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E-raamat: Multi-Scale Continuum Mechanics Modelling of Fibre-Reinforced Polymer Composites

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Multi-Scale Continuum Mechanics Modelling of Fibre-Reinforced Polymer CompositesSuurem pilt
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Multi-scale modelling of composites is a very relevant topic in composites science. This is illustrated by the numerous sessions in the recent European and International Conferences on Composite Materials, but also by the fast developments in multi-scale modelling software tools, developed by large industrial players such as Siemens (Virtual Material Characterization toolkit and MultiMechanics virtual testing software), MSC/e-Xstream (Digimat software), Simulia (micromechanics plug-in in Abaqus), HyperSizer (Multi-scale design of composites), Altair (Altair Multiscale Designer)

This book is intended to be an ideal reference on the latest advances in multi-scale modelling of fibre-reinforced polymer composites, that is accessible for both (young) researchers and end users of modelling software. We target three main groups:

This book aims at a complete introduction and overview of the state-of-the-art in multi-scale modelling of composites in three axes:

• ranging from prediction of homogenized elastic properties to nonlinear material behaviour

• ranging from geometrical models for random packing of unidirectional fibres over meso-scale geometries for textile composites to orientation tensors for short fibre composites

• ranging from damage modelling of unidirectionally reinforced composites over textile composites to short fibre-reinforced composites

The book covers the three most important scales in multi-scale modelling of composites: (i) micro-scale, (ii) meso-scale and (iii) macro-scale. The nano-scale and related atomistic and molecular modelling approaches are deliberately excluded, since the book wants to focus on continuum mechanics and there are already a lot of dedicated books about polymer nanocomposites.

A strong focus is put on physics-based damage modelling, in the sense that the chapters devote attention to modelling the different damage mechanisms (matrix cracking, fibre/matrix debonding, delamination, fibre fracture,…) in such a way that the underlying physics of the initiation and growth of these damage modes is respected.

The book also gives room to not only discuss the finite element based approaches for multi-scale modelling, but also much faster methods that are popular in industrial software, such as Mean Field Homogenization methods (based on Mori-Tanaka and Eshelby solutions) and variational methods (shear lag theory and more advanced theories).

Since the book targets a wide audience, the focus is put on the most common numerical approaches that are used in multi-scale modelling. Very specialized numerical methods like peridynamics modelling, Material Point Method, eXtended Finite Element Method (XFEM), isogeometric analysis, SPH (Smoothed Particle Hydrodynamics),… are excluded.

Outline of the book

The book is divided in three large parts, well balanced with each a similar number of chapters:

  • Part I deals with all "ingredients" to start with multi-scale modelling, limited to elastic property prediction. This typically includes: (i) setting up your geometrical model at micro- or meso-scale (definition of Representative Volume Element (RVE) or Repeating Unit Cell (RUC)), (ii) definition of periodic boundary conditions, (iii) homogenization of the elastic properties, starting from the elastic properties of the constituents, (iv) importance of statistical representation of geometry and stochastic nature of fibre architecture. This should bring all readers at the same level of principles and terminology for multi-scale modelling. Advanced users could eventually skip this first part.

  • Part II deals with nonlinear multi-scale modelling. We build further upon the ingredients from Part I, but now add all kinds of nonlinearities to the simulation at micro- or meso-scale (matrix cracking, delamination, fibre/matrix debonding, delamination, fibre failure, visco-elasto-plasticity-damage of the polymer matrix,…). Not only finite element based techniques are covered, but also much faster inclusion methods (Mori-Tanaka, Eshelby,…) and variational methods.

  • Part III deals with the laminate scale or macro-scale, where all these multi-scale modelling tools are applied for macro-scale ply-based modelling and virtual testing of laminates (in static loading, but also sometimes for prediction of fatigue, post-impact strength,…).

In all three parts, the main three types of fibre reinforcement are covered (unidirectionally reinforced composites, textile composites and short fibre composites).

The chapters are written by leading authorities from academia, and each chapter gives a self-contained overview of a specific topic, covering the state-of-the-art and future research challenges.

