupons with an emphasis on the tuft density and length ofloops was considered [260]. Flexural-torsional behavior of a function-ally graded metal-ceramic sandwich I-beam was investigated in Ref.[261]. The failure of a sandwich panel undergoing an in-plane axialimpact was both experimentally and numerically investigated [262].

Thermal buckling of sandwich plates was analyzed by assumptionthat temperature does not affect the properties of the sandwich mate-rials [263]. Both buckling and vibrations of a metal sandwich beamwith a corrugated core and facings were analyzed [264]. Solutions ofbuckling and wrinkling problems for sandwich plates using severalanalytical models and the Sublaminate Generalized Unified


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Formulation have been published in Ref. [265].A sandwich specimen subject to twist by two concentrated forces

applied at the corners was considered in Ref. [266] where a semi-em-pirical shear correction factor was determined to account for the effectof transverse shear on the compliance in the framework of the classicaltheory expanding the previous model of the test [267]. Elasto-plasticbehavior of cylindrical sandwich shells undergoing static loading wasnumerically investigated using the differential quadrature method[268].

Bolt insert pull-out and flat-wise tension tests were performed on aNomex™ honeycomb sandwich structure to predict the buckling load ofthe honeycomb core [269]. The finite element simulation utilizing pull-out displacement steps of 0.01mm was compared with experimentalresults and found satisfactory both predicting the onset of stiffnessdecay as well as specifying the buckling load for the honeycomb.

Creep of sandwich panels with web-reinforced corers was experi-mentally studied in Ref. [270]. A low-velocity impact of clampedsandwich beams with multiple metal cores was considered in Ref.[271]. Damping mechanisms in elastic-viscoelastic-elastic sandwichbeams consisting of constraining and viscoelastic layers and a baselayer were numerically and experimentally investigated [272].

From a designer point of view, failure maps of a sandwich structurepredicting its failure under prescribed loading conditions would be veryuseful. For example, Vitale et al. considered and validated such mapsfor three-point bending of sandwich beams [273]. The analyzed modesfor various beam materials included core shear, core crushing, facewrinkling, face yielding and face-sheet debonding. Core crushing wasthe dominant failure mode, except for the case of the beams with a jutereinforced polyester core and jute reinforced facing that failed by faceyielding.

Underwater blast tests of sandwich panels with aluminum facingsand a honeycomb core were reported [274]. Failure modes in compo-site panels undergoing an underwater blast loading and accounting forthe fluid-structure interaction were considered in Ref. [275]. A nu-merical study of blast resistance of sandwich panels considering of fivedifferent core patterns formed by honeycomb and variously cut strips ofhoneycomb forming woven configurations, as well as the effect of sandfilling of the core demonstrated that the energy dissipation can bedoubled by an appropriate choice of the design [276]. An optimizationof sandwich structures to maximize their blast mitigation was presentedin Ref. [277].

Damage in aluminum foam core sandwich structures subject to alow-velocity impact was experimentally and analytically investigated inRef. [278]. An underwater impulse loading of cylindrical sandwichstructures was experimentally and numerically studied [279]. Sand-wich panels with a wire-reinforced cellular core subject to a ballisticimpact by steel projectiles at the speeds in the range from 250 to450m/s were considered clearly demonstrating the advantages of ahigher density of wire reinforcements [280].

Slamming of marine sandwich structures consisting of polymericskins and PVC foam cores was experimentally and numerically analyzedin Ref. [281] and in an earlier study considering several cores [282].The response of sandwich ship structures to slamming as well as pos-sible design modifications to withstand this load have been consideredin several recent studies [283] [284], [285].

4.3. Effects of environment (temperature, moisture)

Bending of a sandwich beam subject to a three-point bending with anonuniform through-the-thickness temperature was analyzed usingFSDT modified to account for the degradation of the core properties dueto temperature in Ref. [286]. The analytical results were successfullycompared to experimental data confirming a uniform distribution of thetransverse shear stress through the thickness of the core, as assumed inFSDT; the natural conclusion was that the failure of the core originatesat the region experiencing the highest temperature. The response of

sandwich beams subject to a combined thermomechanical load wasfurther investigated in Ref. [287] using HSDT. The limitations of HSDTwere emphasized since this theory does not account for the physicalnonlinearity of the constituent materials that was present in the ex-perimentally tested specimens. On the contrary, FEA results accountingfor both geometric and physical nonlinear effects were in a closeagreement with the experimental data. The effect of a nonuniformthrough-the-thickness temperature on the mode of failure of sandwichbeams undergoing compression (in particular, the compression of thesection of the cross section induced in a four-point bending test) wasexperimentally, numerically and analytically investigated in Ref. [288]demonstrating a possible shift in the mode of failure from the facingyielding of aluminum facings to wrinkling.

