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:
1. 7.1 Introduction - p. 179 2. 7.2 Description of Maxwell’s methodology for estimating effective properties - p. 180 3. 7.3 Effective elastic properties for composites with aligned spheroidal reinforcements - p. 183 4. 7.4 Effective thermal expansion coefficients - p. 190 5. 7.5 Maxwell’s method of estimating conductivity - p. 191 6. 7.6 Extension of Maxwell’s methodology for conductivity to anisotropic ellipsoidal particles - p. 195 7. 7.7 Differential effective medium theory - p. 202 8. 7.8 Conclusion - p. 210 9. Acknowledgments - p. 215 10. References - p. 215 11. Part II: Constitutive modelling of material nonlinearity and damage at micro- and meso-scale - p. 215 12. 8. Modelling nonlinear material response of polymer matrices used in fibre-reinforced composites - p. 219 13. 9. Modelling fibre–matrix interface debonding and matrix cracking in composite laminates - p. 243 14. 10. Modelling defect severity for failure analysis of composites - p. 275 15. 11. Micromechanical modelling of interlaminar damage propagation and migration - p. 307 16. 12. Modelling the longitudinal failure of fibre-reinforced composites at microscale - p. 349 17. 13. Multiscale modelling and experimental observation of transverse tow cracking and debonding in textile composites - p. 379 18. 14. Experimental-numerical characterization of the nonlinear microstructural behavior of fibre-reinforced polymer structures - p. 405 19. Part III: Macro-scale ply-based modelling and virtual testing of composite laminates - p. 426 20. 15. Virtual identification of macroscopic material laws from lower scales - p. 429 21. Abstract - p. 429 22. 15.1 Introduction - p. 429 23. 15.2 Mesoscale model - p. 433 24. 15.3 Microscale model - p. 436 25. 15.4 Virtual identification - p. 444 26. 15.5 Verification and numerical validation - p. 450 27. 15.6 Conclusions - p. 457 28. References - p. 457 29. 16. Modelling damage evolution in multidirectional laminates: micro to macro - p. 463 30. 17. Physics-based methodology for predicting ply cracking and laminate failure in symmetric composite laminates under multiaxial loading condition - p. 509 31. 18. Mesoscale modelling of delamination using the cohesive zone model approach - p. 555 32. 19. Stochastic virtual testing laboratory for unidirectional composite coupons: from conventional to dispersed-ply laminates - p. 579 33. 20. Multiscale modelling of open-hole composite laminates and three-dimensional woven composites - p. 609 34. 21. Multiscale modelling of laminated composite structures with defects and features - p. 637 35. 22. A multiscale damage-based strategy to predict the fatigue damage evolution and the stiffness loss in composite laminates - p. 669 36. 23. Hybrid multiscale modelling of fatigue and damage in short fibre reinforced composites - p. 691 37. Index - p. 721
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:
1. 7.1 Introduction - p. 179 2. 7.2 Description of Maxwell’s methodology for estimating effective properties - p. 180 3. 7.3 Effective elastic properties for composites with aligned spheroidal reinforcements - p. 183 4. 7.4 Effective thermal expansion coefficients - p. 190 5. 7.5 Maxwell’s method of estimating conductivity - p. 191 6. 7.6 Extension of Maxwell’s methodology for conductivity to anisotropic ellipsoidal particles - p. 195 7. 7.7 Differential effective medium theory - p. 202 8. 7.8 Conclusion - p. 210 9. Acknowledgments - p. 215 10. References - p. 215 11. Part II: Constitutive modelling of material nonlinearity and damage at micro- and meso-scale - p. 215 12. 8. Modelling nonlinear material response of polymer matrices used in fibre-reinforced composites - p. 219 13. 9. Modelling fibre–matrix interface debonding and matrix cracking in composite laminates - p. 243 14. 10. Modelling defect severity for failure analysis of composites - p. 275 15. 11. Micromechanical modelling of interlaminar damage propagation and migration - p. 307 16. 12. Modelling the longitudinal failure of fibre-reinforced composites at microscale - p. 349 17. 13. Multiscale modelling and experimental observation of transverse tow cracking and debonding in textile composites - p. 379 18. 14. Experimental-numerical characterization of the nonlinear microstructural behavior of fibre-reinforced polymer structures - p. 405 19. Part III: Macro-scale ply-based modelling and virtual testing of composite laminates - p. 426 20. 15. Virtual identification of macroscopic material laws from lower scales - p. 429 21. Abstract - p. 429 22. 15.1 Introduction - p. 429 23. 15.2 Mesoscale model - p. 433 24. 15.3 Microscale model - p. 436 25. 15.4 Virtual identification - p. 444 26. 15.5 Verification and numerical validation - p. 450 27. 15.6 Conclusions - p. 457 28. References - p. 457 29. 16. Modelling damage evolution in multidirectional laminates: micro to macro - p. 463 30. 17. Physics-based methodology for predicting ply cracking and laminate failure in symmetric composite laminates under multiaxial loading condition - p. 509 31. 18. Mesoscale modelling of delamination using the cohesive zone model approach - p. 555 32. 19. Stochastic virtual testing laboratory for unidirectional composite coupons: from conventional to dispersed-ply laminates - p. 579 33. 20. Multiscale modelling of open-hole composite laminates and three-dimensional woven composites - p. 609 34. 21. Multiscale modelling of laminated composite structures with defects and features - p. 637 35. 22. A multiscale damage-based strategy to predict the fatigue damage evolution and the stiffness loss in composite laminates - p. 669 36. 23. Hybrid multiscale modelling of fatigue and damage in short fibre reinforced composites - p. 691 37. Index - p. 721