• all software users, R&D people and researchers that have some knowledge in general continuum mechanics modelling of composites, but have never worked in the field of multi-scale modelling,

• this book should also provide a strong theoretical background to the end users of commercial multi-scale modelling tools, and warn them for the pitfalls and difficulties in obtaining results with such software,

• for advanced users and researchers in multi-scale modelling, the book will still be of much value, because almost nobody will cover in his/her own research the complete field of knowledge that is described in this book.

List of contributors
xvii
Preface xxi
Part I Geometry construction and homogenization of linear elastic material behaviour at micro-and meso-scale
1(216)
1 Multiscale framework. Concept of geometry, materials, load conditions, and homogenization
3(28)
David Garoz Gomez
1.1 Introduction
3(3)
1.2 Microscale
6(10)
1.2.1 Microscale geometry based on a representative volume element
6(2)
1.2.2 Constituents of the microscale
8(2)
1.2.3 Load conditions at microscale
10(6)
1.3 Mesoscale
16(5)
1.3.1 Mesoscale geometry based on a representative unit cell
16(2)
1.3.2 Materials of the mesoscale
18(1)
1.3.3 Load conditions at the mesoscale
19(2)
1.4 Macroscale
21(2)
1.4.1 Macroscale geometry
22(1)
1.4.2 Materials of the macroscale
22(1)
1.4.3 Load conditions at the macroscale
23(1)
1.5 Transition between scales. Computational homogenization
23(5)
1.5.1 Transition from micro to mesoscale. First-order homogenization
25(2)
1.5.2 Transition from meso to macroscale. Second-order homogenization based on kinematics of thin plate theory
27(1)
1.6 Structure of the book
28(1)
References
28(3)
2 Microscale representative volume element: generation and statistical characterization
31(24)
Antonio R. Melro
Riccardo Manno
Chapter points
31(1)
2.1 Introduction
31(1)
2.2 Spatial distribution of fibres inside a representative volume element
32(1)
2.3 Methods to generate transverse randomness of fibres
32(1)
2.4 Algorithm to generate a representative volume element
33(8)
2.4.1 Main flowchart
34(1)
2.4.2 Step 1: Hard-core model
35(2)
2.4.3 Step 2: stirring the fibres
37(2)
2.4.4 Step 3: fibres in the outskirts
39(2)
2.5 Statistical validation of random distributions
41(6)
2.5.1 Voronoi polygon areas and neighboring distances
42(1)
2.5.2 Neighboring fibre distances
43(1)
2.5.3 Neighboring fibre orientation
44(1)
2.5.4 Ripley's K function
44(2)
2.5.5 Pair distribution function
46(1)
2.6 Elastic properties of transverse isotropic materials
47(5)
2.6.1 Analytical methods
47(2)
2.6.2 Material properties of constituents
49(1)
2.6.3 Periodic boundary conditions
49(3)
2.6.4 Comparison of numerical and analytical methods
52(1)
2.7 Conclusion
52(1)
References
53(2)
3 Geometry modelling and elastic property prediction for short fibre composites
55(24)
Jorg Hone
3.1 Composites with uncertain microstructures
55(2)
3.2 Mathematical aspects of RVE size and effective properties
57(2)
3.3 Stochastic methods
59(7)
3.3.1 General probability measures
59(3)
3.3.2 Measures for microstructural uncertainty for random composites
62(3)
3.3.3 Experimental characterization of microstructures
65(1)
3.4 Elastic properties for composites with random microstructures
66(7)
3.4.1 Single and aligned fibre problem
67(4)
3.4.2 Ensemble averaging
71(1)
3.4.3 Use of orientation tensors
72(1)
3.5 Stochastic mechanics of composite materials
73(3)
3.5.1 Stochastic microstructural modelling
73(1)
3.5.2 Stochastic material models
74(2)
3.6 Summary
76(1)
References
76(3)
4 Modelling approaches for constructing the geometry of textiles at the mesoscale level
79(26)
Yordan Kyosev
4.1 Introduction
79(2)
4.2 3D Sketching or topology-based methods
