A Review of Explicit Finite Element

A Review of Explicit Finite ElementSoftware for Composite Impact Analysis

MINH Q. NGUYEN,1 DAVID J. ELDER,

1 JAVID BAYANDOR,1,*

RODNEY S. THOMSON2AND MURRAY L. SCOTT

2

1The Sir Lawrence Wackett Centre for Aerospace Design Technology

Royal Melbourne Institute of Technology, GPO Box 2476V

Melbourne 3001, Victoria, Australia2Cooperative Research Centre for Advanced Composite Structures Limited

506 Lorimer Street, Fishermens Bend

Victoria 3207, Australia

ABSTRACT: As explicit finite element (FE) codes improve and advanced materialmodels become available, such tools will find more widespread application within theaerospace industry, as ‘what-if ’ simulations become more manageable withincreasing computing power and greater modeling realism. This paper describesthe investigation of three commercial explicit FE analysis packages, LS-Dyna,MSC.Dytran, and Pam-Shock, to determine their capabilities in predicting barelyvisible impact damage (BVID) in composite structures. The investigation isconducted by first determining the suitability of the codes in constructing an FEmodel of a stiffened panel, solving for BVID and retrieving results. The results arein turn compared to experimental data in order to gauge the suitability of the codesfor composite design and analysis. Comparisons of the FE simulations toexperimental data include damage development and degradation, as well as thetime–history responses. The Chang–Chang failure theory with brittle degradationwas used for both LS-Dyna and MSC.Dytran, while the biphase model was used forPam-Shock. Results indicated that the general shape of the force–time curves aswell as the peak forces were predicted reasonably well. However, all simulationspredicted a trough that was much less significant than the test results, as well as ashorter impact duration.

KEY WORDS: explicit analysis, finite element, composite damage, elementformulation.

INTRODUCTION

THE EXPLICIT FINITE element (FE) software codes of LS-Dyna (Version 950e),MSC.Dytran (Version 2000) and Pam-Shock (Version 2000) are commercial tools

employed within various engineering industries. Both the aerospace and automotive

*Author to whom correspondence should be addressed. E-mail: [email protected]

Journal of COMPOSITE MATERIALS, Vol. 39, No. 4/2005 375

0021-9983/05/04 0375–12 $10.00/0 DOI: 10.1177/0021998305046739� 2005 Sage Publications

industries have accepted simulation as part of the design process to minimize design costsand create more efficient structures. Prototyping and testing are always performed toverify the design, but simulation has become a standard practice throughout the designprocess.

As explicit FE codes improve and advanced material models become available, suchtools will find more widespread application within the aerospace sector, as ‘what-if ’simulations become manageable with increasing computing power and greater modelingrealism. This paper aims to provide a review of the ability of the above-mentioned codes inpredicting barely visible impact damage (BVID) for stiffened composite panels, using asingle-layer 2-D shell model approach. This is achieved by evaluating the ability of theprogram to construct an FE model of the stiffened panel, solve for BVID, retrieve results,and compare this to experiment. The ability of the program to model the damage thatarises from the impact load will provide a gauge to its suitability for advanced compositedesign and analysis applications.

When considering structural analysis applications, implicit FE methods can be used instatic and dynamic analyses, where linear or moderate nonlinear effects are to beinvestigated. The implicit method formulates a group of matrices that allows the structuralproblem to be characterized by mathematical representation of key qualities of thestructure, such as mass and stiffness. With the use of a computer, solutions of the matrixrelationships can be obtained to allow a solution to the boundary value differentialequation sets. One disadvantage with this approach, is that it requires the inversion of thestiffness matrix which requires extensive computation resources, particularly memory.

The advantage of the explicit FE method is that due to the nature of the computationalapproach, extremely small time steps coupled with an iterative solving method, produce anunequaled ability to solve time-domain dynamic problems with extreme nonlinearitiesfrom material and geometrical effects. Solving such problems requires significantly fewercomputational resources, but the very small time step means that only short durationevents can be analyzed in an acceptable length of time. In this paper, describing BVIDresulting from low speed impact, the geometric nonlinear ability of the explicit codes isused in the form of impactor–composite contact and the large deflections resulting fromimpact, as shown in Figure 1(a). The nonlinear material damage analysis capabilities ofthese codes are also used in the form of material stiffness degradation associated with

Figure 1. (a) Displacement contour due to impact on a stiffened composite panel using LS-Dyna and(b) penetration failure of the panel as predicted in MSC.Dytran.