Multifunctional coatings of sandwich panels slowing the heattransfer as well as increasing the strength and stiffness were consideredaccounting for the effect of temperature on the constituent propertiesand using a thermal loading profile typical for a supersonic flight [289].Both the lower temperature of the colder sandwich panel surface as wellas improved strength and stiffness were achieved with a minimumweight penalty.

ZrB2-SiC-graphite corrugated core sandwich panels were manu-factured and studied for high-temperature applications [290]. Suchpanels retained high compression strength even at 1600 °C, while re-maining 60% lighter than the bulk material. This study expands theprevious research by the same group manufacturing and testing ceramiccorrugated core panels [291].

Thermo-mechanical response of axisymmetric circular sandwichplates was analyzed using a nonlinear version of HSDT as well as FEAand accounting for the effect of temperature on the material propertiesof the foam core [292]. A temperature-induced foam core degradationwas accounted for, while the assumption of a negligible in-plane stiff-ness of the core adopted in the analytical study was confirmed througha comparison with the finite element solution.

The significance of accounting for a physically nonlinear response ofthe foam of a sandwich beam subject to a thermo-mechanical loadingwas demonstrated in Ref. [287]. This experimental and numerical studyalso demonstrate limitation of HSDT that accounts only for geometricnonlinearity.

Thermal conductivity of sandwich panels with balsa, honeycomband Divinycell® cores was investigated [293]. Sound transmission lossin sandwich panels operating at an elevated temperature was con-sidered in Ref. [294].

Free vibrations of elastically supported sandwich beams with FGMfacings subject to temperature were considered by LW and FSDT the-ories [295]. Temperature-induced vibrations of sandwich metal-ceramic plates and shells with temperature-dependent material prop-erties were investigated using a layer-wise HSDT by Pandey et al. [296].

Free vibrations of sandwich plates subjected to an elevated tem-perature were analyzed using the Carrera's unified formulation (CUF)and the hierarchical trigonometric Ritz method [297,298]. CUF ispresented in its generalized version allowing to produce hierarchicallya wide range of advanced equivalent single layer, zig-zag and layer-wise plate theories including the capability to choose the desired ex-pansion order for each unknown in the displacement field. Using CUFenables the authors to reduce the solution to ESL, Murakami zig-zagand LW formulations. The authors concluded that the LW approachmust be employed for thick sandwich panels and in case of a high fa-cing-to-thickness ratio. The feasibility of neglecting certain terms in thedisplacement field reducing the amount of time necessary for the ana-lysis was also considered.

The detrimental effect of a prolonged exposure to moisture on theproperties of E-glass/polyester facings, PVC foam core sandwich wasexperimentally demonstrated in Refs. [299] [300], reflecting a reduc-tion in both flexural strength and stiffness. The facing-core interfacefracture toughness was degraded as a result of exposure to sea water.The effect of moisture on adhesive bondline strength in sandwich


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structures was experimentally studied in Ref. [301]. Ishikawa et al.[302] suggested that excessive deformations in sandwich panels withRohacell core subject to tensile load and moisture are introduced be-cause of the moisture absorption in a high-moisture and high-tem-perature environment. The analytical solution for buckling and freevibration problems in a functionally graded sandwich panel resting on alinear elastic foundation was developed using a quasi-parabolic shearstress distribution through the thickness and accounting for thermaland/or moisture presence in Ref. [303]. A LW approach was used toanalyze the response of sandwich plates to a combination of thermal,moisture and mechanical loads [304].

Hydrophobic thin barrier films protecting sandwich structureagainst moisture penetration were considered in Ref. [305]. Usingbarrier films as the outermost ply in sandwich structures to reducemoisture penetration was discussed in Ref. [306].

4.4. Sandwich structures exposed to fire and their post-fire properties

During fire, the combination of thermally-induced stresses, changesin the material properties and the convergence of polymeric materialsinto char can result in failure of the sandwich structure. The probabilityof such failure increases with time of exposure to fire, as the charredzone expands. After fire, the structure is often damaged, including theregion with charred material as well as possible damage accumulatedduring the event. Accordingly, the residual properties of such structureare an important aspect dictating its strength and stiffness as well as thesafety of its continuous use.