81(11)
4.2.1 Woven structures
81(1)
4.2.2 Braided structures
82(4)
4.2.3 Knitted structures
86(4)
4.2.4 Sewing stitches
90(2)
4.3 Yarn volume definition
92(5)
4.3.1 Approaches for yarn volume definition
92(2)
4.3.2 Yarn interpenetrations
94(3)
4.4 Relaxation of the idealized geometry
97(2)
4.4.1 Direct application of the principle of the minimal potential energy
97(1)
4.4.2 Using finite element solver
98(1)
4.4.3 Digital chain
98(1)
4.5 Other approaches
99(1)
4.5.1 Process simulation
99(1)
4.5.2 Image reconstruction
99(1)
4.6 Remark about data exchange formats
99(1)
4.7 Conclusions
99(1)
References
100(5)
5 Construction of representative unit cells for FE analysis of textile composite plies
105(36)
R.D.B. Sevenois
5.1 Introduction
105(2)
5.2 Input for representative unit cell generation
107(3)
5.3 Types of representative unit cells
110(6)
5.3.1 Idealized representative unit cell
111(2)
5.3.2 Voxel representative unit cell
113(1)
5.3.3 In situ representative unit cell
114(1)
5.3.4 Measurement enhanced shape identification representative unit cell
115(1)
5.4 Application and comparison of an idealized, in situ, and measurement enhanced shape identification representative unit cell to the same experimental dataset
116(19)
5.4.1 In situ observations and μ-CT measurments
116(4)
5.4.2 Idealized representative unit cell
120(2)
5.4.3 In situ representative unit cell
122(1)
5.4.4 Measurement enhanced shape identification representative unit cell
123(4)
5.4.5 Material properties, boundary conditions, and mesh quality
127(3)
5.4.6 Comparison of stiffness and stress prediction
130(5)
5.5 Discussion
135(1)
5.6 Conclusion and further reading
136(1)
References
136(5)
6 Detailed comparison of analytical and finite element---based homogenization approaches for fibre-reinforced composites
141(38)
Sergey G. Abaimov
Iskander S. Akhatov
Stepan V. Lomov
6.1 Introduction. Multiscale nature of fibre-reinforced composites
141(2)
6.2 Micromechanics of unidirectional fibre-reinforced composites
143(4)
6.3 Advantages and limitations in homogenization for multiphase composites
147(10)
6.3.1 Limited applicability of homogenization schemes
147(6)
6.3.2 Heuristic use of Mori---Tanaka method for a complex microstructure
153(4)
6.4 Decomposition of a multiscale homogenization
157(5)
Appendix 6.4A The first Hill tensor for an ellipsoidal inhomogeneity in a transversely isotropic matrix
162(2)
6.5 Inhomogeneity-based method for curved fibre assemblies and textile composites
164(7)
6.5.1 Building the equivalent ellipsoidal inhomogeneities assembly
165(2)
6.5.2 Software implementation and validation
167(4)
6.6 Conclusion and outlook
171(1)
References
172(7)
7 Applications of Maxwell's methodology to the prediction of the effective properties of composite materials
179(38)
L.N. Mccartney
1.1 Introduction
179(1)
7.2 Description of Maxwell's methodology for estimating effective properties
180(3)
7.2.1 Description of cluster geometry
181(2)
7.3 Effective elastic properties for composites with aligned spheroidal reinforcements
183(7)
7.3.1 Composites reinforced with isotropic spherical inclusions
187(1)
7.3.2 Composites reinforced with aligned transverse isotropic cylindrical fibres
188(1)
7.3.3 Composites reinforced with aligned short fibres
189(1)
7.4 Effective thermal expansion coefficients
190(1)
7.5 Maxwell's method of estimating conductivity
191(4)
7.5.1 A simple example
192(3)
7.6 Extension of Maxwell's methodology for conductivity to anisotropic ellipsoidal particles
195(7)
7.6.1 Far-field distribution
195(2)
7.6.2 Maxwell's method of estimating orthotropic conductivities
197(2)
7.6.3 Some special results
199(3)
7.7 Differential effective medium theory
202(8)
7.7.1 Description of the differential method of estimating effective conductivities