376 M. Q. NGUYEN ET AL.

lamina matrix and fiber damage, as shown in Figure 1(b), which illustrates impactorpenetration through a composite surface.

IMPACT DAMAGE RESPONSE OF COMPOSITE MATERIALS

Owing to the complex response of advanced composite structures to dynamic loadingconditions, a significant amount of research effort has focused on investigating thedamage, crashworthiness, and behavior of such structures under impact [1,2]. Impactdamage in composites occurs when a foreign object causes through-the-thickness and/orin-plane fracture in the material. Even in the low-velocity cases, where the damage maynot be clearly visible, the loss in laminate strength can be dramatic. This loss can bedetermined by considering the residual strength after the impact event. The extent of thestrength reduction and degradation depends on the energy and the number of impacts.Damaged areas can be investigated visually or by using optical or electron microscopy,ultrasonic C-scanning, and acoustic imaging.

Impact damage in composite plates is a combination of major failure modes:delamination, matrix cracking, and fiber breakage [3,4]. The first two types of failureare dependent on the properties of the resin matrix, whereas fiber breakage is moreresponsive to the fiber specifications and characteristics and is usually caused by higherenergy impacts.

Matrix Cracking

Matrix cracks in an impacted composite plate are caused by stress concentrations at thefiber–matrix interface and are produced by tensile stress. A high tensile stress results in alonger and denser cracking pattern [3]. External matrix cracking can be used to estimatethe internal delamination under low-velocity impact. Most polymer matrices used inadvanced fiber composite materials can undergo a limited deformation prior to fracture.Therefore, their contribution to the impact energy absorbed is relatively insignificant. Thetotal energy absorbed by matrix cracking is equal to the product of the surface energy andthe small area produced by the crack. Larger crack areas are normally caused by crackbranching, in which case the cracks run in the direction normal to the general direction offracture. In many cases the surface area created by such cracks is much larger than thearea parallel to the primary cracks, increasing the fracture energy significantly. This, ineffect, can increase the toughness of composites or the total energy of damage absorbedduring impact.

Delamination

Different orientation of the plies can promote delamination of two adjacent plies due tothe stiffness mismatch at their interface. The delamination areas are influenced directly bychanges in the energy of impact. The cracks, which can initiate delaminations, canpropagate through the plies and may be arrested as the crack tips reach the fiber–matrixinterface in the adjacent plies. Because of high shear stress in the matrix adjacent to the

Explicit Finite Element Software for Composite Impact Analysis 377

crack tips, the crack may also split from the base and start growing at the interface parallelto the plane of the plies. Such delaminations absorb a significant amount of energy.

Fiber Breakage

Fiber breakage can be a direct result of crack propagation in the direction perpendicularto the fibers. If sustained, the fiber breakage will eventually grow to form a completeseparation of the laminate. Reaching the fracture strain limit in a composite componentresults in fiber breakage. For the same impact energy, higher capacity of fibers to absorbenergy results in less fiber breakage and a higher residual tensile strength. Secondarymatrix damage, which occurs after initial fiber failure, is also reduced allowing residualcompressive strength to increase. Brittle fibers, such as carbon fiber, have low fracturestrain and hence provide a low energy absorbing capability. Nevertheless, although fiberssignificantly contribute to the high strength of composite materials, the fracture of fibersaccounts only for a small fraction of the total energy absorbed. It should however be notedthat the fibers greatly influence the failure modes and hence the total energy required tocause damage [5].

MODELING IMPACT DAMAGE IN EXPLICIT FE CODES

Damage development in a laminate subjected to impact is complex. This is due to thefact that there are several interacting failure modes present during the impact. To predictdamage behavior, it is required that impact forces and induced stresses are fullydetermined and an appropriate failure criterion for initial failure is identified. Stiffness is adominant parameter and controls the mode of fracture. At low velocities, more flexiblestructures mainly respond by bending, which produces high tensile stresses in the lowestply. These tensile stresses produce matrix cracks that are deflected at the lowest interfaceto form a delamination. This delamination, in turn, is deflected by the matrix cracks in thelayer above (Figure 2(a)). At medium level velocities, damage also occurs due to highcontact stresses on the impact surface, as shown in Figure 2(b) [6,7].