The modes of failure of sandwich structures subject to fire includethe loss of strength, buckling, wrinkling and the facing-core debonding.In particular, the latter mode was numerically investigated for sand-wich panels consisting of glass/vinyl ester facings and a balsa core andsubject to a combination of compression and fire in Ref. [307]. Thenumerical analysis was conducted using a thermomechanical Abaqusmodel that was validated through a comparison of the predicted time tofailure with experiments. The behavior of sandwich structures subjectto a combined tension and fire was analytically analyzed and experi-mentally validated in Ref. [308].

The effect of fire on the performance of polymeric composites ispredominantly related to a damage to matrix. Accordingly, if the fibersare aligned along the tensile load, the fire is not nearly as dangerous asin the case of different fiber orientations or misalignments in the facingsas was demonstrated for sandwich panels with plain woven facings andbalsa core in Ref. [309].

An experimental observation made in Ref. [310] suggested thatporosity acquired in the resin during decomposition at 180–200 °C mayserve as debonding crack initiation sites. Changing the core materialand applying intumescent coating to the sandwich panel subject to firecan increase time to failure by hundreds percent [311]. Wrinkling offacings in sandwich panels subject to fire, accounting for the propertydegradations, was also studied [312]. Both reinforcing foam cores withglass stitches as well as using flame retardants were shown effective incompressed sandwich panels subject to fire where the time to failurewas increased several times compared to the benchmark panel in someof the tested specimens [311]. A fire retardant sandwich structure wasdeveloped using a phenolic coating and an aramid/phenolic protectivelayer on the surface of an aramid/glass facings and a phenolic foamfilled Nomex honeycomb core [313].

Although a lion share of experimental and numerical research onthe effect of fire on sandwich structures has been concentrated on thespecimens with glass-epoxy fiber facings, data was also collected forsandwich structures with carbon/epoxy facings [314]. Using of biofi-bers in the facings of sandwich structures and protecting them from firethrough either insulative silica-based materials added to the matrix orwith fire-retardant coatings have also been investigated [315], [316].

Residual properties of sandwich structures after fire represent aparticular interest in practical situations. An advanced analytical model

was employed in Ref. [317] to predict the char zone propagationthroughout a sandwich beam subject to fire, assess the decompositionof facings and core and predict the residual stiffness and strength. Themodel was validated by comparison with experimental data on E-glass/vinyl ester woven facings and balsa core specimens.

In addition to the effect of fire on dry sandwich structures, the effectof water absorption prior to the fire event on the structural response ofthe structure represents significant interest, particularly in marine ap-plications. This effect has been explored in Ref. [318] on the example ofE-glass/vinyl ester facings, balsa core sandwich panels demonstratingboth a reduced tensile strength as well as a lower fire resistance, pri-marily due to the detrimental effect of moisture on the facing material,including plasticization of the matrix and a degradation of the fiber-matrix interface.

5. Sample recent applications

Sandwich structures have found many applications in virtuallyevery branch of industry. Accordingly, we list here only the most recentrepresentative examples of their applications, excluding hundreds ofpapers on the subject. The applications that are considered includeaerospace, civil engineering, marine and naval engineering and bio-medical areas.

The effect of the core on sound transmission of sandwich panels inaerospace applications was considered including the analysis of bothhoneycomb and foam cores [319]. A redesign of a rotorcraft sandwichroof minimizing structure-borne sound and optimizing the sound powertransmission loss was reported [320]. In the optimized design, the crosssection was split into two thinner subpanels with an air gap betweenthem. A sandwich radome wall capable of operating at temperatures upto 800 °C was considered in Ref. [321]. Sandwich panel shields forprotection of spacecraft from orbital debris were developed and ana-lyzed [322]. Using fiber Bragg grating embedded ultrasonic transducerenabled to nondestructively assess disbands in an aircraft vertical sta-bilizer with aluminum honeycomb core and composite skins [323]. Anew imaging system for the identification of modal frequencies andmodal shapes has recently been applied to identify these parameters inthe sandwich panel of the gondola of a stratospheric ballooning project[324].

The concept of a nonablative lightweight thermal protection system(NALT) currently considered in Japan for Mars exploration is shown inFig. 8 [325]. The system consists of a carbon/carbon composite skin,insulator tiles, and a honeycomb sandwich panel, the function of theseelements being heat resistance, thermal insulation, and structuralstrength, respectively.

Among the civil engineering applications, light weighted and toughinsulated concrete sandwich panels with fiber reinforced plastic seg-mental shear connectors have been used for roof and floor structures

Fig. 8. A concept of a nonablative lightweight thermal protection system (NALT) [325].Reproduced with permission from Elsevier.