203(1)
7.7.2 Multiphase dilute distributions
204(1)
7.7.3 Multiphase concentrated systems
205(2)
7.7.4 Examples with explicit solutions
207(3)
7.8 Conclusion
210(5)
7.8.1 Elastic constants
211(2)
7.8.2 Thermal expansion coefficients
213(1)
7.8.3 Conductivity (electrical or thermal)
214(1)
7.8.4 Differential effective medium theory
214(1)
Acknowledgments
215(1)
References
215(2)
Part II Constitutive modelling of material nonlinearity and damage at micro- and meso-scale
217(210)
8 Modelling nonlinear material response of polymer matrices used in fibre-reinforced composites
219(24)
F.A. Gilabert
8.1 Introduction and scope
219(1)
8.2 General framework for finite deformations
220(3)
8.3 Sources of nonlinearity
223(12)
8.3.1 Visco-elasticity
223(3)
8.3.2 Visco-plasticity
226(3)
8.3.3 Rubbery response
229(2)
8.3.4 Damage
231(4)
8.4 Sample case: damage of polymer micro-fibre
235(4)
8.5 Conclusion
239(1)
Acknowledgments
239(1)
References
239(4)
9 Modelling fibre-matrix interface debonding and matrix cracking in composite laminates
243(32)
F. Paris
M.L. Velasco
E. Correa
9.1 Introduction
243(2)
9.2 Tools and materials
245(6)
9.2.1 The problem studied
245(2)
9.2.2 Contact between solids
247(1)
9.2.3 Interfacial fracture mechanics
248(1)
9.2.4 Boundary element method
249(1)
9.2.5 Materials
250(1)
9.2.6 Equipment and procedures for the experimental observations
250(1)
9.3 Integrated multiscale modelling of a laminate: study of the debonding between fibre and matrix
251(5)
9.3.1 Cell with a single fibre with damage along the interface
251(2)
9.3.2 Cell with two fibres with damage along the interfaces
253(3)
9.4 Integrated multiscale modelling of a laminate: study of the matrix cracking
256(9)
9.4.1 Cell with a single fibre with a kinked crack: influence on the predictions of the properties of the materials involved in the model
257(7)
9.4.2 Cell with a single fibre with a kinked crack: study on the effect of the thickness of the 90-degree ply
264(1)
9.5 Scale effect considerations in laminates based on micromechanical studies
265(7)
9.6 Conclusions
272(1)
Acknowledgments
272(1)
References
273(2)
10 Modelling defect severity for failure analysis of composites
275(32)
Ramesh Talreja
10.1 Introduction
275(2)
10.2 Transverse cracking in unidirectional composites
277(1)
10.3 Representative volume element construction
278(13)
10.3.1 Degree of nonuniformity of fibre distribution---square-shaped representative volume element
282(4)
10.3.2 Fibre mobility---based representative volume element construction---fibre clustering
286(5)
10.4 Stress and failure analysis---transverse tension
291(10)
10.4.1 Square-shaped representative volume element with nonuniform fibre distribution
293(4)
10.4.2 Fibre mobility---based representative volume element with fibre clustering
297(4)
10.5 Formation of transverse cracks
301(2)
10.6 Discussion of results
303(1)
10.7 Conclusion
304(1)
Acknowledgments
305(1)
References
305(2)
11 Micromechanical modelling of interlaminar damage propagation and migration
307(42)
L.F. Varandas
G. Catalanotti
A. Arteiro
Antonio R. Melro
B.G. Falzon
Chapter points
307(1)
11.1 Introduction
307(2)
11.2 Micromechanical frameworks
309(4)
11.2.1 Generation of the unit cells
310(1)
11.2.2 Material constitutive models
310(3)
11.3 Interlaminar crack propagation and migration
313(13)
11.3.1 Micromechanical finite element model
316(3)
11.3.2 Effect of ply thickness
319(2)
11.3.3 Effect of off-axis angle
321(3)
11.3.4 Shear stress sign and migration angle
324(2)
11.4 Mode II delamination and effect of the through-thickness compressive stress
326(14)
11.4.1 Micromechanical finite element model
329(3)
11.4.2 Dependency of unit cell size
332(2)
