Introduction CUF Taylor Models Component-Wise Approach Progressive Damage Model Numerical Results Conclusion PROGRESSIVE DAMAGE ANALYSIS OF COMPOSITE STRUCTURES VIA ONE-DIMENSIONAL CARRERA UNIFIED FORMULATIONS Erasmo Carrera*, Ibrahim Kaleel * and Marco Petrolo* *Department of Mechanical and Aerospace Engineering, Politecnico di Torino Full International Conference on Composite Structures, ICCS19 5-9 September 2016, Porto (Portugal) Erasmo Carrera, Ibrahim Kaleel and Marco Petrolo CARRERA UNIFIED FORMULATION - COMPONENT-WISE 1D MODELS - POLITECNICO DI TORINO (ITALY) - WWW.MUL2.COM
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Introduction CUF Taylor Models Component-Wise Approach Progressive Damage Model Numerical Results Conclusion
PROGRESSIVE DAMAGE ANALYSIS OFCOMPOSITE STRUCTURES VIA
ONE-DIMENSIONAL CARRERA UNIFIEDFORMULATIONS
Erasmo Carrera*, Ibrahim Kaleel* and Marco Petrolo*
*Department of Mechanical and Aerospace Engineering,Politecnico di Torino
Full
International Conference on Composite Structures, ICCS195-9 September 2016, Porto (Portugal)
Erasmo Carrera, Ibrahim Kaleel and Marco Petrolo
CARRERA UNIFIED FORMULATION - COMPONENT-WISE 1D MODELS - POLITECNICO DI TORINO (ITALY) - WWW.MUL2.COM
Introduction CUF Taylor Models Component-Wise Approach Progressive Damage Model Numerical Results Conclusion
MUL2 - Our Research Group
Marie Curie Project onComposites
Full
www.fullcomp.net
Erasmo Carrera, Ibrahim Kaleel and Marco Petrolo
CARRERA UNIFIED FORMULATION - COMPONENT-WISE 1D MODELS - POLITECNICO DI TORINO (ITALY) - WWW.MUL2.COM
Introduction CUF Taylor Models Component-Wise Approach Progressive Damage Model Numerical Results Conclusion
The FULLCOMP projectFULLy integrated analysis, design, manufacturing and health-monitoring of COMPosite structures
The FULLCOMP project is funded by the European Commission under aMarie Sklodowska-Curie Innovative Training Networks grant for European Training Networks(ETN).
The FULLCOMP partners are:1 Politecnico di Torino (Italy) - Coordinator2 University of Bristol (UK)3 Ecole Nationale Superieure d’arts et Metiers (Bordeaux, France)4 Leibniz Universitaet Hannover (Germany)5 University of Porto (Portugal)6 University of Washington (USA)7 RMIT (Australia)8 Luxembourg Institute of Technology9 Elan-Ausy, Hamburg, (Germany)
FULLCOMP has recruited 12 PhD students who will work in an international framework todevelop integrated analysis tools to improve the design of composite structures.
The full spectrum of the design of composite structures will be dealt with, such as manufacturing,health-monitoring, failure, modeling, multiscale approaches, testing, prognosis, and prognostic.The FULLCOMP research activity is aimed at many engineering fields, e.g. aeronautics,automotive, mechanical, wind energy, and space.
www.fullcomp.net
Erasmo Carrera, Ibrahim Kaleel and Marco Petrolo
CARRERA UNIFIED FORMULATION - COMPONENT-WISE 1D MODELS - POLITECNICO DI TORINO (ITALY) - WWW.MUL2.COM
Introduction CUF Taylor Models Component-Wise Approach Progressive Damage Model Numerical Results Conclusion
Overview
1 Description of the Carrera Unified Formulation for refined models(CUF).
2 Main 1D CUF capabilities overview (1D Taylor- and Lagrange-basedmodels).
3 Numerical examples dealing with different applications (aerospacestructures, composites, Bio Structures).
4 Introduction to the Component-Wise approach (CW).
5 Progressive Damage Model
6 Numerical Results
Erasmo Carrera, Ibrahim Kaleel and Marco Petrolo
CARRERA UNIFIED FORMULATION - COMPONENT-WISE 1D MODELS - POLITECNICO DI TORINO (ITALY) - WWW.MUL2.COM
Introduction CUF Taylor Models Component-Wise Approach Progressive Damage Model Numerical Results Conclusion
Brief Overview of Beam Refinement Methods andContributors
Emphasizes theimportance of refinedhigher order models
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Displacement [m]
0
1
2
3
4
5
6
7
For
ce [N
]
×105
Analytical
CUF
ABAQUS
Type NDOF Uz at yield load Uz at limit load Plastic Strength Factor
Value Error Value Error [%] Value Error [%]
[m] [%] [m] [%] [%]
Analytical - 2.080 - 4.622 - 1.5 -
ABQ - 3D 22,590 2.077 0.14 4.281 7.38 1.55 3.57
Taylor
EBBM 279 2.083 0.16 3.13 32.39 - -
TBM 279 2.084 0.18 3.13 32.38 - -
N = 1 279 2.084 0.18 3.13 32.38 - -
N = 2 558 2.072 0.40 4.21 8.98 1.59 6.00
N = 3 930 2.072 0.39 4.42 4.80 1.52 1.33
Erasmo Carrera, Ibrahim Kaleel and Marco Petrolo
CARRERA UNIFIED FORMULATION - COMPONENT-WISE 1D MODELS - POLITECNICO DI TORINO (ITALY) - WWW.MUL2.COM
Introduction CUF Taylor Models Component-Wise Approach Progressive Damage Model Numerical Results Conclusion
Lagrange-Based 1D Models, LE
ux = Lτ uxτuy = Lτ uyτuz = Lτ uzτ
L9 polynomials - Isoparametric
Lτ =14(r2 + r rτ)(s2 + ...