An issue of critical importance is modeling the behavior of the lamina and laminateduring failure. This is known as degradation (material softening) of the composite andresults from the overstressing of the lamina, producing breakage and/or crushing of thefiber and resin matrix. Two important damage estimates are included in the explicitsoftware reviewed, which are defined as follows:

. Elastic damage: In a number of explicit FE codes, including MSC.Dytran, theestimate of damage can be determined using the stress output from a linear elastic

(a) (b)

Figure 2. Damage development in (a) flexible and (b) rigid structures [6,7].


material analysis. In this treatment, a damage index is determined at the completion ofthe analysis that represents a factor of the stress in the material relative to thetheoretical material failure stress.

. Postfailure degradation: All the explicit FE codes reviewed have this capability. Theplies within the laminate are checked against the specified failure criteria at each timestep in the computation. If a ply is found to have failed, its elastic stiffness parameters(E11, E22, G12, and �12) are degraded to simulate the material ‘softening’ that iseffectively seen in practice. This represents a material nonlinearity.

The treatment of this nonlinear material property (postfailure degradation) inMSC.Dytran and LS-Dyna is divided into three distinct parts: initiation of failure,selection of elastic properties (E11, E22, G12, and �12) for degradation, and degradation ofthe properties at a defined rate or strain. Pam-Shock uses a more complex biphase modelthat integrates the above three stages. The different phases of the Pam-Shock processbecome indistinguishable to the user. In addition, all the mentioned explicit FE codesallow user-defined subroutines to be incorporated, making it possible for the user tocustomize the failure and degradation theories. Implementation of user-defined sub-routines requires specialized programming knowledge, and can be less computationallyefficient than built-in routines [8]. Table 1 indicates the standard 2-D composite failurecriteria that are available in the codes reviewed.

MSC.Dytran Degradation Model

In MSC.Dytran, the elastic material parameters E11, E22, G12, and �12 are degradedlinearly in accordance with a user-defined time or step parameter. A small time intervalproduces a brittle failure and a large time interval is more akin to a plastic failure. Theinitiation of degradation in any one of the elastic material parameters (E11, E22, G12, and�12) can be associated with one or more failure modes as defined by the user. The defaultsettings are shown in Table 2. By adjusting this table within the MSC.Dytran input file,

Table 2. Default degradation rules in MSC.Dytran.

Material constant

Failure Mode

Fibertension

Fibercompression

Matrixtension

Matrixcompression Shear

E11 X XE22 X X X XG12 X X X X�12 X X X

Table 1. Composite failure criteria available in explicit FE codes.

CodeTsai–Hill

Tsai–Wu

ModifiedTsai–Wu

Maximumstress

Maximumstrain

Chang–Chang Hashin Biphase

MSC.Dytran X X X X X X XLS-Dyna X X XPam-Shock X


the user can define which elastic properties are degraded with each failure mode. Thisallows for a large range of relationships to be considered, ranging from elastic damageestimates, in which no material softening occurs, to postfailure degradation estimates withmany permutations in the initiation and rate of degradation. If the user defines that nodegradation is to be initiated, MSC.Dytran will still provide an estimate of the elasticdamage index, under these conditions.

LS-Dyna Degradation Model

The degradation of the elastic parameters (E11, E22, G12, and �12) is strain dependent,not time dependent as with MSC.Dytran. LS-Dyna basically has three standarddegradation laws, as follows:

. Brittle: When the composite ply is deemed to have reached failure conditions, theappropriate ply properties are immediately degraded to zero stiffness and strength. Theoverall stiffness and stress distribution of the plies is adjusted accordingly.

. Plastic: When the composite ply is deemed to have reached a failure condition, theappropriate ply stiffnesses are immediately degraded to zero, but force resistancecontribution to the overall laminate is maintained.

. Evolution Law: The stiffness of each ply can be assigned a continuous curve thathas a relative linear elastic section, starting at zero strain, followed by a small plasticsection and finally a softening section. The curve is smooth and continuous andrepresents a typical nonlinear material that may be associated with many types of realmaterials.