11.4.3 Effect of through-thickness compressive stress
334(6)
11.5 Concluding remarks and outlook
340(1)
Acknowledgments
341(1)
References
341(8)
12 Modelling the longitudinal failure of fibre-reinforced composites at microscale
349(30)
G. Catalanotti
L.F. Varandas
Antonio R. Melro
T.A. Sebaey
M.A. Bessa
B.G. Falzon
Chapter points
349(1)
12.1 Introduction
349(1)
12.2 Representative volume element generation: focusing on the fibre waviness
350(10)
12.2.1 Spatial descriptors for fibre waviness
351(1)
12.2.2 Algorithm for representative volume element generation
352(6)
12.2.3 Generation of the representative volume elements in Rhino and Abaqus
358(2)
12.3 Constitutive models
360(4)
12.3.1 Fibre
360(1)
12.3.2 Matrix
361(3)
12.3.3 Interface
364(1)
12.4 Micromechanical simulations
364(9)
12.4.1 Longitudinal tension
365(3)
12.4.2 Longitudinal compression
368(5)
12.5 Conclusions
373(1)
Acknowledgments
374(1)
References
374(5)
13 Multiscale modelling and experimental observation of transverse tow cracking and debonding in textile composites
379(26)
Martin Hirsekorn
13.1 Introduction
379(2)
13.2 Damage phenomena in textile composites
381(2)
13.3 Modelling of crack initiation and propagation
383(12)
13.3.1 A mesoscale repeating unit cell
383(2)
13.3.2 A coupled stress and energy criterion for crack initiation
385(3)
13.3.3 Crack initiation in complex 3D structures
388(4)
13.3.4 Modelling crack propagation
392(2)
13.3.5 Results for a four-layer plain-weave composite
394(1)
13.4 Experimental observation of damage
395(5)
13.4.1 Experimental setup
395(1)
13.4.2 Digital image correlation with mechanical regularization
396(2)
13.4.3 Comparison between experimental and numerical results
398(2)
13.5 Conclusions and perspectives
400(1)
References
401(4)
14 Experimental-numerical characterization of the nonlinear microstructural behavior of fibre-reinforced polymer structures
405(22)
Michael Schober
Kerstin Dittmann
Peter Gumbsch
Jorg Hohe
14.1 Microstructural effects on macro-mechanical material properties
405(2)
14.2 Experimental-numerical characterization approach
407(7)
14.2.1 Micro-tensile testing
408(1)
14.2.2 Numerical modelling of tensile test experiments
409(5)
14.3 Results of the experimental-numerical investigation
414(11)
14.3.1 Micro-tensile test results
414(3)
14.3.2 Numerical assessment of the experimental results
417(8)
14.4 Summary
425(1)
References
425(2)
Part III Macro-scale ply-based modelling and virtual testing of composite laminates
427(294)
15 Virtual identification of macroscopic material laws from lower scales
429(34)
David Garoz Gomez
15.1 Introduction
429(4)
15.2 Mesoscale model
433(3)
15.2.1 Geometry of the mesoscale model
433(1)
15.2.2 Material model of the ply
433(1)
15.2.3 Load conditions on the laminate
434(2)
15.3 Microscale model
436(8)
15.3.1 Geometry of the representative volume element
436(1)
15.3.2 Material properties of the constituents
437(3)
15.3.3 Load conditions on the ply
440(2)
15.3.4 Homogenization
442(1)
15.3.5 Numerical parameters
442(2)
15.4 Virtual identification
444(6)
15.4.1 Six load cases
445(1)
15.4.2 Virtual mechanical test on the [ ±45]2s laminate
445(2)
15.4.3 Virtual mechanical test on the [ ±67.5]2s laminate
447(3)
15.5 Verification and numerical validation
450(7)
15.5.1 Randomness of fibre distribution
451(1)
15.5.2 Verification of the virtual identification
452(1)
15.5.3 Numerical validation of the virtual identification
453(3)
15.5.4 Comparison with experimental identifications
456(1)
15.6 Conclusions
457(1)
References
457(6)
16 Modelling damage evolution in multidirectional laminates: micro to macro
463(46)
John Montesano
Farzad Sharifpour
16.1 Introduction
463(3)
16.2 Multiscale assessment of damage in fibre-reinforced plastic laminates
466(7)
