Multiscale Modeling Approaches for Composites outlines the fundamentals of common multiscale modeling techniques and provides detailed guidance for putting them into practice. Various homogenization methods are presented in a simple, didactic manner, with an array of numerical examples.
The book starts by covering the theoretical underpinnings of tensors and continuum mechanics concepts, then passes to actual micromechanic techniques for composite media and laminate plates. In the last chapters the book covers advanced topics in homogenization, including Green’s tensor, Hashin-Shtrikman bounds, and special types of problems. All chapters feature comprehensive analytical and numerical examples (Python and ABAQUS scripts) to better illustrate the theory.
1. 7.1 Introduction - p. 148 2. 7.2 Stress–strain relation for an orthotropic material - p. 149 3. 7.3 Hooke's law for an orthotropic lamina under the assumption of plane stress - p. 156 4. 7.4 Stress–strain relations for a lamina of arbitrary orientation: off–axis loading - p. 158 5. 7.5 Macromechanical response of a laminate composite thin plate - p. 170 6. References - p. 195 7. Part III: Special topics in homogenization - p. 195 8. Chapter 8. Composite sphere/cylinder assemblage - p. 199 9. Abstract - p. 199 10. Contents - p. 199 11. 8.1 Composite sphere assemblage - p. 199 12. 8.2 Composite cylinder assemblage - p. 208 13. 8.3 Eshelby's energy principle - p. 221 14. 8.4 Universal relations for fiber composites - p. 226 15. 8.5 Examples - p. 229 16. References - p. 235 17. Chapter 9. Green's tensor - p. 237 18. Chapter 10. Hashin–Shtrikman bounds - p. 251 19. Chapter 11. Mathematical homogenization theory - p. 271 20. Chapter 12. Nonlinear composites - p. 299 21. Appendix A. Fiber orientation in composites - p. 325 22. Index - p. 339
Multiscale Modeling Approaches for Composites outlines the fundamentals of common multiscale modeling techniques and provides detailed guidance for putting them into practice. Various homogenization methods are presented in a simple, didactic manner, with an array of numerical examples.
The book starts by covering the theoretical underpinnings of tensors and continuum mechanics concepts, then passes to actual micromechanic techniques for composite media and laminate plates. In the last chapters the book covers advanced topics in homogenization, including Green’s tensor, Hashin-Shtrikman bounds, and special types of problems. All chapters feature comprehensive analytical and numerical examples (Python and ABAQUS scripts) to better illustrate the theory.
1. 7.1 Introduction - p. 148 2. 7.2 Stress–strain relation for an orthotropic material - p. 149 3. 7.3 Hooke's law for an orthotropic lamina under the assumption of plane stress - p. 156 4. 7.4 Stress–strain relations for a lamina of arbitrary orientation: off–axis loading - p. 158 5. 7.5 Macromechanical response of a laminate composite thin plate - p. 170 6. References - p. 195 7. Part III: Special topics in homogenization - p. 195 8. Chapter 8. Composite sphere/cylinder assemblage - p. 199 9. Abstract - p. 199 10. Contents - p. 199 11. 8.1 Composite sphere assemblage - p. 199 12. 8.2 Composite cylinder assemblage - p. 208 13. 8.3 Eshelby's energy principle - p. 221 14. 8.4 Universal relations for fiber composites - p. 226 15. 8.5 Examples - p. 229 16. References - p. 235 17. Chapter 9. Green's tensor - p. 237 18. Chapter 10. Hashin–Shtrikman bounds - p. 251 19. Chapter 11. Mathematical homogenization theory - p. 271 20. Chapter 12. Nonlinear composites - p. 299 21. Appendix A. Fiber orientation in composites - p. 325 22. Index - p. 339