It should be noted that the relationships between the individual material constants (E11,E22, G12, and �12) and the onset of softening are defined by a table, similar to Table 2, butthe relationships in this table cannot be modified by the user. The onset of materialdegradation is mandatory once the critical damage level has been reached, so that elasticdamage estimates cannot be calculated by LS-Dyna.

Pam-Shock Biphase Composite Failure and Degradation Model

The biphase model distinguishes between the fiber and the matrix behavior, failure anddegradation, and then superimposes the effects of the two phases. The biphase modelprojects a model of a heterogeneous material adapted to reinforced unidirectionalcomposite materials with continuous fibers. The failure approach available within thismodel encompasses failure, degradation, and residual strength parameters under the samemodule.

In the biphase model, the behavior of a unidirectional ply is described by defining twophases, the continuous fibers and the matrix. In this model, fibers have an unidirectionalbehavior that is brittle elastic with damage, while the matrix is brittle orthotropic elastic,or elastic damaging. The tensile and compressive behaviors of each phase is alsoconsidered. The total material stiffness is determined through superposition of the twophases, whereas the stresses are calculated separately and, together with damage (e.g.,matrix cracking and fiber rupture), can be propagated independently according to thecriteria selected in the preprocessing stage.


EXPLICIT 2-D SHELL ELEMENTS

Unlike the implicit codes, where element choice is usually a function of optimizing thequality of the output required, explicit codes have been designed for a different purposeand this is reflected in the elements provided. In normal explicit crashworthiness analysis(such as those used by the car industry), computational time of the finite elements is ofutmost importance. As a general comment, the crashworthiness industry requires ever-increasing model sizes to keep pace with transport safety requirements. Because ofongoing increases in model size, it can be said that over the past 20 years, the model runtimes for the car industry have been increasing in duration despite the continuous increasein computer speeds [10].

In response to this need for fast computation times, much effort has gone into thedevelopment of elements that require the minimum mathematical instructions per timestep. These elements are known as under integrated (UI) elements. They are formulatedusing the simplest of numerical constructs but will still provide robust predictions underlarge strain regimes. Additionally, these explicit flat elements (unlike the implicit four-node shell formulations) are capable of significant warping (up to 20�) without undulyaffecting the element accuracy. All codes reviewed in this report have a selection of UIshell elements that satisfy the fast computational needs for large models, as indicated inTable 3. Most codes also have more accurate, but slower, fully integrated (FI) andselectively reduced integration (SRI) elements available.

FINITE ELEMENT MODELING

The benchmark problem used to investigate the codes is based on a carbon fibercomposite-stiffened panel with dimensions of 900� 330� 3.5mm3, with two45� 4.66mm2 longitudinal stiffeners, as shown in Figure 3. The structure was modeledusing four-node, UI, single-layer shell elements with the size varying to meet theconvergence requirements of the model. The Belytschko–Tsay formulation was used inLS-Dyna and Pam-Shock, whereas, the Key–Hoff formulation was applied inMSC.Dytran. UI elements inherently provide poor elastic strain predictions due to aconstant bending and shear stress field over the element length due to the single Gausspoint integration. Hence, high mesh densities were used to compensate for the reducedaccuracy of the UI elements.

A graded mesh for the skin was adopted with an element size of 0.45mm at the impactpoint for the elastic damage estimate. This rigorous mesh density was required due to theactual contact diameter between the impactor and the shell elements being of the order ofonly 3mm. The small element length was required to emulate accurate bending and sheardeformations where the shell was constrained to have the same bending radius as theimpactor in the contact area. The element bending stress convergence with respect to size isshown in Figure 4(a).

The impactor was modeled as a hemispherical, infinitely rigid member. Additional FEruns were executed using a solid steel impactor modeled with four-node, tetrahedronelements, as shown in Figure 4(b). The deformation of the solid elements, compared to therigid impactor, slightly reduced the bending radius of the shell and hence reduced thebending stress in the composite of the order of only a few percent. The excessivecomputational times produced with the solid element impactor model resulted in a rigid


Table 3. Examples of typical four-node elements available.