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[326]. Sandwich panels providing insulation, waterproofing, durabilityand load-bearing capacities for building applications and consisting ofpolystyrene/cement mixed cores and thin cement sheet facings wereinvestigated in Ref. [327]. Biodegradable sandwich structures withhardwood facings, mushroom foam core and natural glue adhesivesuitable for civil engineering applications were considered [328].Sandwich structures with thick glass facings and glass fiber reinforcedpolymer core may also be attractive in glazing applications [329]. Apedestrian footbridge using sandwich construction was built and testedin Gdansk [330].

A design of composite sandwich structures for a roof of railwayvehicle, addressing such factors as cost, manufacturing and optimiza-tion of design was reported [331]. Low-velocity impact of sandwichstructures in railroad cars was studied in Ref. [332]. An optimization ofan urban transit carbody using sandwich construction for such elementsas roof, walls and underframe was considered demonstrating a potentialfor up to 29% weight reduction [333]. Damage resistance of sandwichpanels employed in transportation structures where they are subject toa low-velocity impact was considered in Ref. [334] using a three-di-mensional FEA. An optimum design of glass/epoxy facings sandwichpanels intended for rescue vehicles in the Arctic, and incorporating athermal insulating core and external heat shield was developed in Ref.[335].

Besides the references relevant to the air and underwater blast re-sistance of sandwich structures cited above, the air and water blastresponse of marine sandwich structures have recently been comparedaccounting for the fluid-structure interaction and using FSDT and FEAto model the structure [336]. It was shown that the water-structureinteraction significantly reduced deformations and the rate of responseof the structure. Deformations and failure of sandwich panels under-going an underwater blast were investigated, accounting for the da-mage in the facings and core as well as delamination [337]. One of theobservations in this paper was that the foam core mitigates the impulsetransmitted to the back facing and plays an important role in preservingthe bending stiffness of the panel.

Fatigue in sandwich L-joints used in marine sandwich structures wasexperimentally studied in Ref. [338]. A degradation in the fatigue re-sponse of marine sandwich structures exposed to sea water was alsoinvestigated [339]. The effect of slamming on the transverse shearforces in sandwich structures used in high-speed marine crafts wasexperimentally investigated in Ref. [340]. Indentation impact of marinesandwich structures inflicted by rock of various geometries, i.e. conical,pyramidal and flat-ace cylindrical shapes, was experimentally studied[341]. Wave impact testing of marine sandwich structures was dis-cussed in Ref. [284]. Other recent studies specifically concerned withvarious aspects of marine applications include [342] [343], and [344].

Among the most recent applications of sandwich designs in elec-tronics, a sandwich structure with a porous acrylonitrile butadienestyrene (ABS) thermoplastic core between two solid ABS facings wasstudied for radio frequency antenna applications [345]. Kagome coresandwich composites were suggested for the absorption of microwaves[346]. A wearable energy harvester representing a sandwich structurewas suggested to utilize energy of knees motion [347]. Flexible piezo-electric touch sensors representing a sandwich structure with electrodeand functional PZT/Pt electrode layers and a flexible substrate weredescribed in Ref. [348]. Sandwich structures are also found in flexibleelectronics (e.g. [349] [350]) and in dielectric radar domes [351].Manufacturing issues of a conformal sandwich antenna were discussedin Ref. [352]. Relevant application examples also include already citedpapers [150,151].

Energy absorption features of sandwich structures and their ele-ments that can be important in almost all industrial areas have beenintensely investigated. For example, Wang et al. considered tandemaluminum alloy honeycomb arrays that can be incorporated in thesandwich energy absorbent devices [353]. A further study of axiallycompressed tandem hexagonal honeycomb structures demonstrated

their advantages as compared to a single honeycomb block, particularlyproviding higher energy absorption, while maintaining the same load-carrying capacity. Experimental and numerical work elucidated theeffect of impactor velocity and effective mass density on the perfor-mance of aluminum honeycomb [354].

An original concept of an energy absorber representing a metallicsquare tube structure filled with a honeycomb core was demonstratedand its response was thoroughly investigated using experimental andnumerical approach [355]. Another recent concept that can be effec-tively applied to both cores of sandwich structures as well as energyabsorbers is using honeycomb with cells filled with circular tubes[356]. Experimentally investigated tube fillers in honeycomb includedcircular carbon fiber reinforced polymer tubes and circular aluminumtubes in different filling patterns. It was demonstrated that mechanicaland energy absorption properties of a honeycomb can be improvedusing tubular fillings. A theoretical approach to the evaluation of theenergy absorption capacity of an axially compressed honeycomb corewere developed using the minimum energy principle and subsequentlyvalidated in experiments [357]. The response of honeycomb under-going an oblique loading was considered in Refs. [358,359]. It wasshown that the mode of failure is dependent on the angle of impact. Atthe angle smaller than 20°, the failure is manifested in an axial pro-gressive plastic collapse, in the range of the impact angles between 25°and 40°, the axial progressive collapse is combined with rotation, atlarger angles, the cells of honeycomb topple down, followed with acompressive failure mode. It would be interesting to expand this studyincorporating the effect of facings that may prevent the realization ofsome of the modes, particularly at an oblique impact.