Cross-Section Elements
Cross-Section
nodes
Disconnected
nodes
Beam element
Beam node
Lagrange node above the first beamnode cross-section
Lagrange node above the second beamnode cross-section
DOFs: pure displacements of each Lagrangenode (3 DOFs per Lagrange node)
Lagrange nodes can be placed abovethe physical surface of the structure
3D Geometry from CAD
LE Modeling
Computational Model
Erasmo Carrera, Ibrahim Kaleel and Marco Petrolo
CARRERA UNIFIED FORMULATION - COMPONENT-WISE 1D MODELS - POLITECNICO DI TORINO (ITALY) - WWW.MUL2.COM
Introduction CUF Taylor Models Component-Wise Approach Progressive Damage Model Numerical Results Conclusion
The Component-Wise Approach
Only displacements as unknowns.Each component of the structure is modeled via beams only.No need of reference surfaces. This might be useful in a CAD-FEM interface scenario.No need of homogenization techniques.
Erasmo Carrera, Ibrahim Kaleel and Marco Petrolo
CARRERA UNIFIED FORMULATION - COMPONENT-WISE 1D MODELS - POLITECNICO DI TORINO (ITALY) - WWW.MUL2.COM
Introduction CUF Taylor Models Component-Wise Approach Progressive Damage Model Numerical Results Conclusion
Aircraft Wing
X
Z
c
E. Carrera, A. Pagani and M.Petrolo,Component-wise MethodApplied to Vibration of WingStructures,Journal of AppliedMechanics, 80(4), 2013.doi:10.1115/1.4007849.
Shell-like modal shapes by means of a BEAM MODEL
Mode 54 - 246.7 Hz
Natural frequencies [Hz]
Mode 1D-LE SOLID
1 4.23 4.22
2 21.76 21.69
3 25.15 24.78
4 31.14 29.18
5 59.26 56.12
6 66.65 62.41
7 74.23 68.77
Computational costs
CUF LE ≈ 20,000 DOFs
SOLID ≈ 190,000 DOFs
Erasmo Carrera, Ibrahim Kaleel and Marco Petrolo
CARRERA UNIFIED FORMULATION - COMPONENT-WISE 1D MODELS - POLITECNICO DI TORINO (ITALY) - WWW.MUL2.COM
Introduction CUF Taylor Models Component-Wise Approach Progressive Damage Model Numerical Results Conclusion
1. Moure et al., Damage evolution in open-hole laminated composite plates subjected to in-plane loads, 2015
Erasmo Carrera, Ibrahim Kaleel and Marco Petrolo
CARRERA UNIFIED FORMULATION - COMPONENT-WISE 1D MODELS - POLITECNICO DI TORINO (ITALY) - WWW.MUL2.COM
Introduction CUF Taylor Models Component-Wise Approach Progressive Damage Model Numerical Results Conclusion
Main Conclusions and Perspectives
Accurate 3D stress fields obtained through CUF is successfully employed fordamage propagation analysis
Framework is able to predict the failure strength of composites (un-notched) withinacceptable limits
Computationally efficient higher-order non-linear finite element framework isdeveloped
Future extensions
Failure strength estimation of notched compositesComponent wise (fiber and matrix) damage propagationExtension of damage analysis for explicit schemeInclusion of other damage initiation criteria
Erasmo Carrera, Ibrahim Kaleel and Marco Petrolo
CARRERA UNIFIED FORMULATION - COMPONENT-WISE 1D MODELS - POLITECNICO DI TORINO (ITALY) - WWW.MUL2.COM
Introduction CUF Taylor Models Component-Wise Approach Progressive Damage Model Numerical Results Conclusion
PROGRESSIVE DAMAGE ANALYSIS OFCOMPOSITE STRUCTURES VIA
ONE-DIMENSIONAL CARRERA UNIFIEDFORMULATIONS
Erasmo Carrera*, Ibrahim Kaleel* and Marco Petrolo*
*Department of Mechanical and Aerospace Engineering,Politecnico di Torino
Full
International Conference on Composite Structures, ICCS195-9 September 2016, Porto (Portugal)
Erasmo Carrera, Ibrahim Kaleel and Marco Petrolo
CARRERA UNIFIED FORMULATION - COMPONENT-WISE 1D MODELS - POLITECNICO DI TORINO (ITALY) - WWW.MUL2.COM