Code ElementElementtype

Plan integrationpoints

Throughthicknessintegration points

Sheardistribution

Sheardeformation

Speed ofcomputation(See note (i))

Shell bendingaccuracy

MSC.Dytran Key–Hoff UI 1 1 per ply Average Yes 1.5 See note iiiBelytschko–Tsay UI 1 1 per ply Average Yes 1 See note iiiHughes–Lui UI 1 1 per ply Average Yes 2.5–3.5 See note iii

LS-Dyna Hughes–Lui UI 1 Multiple per ply Ave or Cal Yes 2.5–3.5 See note iii(See note (ii)) Belytschko–Tsay UI 1 Multiple per ply Ave or Cal Yes 1 See note iii

Belytschko–Wong-Chiang UI 1 Multiple per ply Ave or Cal Yes 1.1 See note iiiS/R Hughes–Lui SRI 2�2 Multiple per ply Ave or Cal Yes 10–20 See note ivFully Integrated FI 2�2 Multiple per ply Ave or Cal Yes 4 See note v

Pam-Shock Belytschko–Tsay UI 1 1 per ply Average Yes 1 See note iiiBelytschko–Wong-Chiang UI 1 1 per ply Average Yes 1.5–2 See note iiiHughes–Tezduyar SRI 2�2 1 per ply Average Yes 4 See note iv

Notes:(i) All computation speeds compared to the fastest element, BLT, which is defined as unity [10,11].(ii) The eight-node thick shell element in LS-Dyna is a solid and cannot be used in conjunction with composite materials, hence is not covered in this paper.(iii) This element cannot guarantee convergence for out-of-plane bending.(iv) This element can guarantee convergence for out-of-plane bending.(v) This element can guarantee convergence for out-of-plane bending, however may suffer from an overly stiff solution due to shear lock.

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body-type impactor being used for practical reasons with little loss in accuracy. Theseparation distance between the impactor face and the composite center-line was taken asone-half of the composite thickness (i.e. contact between the impactor and the laminateoccurred at the composite face). The mass of the impactor was 1.53 kg with an incidentenergy of 40 J. The location of the impacts was at the center of the panel.

SIMULATION RESULTS AND DISCUSSION

The effect of introducing damage and degradation into the MSC.Dytran FE simulationis shown in Figure 5 for a 40 J impact case. In this case, the Chang–Chang failure criterioncoupled with brittle degradation was used. Results show that the initiation of damage anddegradation is associated with a sharp drop in contact force, with the first drop occurringat a contact force of 4 kN. The introduction of damage and degradation resulted in areduction in the magnitude of the peaks in the force–time history and also extended thecontact duration. There was also more high-frequency variations in the contact force dueto the sudden degradation of the ply stiffness properties as failure was predicted to occur.

Comparisons between the experimental and predicted force–time histories are presentedin Figure 6, with all FE simulation results including the conditions of composite damagedevelopment and degradation. The Chang–Chang failure theory with brittle degradationwas used for both LS-Dyna and MSC.Dytran, while Pam-Shock used the biphase model.

(a) (b)

900 mm

330 mm

Figure 3. (a) Geometry of the stiffened panel and (b) the physical impact experimental test set-up.

1900

1950

2000

2050

2100

2150

2200

0 1 2 3

(a) (b)

Ele

men

t str

ess

(MPa

)

Element size (mm)

Figure 4. (a) Fiber stress as a function of element size for a 40 J impact case and (b) meshed impactor andimpact zone.


For this impact energy level, the general shape of the curves and the peak forces werepredicted reasonably well. However, all simulations predicted a trough between the twopeaks that was much less significant in the test results. The most significant difference wasthat the predicted contact duration was shorter in the analyses than what occurred duringtesting. The initial and final slopes of the force–time histories were predicted to be muchsteeper than the test results. The major cause for these discrepancies is believed to be thequality of the end boundary conditions used during testing. The clamping method, whichconsisted of four G-clamps onto wooden blocks, would have allowed movement andadded a degree of damping to the system, thus affecting the dynamic response of the panel.A less significant source of error would be 3-D effects not accounted for in modeling thepanel and impactor. In particular, modeling the impactor as a rigid projectile was asimplification of the actual pendulum impactor, which travels through an arc during theimpact event, and has its own elastic dynamic response.

Figure 7 shows a comparison of the BVID predictions for the codes compared to theexperimental test average. It was noted that very similar damage areas were predicted

0

1

2

3

4

5

6

4 6 8 10 12 14 16

Time (ms)

Elastic

Damage with degradation

Figure 5. Effect of damage and degradation on the force–time histories for the 40 J impact.