Besides engineering applications, sandwich structures, their theoryand methods of analysis have a great potential in biomedical applica-tions as well as in the characterization of bones and tissues. For ex-ample, sandwich bone fracture fixation plates with glass/epoxy facingsand flax/epoxy core were experimentally investigated in uniaxial ten-sion/compression, three-point bending and Rockwell hardness tests[360] and found superior to conventional metallic counterparts. Theskull is effectively a sandwich structure including layers of a densecortical bone and a porous cancellous bone core; its deformationsleading to traumatic brain injury as a result of vehicle crushes werestudied accounting for the effects of age and gender [361]. The cal-varium (skullhead) layers thickness were investigated finding that theouter cortical facing is significantly thicker than the inner counterpart[362]. Using honeycomb in the soles of protective boots behaving as asandwich structure was experimentally investigated in Ref. [363]where filling the core cells with glass microspheres was shown effectivefor the maximum energy absorption.

6. Conclusions

The present review outlines the major trends in research and de-velopment of sandwich structures concentrating on the most recentwork. The major conclusions the authors draw from the reviewed stu-dies are:

1. Modelling of sandwich structures requires progressively sophisti-cated methods accounting for the three-dimensional effects, phy-sical and geometric nonlinearities and constitutive relations for thenewly developed materials. Pressing needs include addressing newor previously underexplored phenomena, such as environmentaleffects on the engineering constants, interaction of failure modes,and multiscale response of the material, from nanoscale to macro-scale. Two principal directions of macromechanical modelling are alayerwise and equivalent single layer approaches.

2. New sandwich designs and concepts are actively investigated andintroduced into practice. Many such concepts are developed for thecore aiming at improving its functionality both transferring anddistributing applied loads among the facings as well as enhancing


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toughness of the structure. In addition to widely used honeycomb,cellular and balsa cores, various truss-core designs are extensivelyinvestigated. Among recent developments is using functionallygraded core enabling a better tailoring of the response of thestructure and an enhanced integrity. Functionally graded, z-pinnedor stitched sandwich structures can provide an enhanced resistanceagainst face/core debonding as well as a higher toughness.

3. Multifunctionality of sandwich structures is a natural design objec-tive. Such features as heat transfer management, radar wave ab-sorption, noise and fire insulation are considered in diverse in-dustrial settings.

4. New material concepts are studied for sandwich structure applica-tions. Examples of materials incorporated into new sandwich de-signs include, but not limited to, nanotubes, shape memory alloyand piezoelectrics, while the aims may vary from enhanced strength,stiffness and toughness to sensing internal damage. One of theconsequences of introducing such materials in the facings and coreis the adaptation of available or development of new micro-mechanical theories capable of an accurate capturing of the struc-tural behavior.

5. Environmental effects, including fire, have been intensely studieddue to their significance in numerous applications. While sandwichstructures can be adopted to incorporate thermal protection layers,internal damage caused by such phenomena is not always easilydetected. Residual properties of damaged sandwich structures arealso of interest both after environmental exposure as well as afterexcessive mechanical loading.

In conclusion, in spite of mature and comprehensive theoretical anddesign methods pertinent to sandwich structures, the ever-increasingrange of applications, loadings and available materials will continue tomotivate theoretical and experimental studies in the foreseeable future.It is also noted that while we only briefly referred to biomedical ap-plications of sandwich structures, both this area as well as a char-acterization of biological tissues adopting sandwich structural theoriesrepresents yet another promising field for research.

Acknowledgements

The second author (George A. Kardomateas) would like to ac-knowledge financial support of the Office of Naval Research, GrantN00014-16-1-2831, as well as the interest and encouragement of theGrant Monitor, Dr. Y.D.S. Rajapakse. Also, the communications with Dr.Adrian Mouritz (Royal Melbourne Institute of Technology) and Dr.Stefanie Feih (Singapore Institute of Manufacturing Technology(SIMTech)) are warmly appreciated.

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Composites Part Bvbirman/papers/Review2018.pdf · 2017. 11. 15. · civil and marine structures. The core of aerospace structures is often aluminum or Nomex honeycomb. In civil engineering

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