16.2.1 Damage modes at different length scales
467(5)
16.2.2 Damage evolution
472(1)
16.3 Overview of multiscale modelling approaches
473(3)
16.3.1 Multiscale modelling framework
473(1)
16.3.2 Multiscale approaches
474(2)
16.4 Modelling damage initiation and evolution at different length scales
476(25)
16.4.1 Modelling damage at the microscale
477(3)
16.4.2 Modelling damage at the mesoscale
480(11)
16.4.3 Continuum-based damage modelling
491(7)
16.4.4 Multiscale modelling for laminates: combining the scales
498(3)
16.5 Conclusions and recommendations
501(1)
References
502(7)
17 Physics-based methodology for predicting ply cracking and laminate failure in symmetric composite laminates under multiaxial loading condition
509(46)
M. Hajikazemi
17.1 Introduction
509(2)
17.2 Laminate geometry and loading
511(1)
17.3 Analysis of undamaged symmetric laminates
512(2)
17.4 Analysis of damaged symmetric laminates
514(13)
17.4.1 Stress transfer and stiffness reduction in cracked symmetric laminates
514(8)
17.4.2 Failure criteria for prediction of ply cracking
522(4)
17.4.3 Algorithm for ply cracking simulation in multiple plies using energy-based criteria
526(1)
17.5 Numerical examples
527(21)
17.5.1 Prediction of properties of undamaged laminates
528(1)
17.5.2 Prediction of laminate thermo-elastic constants with uniformly spaced ply cracks
528(1)
17.5.3 Effect of nonuniform ply cracking on laminate thermo-elastic constants
529(3)
17.5.4 Ply-level homogenization of ply cracking effects
532(2)
17.5.5 Crack growth simulations
534(11)
17.5.6 Ply cracks inducing laminate failure simulations
545(3)
17.6 Closing remarks
548(1)
Acknowledgments
549(1)
References
549(6)
18 Mesoscale modelling of delamination using the cohesive zone model approach
555(24)
Laura Carreras
Gerard Guillamet
Adria Quintanas-Corominas
Jordi Renart
Albert Turon
18.1 Introduction
555(2)
18.1.1 Delamination understood as cracks in the material
555(2)
18.2 Mesoscale modelling of delamination
557(10)
18.2.1 Methods purely based on fracture mechanics
557(2)
18.2.2 Methods based on the cohesive zone model concept
559(6)
18.2.3 Interaction between intralaminar damage and interlaminar damage
565(2)
18.3 Example of application
567(3)
18.3.1 Implementation in an high performance code
567(1)
18.3.2 Case study: curved stiffened panel
567(3)
18.4 Concluding remarks
570(1)
References
571(8)
19 Stochastic virtual testing laboratory for unidirectional composite coupons: from conventional to dispersed-ply laminates
579(30)
Claudio S. Lopes
David Garoz Gomez
Olben Faleo
Bas H.A.H. Tijs
19.1 Introduction
579(2)
19.2 Damage mechanisms in unidirectional laminates
581(12)
19.2.1 Interlaminar damage behavior
582(2)
19.2.2 Intralaminar damage behavior
584(9)
19.3 Virtual testing laboratory
593(6)
19.3.1 Virtual test coupons
594(1)
19.3.2 Constitutive and kinematic aspects
595(2)
19.3.3 Loading, boundary conditions, and simulation procedures
597(1)
19.3.4 Demonstration and validation
597(2)
19.4 Stochastic virtual testing of dispersed-ply coupons
599(4)
19.4.1 Virtual testing configurations
599(1)
19.4.2 Virtual versus experimental testing results
600(3)
19.5 Conclusions
603(1)
Acknowledgments
603(1)
References
604(5)
20 Multiscale modelling of open-hole composite laminates and three-dimensional woven composites
609(28)
Deepak K. Patel
Anthony M. Waas
20.1 Introduction
609(1)
20.2 Implementation of multiscale method
610(2)
20.3 Open-hole tensile test of laminated composites
612(10)
20.3.1 Unidirectional and angle ply laminae
613(4)
20.3.2 Multidirectional laminates
617(5)
20.4 Unnotched tensile test of three-dimensional woven textile composites (3DWTCs)
622(10)
20.4.1 Multiscale modelling of three-dimensional woven textile composites: macro---meso---microscale