0

1

2

3

4

5

6

0 2 4 6 8 10 12 14 16

Adjusted Time (ms)

Con

trac

t For

ce (

kN)

Average test results

Pam-Shock

MSC.Dytran

LS-Dyna

Figure 6. Test and analysis force–time histories for the 40 J case.


using the Chang–Chang failure criterion with degradation using MSC.Dytran andLS-Dyna, however one failure theory that stands out from the others is the Pam-Shockbiphase model.

The Pam-Shock biphase model was found to require extensive property and degra-dation data compared with the other failure theories investigated in this work and led todifficulties in obtaining accurate data. As a consequence, approximations in some of theparameters required by the Pam-Shock biphase model are believed to contribute to thediscrepancy in the results. Another factor influencing the biphase results was interpreta-tion of the damage. Whereas the other failure theories assume elastic behavior untilfailure, the biphase model predicts damage development and corresponding degradationof the properties from an initial strain level well below the ultimate strain of the material.

CONCLUSIONS

The FE packages of MSC.Dytran, LS-Dyna, and Pam-Shock, were all capable ofcreating a composite damage model, solving for damage and degradation, and thenpostprocessing the damage information. One important capability in these programs wasthe ability to view the composite damage modes in individual plies. Comparison of theforce–time histories indicated that the simulation results predicted the general trends andpeak forces well. The largest difference was found in the duration of the impact event inwhich the simulations predicted a much shorter time for contact. The differences wereattributed to the less than ideal end boundary conditions used during testing which wouldhave allowed movement and added damping to the system.

REFERENCES

1. Carruthers, J.J., Kettle, A.P. and Robinson, A.M. (1998). Energy Absorption Capability andCrashworthiness of Composite Material Structures: A Review, Applied Mechanics Reviews,51(10): 635–549.

2. Davies, G.A.O. and Zhang, X. (1995). Impact Damage Predictions in Carbon CompositeStructures, International Journal of Impact Engineering, 16(1): 149–970.

0

1000

2000

3000

4000

5000

6000

7000

8000

Experiment –Average

MSC.Dytran–(Chang-Chang)

LS-Dyna–(Chang-Chang)

Pam-Shock–(Bi-Phase)

775 1200 1372

6035

Tot

al d

amag

e ar

ea (

mm

2 )

Figure 7. Comparison between test and postfailure degradation for damage area.


3. Greenhalgh, E., Hughes, D., Singh, S. and Roberts, D. (1996). Impact Damage Growth andFailure of Carbon-fibre Reinforced Plastic Skin-stringer Panels, Defence Research Agency,Hampshire, UK. DRA/SMC/CR961118/1.0.

4. Palazotto, A.N., Herup, E.J. and Gummadi, L.N.B. (2000). Finite Element Analysis of Low-velocity Impact Velocity on Composite Sandwich Plates, Composite Structures, 49: 209–927.

5. Hull, D. and Shi, B.Y. (1993). Damage Mechanism Characterisation in Composite DamageTolerance Investigations, Composite Structures, 23: 99–920.

6. Abrate, S. (1991). Impact on Laminated Composite Materials, Applied Mechanics Review, 44:155–589.

7. Abrate, S. (2001). Modeling of Impacts on Composite Structures, Composite Structures, 51:129–938.

8. Bayandor, J., Thomson, R.S., Scott, M.L., Nguyen, M.Q. and Elder, D.J. (2003). Investigationof Impact and Damage Tolerance in Advanced Aerospace Composite Structures, InternationalJournal of Crashworthiness, Chirwa, C. (ed.), 8(3): 297–306.

9. Coutellier, D. and Rozycki, P. (2000). Multi-layered, Multi-material Finite Element forCrashworthiness Studies, Composites Part A, 31: 841–151.

10. Du Bois, P.A. (1999). Course Notes in Crashworthiness Engineering with LS-DYNA, ADVEAEngineering and RMIT Press, Melbourne, Australia.

11. Key, S.W. and Hoff, C.C. (1995). An Improved Constant Membrane and Bending Stress ShellElement for Explicit Transient Dynamics, Computer Methods in Applied Mechanics andEngineering, 33–37.


A Review of Explicit Finite Element

Documents

advanced material models

greater modeling realism

increasing computing power

total energy absorbed

changchang failure theory

elastic damage estimates

composite failure criteria

composite impact analysis