626(1)
20.4.2 Damage and failure modelling of three-dimensional woven textile composites (3DWTCs)
627(2)
20.4.3 Imperfection modelling of three-dimensional woven textile composites: micro-CT image-based modelling
629(1)
20.4.4 Results and discussion
629(3)
20.5 Summary and conclusion
632(1)
Acknowledgments
632(1)
References
633(4)
21 Multiscale modelling of laminated composite structures with defects and features
637(32)
Bassam El Said
Stephen R. Hallett
21.1 Defects and features in laminated composites
637(2)
21.2 Modelling length scales in laminated composites
639(2)
21.3 Multiscale modelling approach overview
641(2)
21.3.1 Parametric representation of composite layups
641(1)
21.3.2 Mesoscale RVE models
642(1)
21.3.3 Surrogate model of defects
642(1)
21.3.4 Deterministic multiscale modelling
642(1)
21.4 Mesoscale models
643(10)
21.4.1 Mesoscale representation of laminated composites stiffness
643(4)
21.4.2 Mesoscale damage modelling
647(4)
21.4.3 Periodic homogenization of composite RVE
651(2)
21.5 Multiscale modelling strategies
653(13)
21.5.1 Surrogate models
653(5)
21.5.2 Deterministic multiscale modelling
658(8)
21.6 Summary
666(1)
References
666(3)
22 A multiscale damage-based strategy to predict the fatigue damage evolution and the stiffness loss in composite laminates
669(22)
Marino Quaresimin
Paolo Andrea Carraro
22.1 Introduction
669(2)
22.2 A damage-based criterion for crack initiation
671(8)
22.3 A damage-based criterion for crack propagation
679(2)
22.4 A crack density prediction model
681(2)
22.5 Stiffness degradation---a shear lag model
683(5)
22.6 Conclusion
688(1)
References
689(2)
23 Hybrid multiscale modelling of fatigue and damage in short fibre reinforced composites
691(30)
Atul Jain
23.1 Introduction
691(1)
23.2 Injection molding process and fibre orientation
692(3)
23.3 Experimental observations of damage and fatigue in short fibre reinforced composites
695(4)
23.4 Review of fatigue modelling of short fibre-reinforced composites
699(3)
23.5 Hybrid multiscale modelling of fatigue
702(11)
23.5.1 Choice of correct homogenization approach
703(1)
23.5.2 Micromechanics-based damage model
704(2)
23.5.3 Master SN curve approach
706(3)
23.5.4 Process integration and component-level simulation
709(4)
23.6 Future work and outlook
713(1)
References
713(8)
Index 721
Wim Van Paepegem is full professor and head of the research group "Mechanics of Materials and Structures" at Ghent University in Belgium. The groups research is focussed on experimental and computational mechanics of fibre-reinforced composites, polymers, foams and additively manufactured polymers and metals, as well as non-destructive testing of those materials. Wim Van Paepegem has published more than 240 peer-reviewed Science Citation Index (SCI) journal papers in these research domains. He is serving as an Editorial Board Member for the international journals "Composites Part B" and "Composites Science and Technology" (both top-ranked in composite field), "Polymer Testing" and "Fatigue and Fracture of Engineering Materials and Structures". He has already received five personal awards for his academic achievements, including the "Best Young Researcher" award from the European Society for Composite Materials, the UGent Prometheus award for research and the Laureate prize of the Royal Flemish Academy of Belgium for Science and Arts. He is currently involved in more than twenty European, national, regional and bilateral research projects and over the last five years, four spin-off companies have been initiated out of his research group. Prof. Van Paepegem is also coordinator of the UGent valorization consortium for composite materials.
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