Advances in Applied Mechanics, Volume 53 in this ongoing series, highlights new advances in the field, with this new volume presenting interesting chapters on Phase field modelling of fracture, Advanced geometry representations and tools for microstructural and multiscale modelling, The material point method: the past and the future, From Experimental Modeling of Shotcrete to Large Scale Numerical Simulations of Tunneling, and Material point method after 25 years: theory, implementation, applications.
1. 1: Introduction - p. page_3 2. 2: Overview of phase-field fracture/damage models - p. page_13 3. 3: Theoretical aspects - p. page_34 4. 4: 1-D analytical solution - p. page_67 5. 5: Finite element discretization and solvers - p. page_86 6. 6: Computational aspects - p. page_98 7. 7: Numerical examples - p. page_112 8. 8: Conclusions - p. page_148 9. Appendix A: A brief recount on variational calculus - p. page_153 10. Appendix B: Positive/negative projection and its application to phase-field fracture models - p. page_155 11. Appendix C: Thermodynamics - p. page_157 12. Appendix D: Comparison with other gradient-damage models - p. page_160 13. Appendix E: Arc-length (path following) methods - p. page_162 14. Acknowledgments - p. page_164 15. Chapter Two: Material point method after 25 years: Theory, implementation, and applications - p. page_185 16. Abstract - p. page_187 17. 1: Introduction - p. page_187 18. 2: A general MPM for solid mechanics - p. page_221 19. 3: Various MPM formulations - p. page_249 20. 4: Implementation aspects - p. page_276 21. 5: Advanced topics - p. page_293 22. 6: Numerical examples - p. page_321 23. 7: Conclusions - p. page_353 24. Appendices - p. page_356 25. Appendix B: Constitutive models - p. page_361 26. Appendix C: An alternative CPDI derivation - p. page_368 27. Appendix D: Moving least square approximations - p. page_370 28. Appendix E: Utilities - p. page_373 29. Appendix F: Explicit Lagrangian finite elements - p. page_376 30. Acknowledgments - p. page_381
Advances in Applied Mechanics, Volume 53 in this ongoing series, highlights new advances in the field, with this new volume presenting interesting chapters on Phase field modelling of fracture, Advanced geometry representations and tools for microstructural and multiscale modelling, The material point method: the past and the future, From Experimental Modeling of Shotcrete to Large Scale Numerical Simulations of Tunneling, and Material point method after 25 years: theory, implementation, applications.
1. 1: Introduction - p. page_3 2. 2: Overview of phase-field fracture/damage models - p. page_13 3. 3: Theoretical aspects - p. page_34 4. 4: 1-D analytical solution - p. page_67 5. 5: Finite element discretization and solvers - p. page_86 6. 6: Computational aspects - p. page_98 7. 7: Numerical examples - p. page_112 8. 8: Conclusions - p. page_148 9. Appendix A: A brief recount on variational calculus - p. page_153 10. Appendix B: Positive/negative projection and its application to phase-field fracture models - p. page_155 11. Appendix C: Thermodynamics - p. page_157 12. Appendix D: Comparison with other gradient-damage models - p. page_160 13. Appendix E: Arc-length (path following) methods - p. page_162 14. Acknowledgments - p. page_164 15. Chapter Two: Material point method after 25 years: Theory, implementation, and applications - p. page_185 16. Abstract - p. page_187 17. 1: Introduction - p. page_187 18. 2: A general MPM for solid mechanics - p. page_221 19. 3: Various MPM formulations - p. page_249 20. 4: Implementation aspects - p. page_276 21. 5: Advanced topics - p. page_293 22. 6: Numerical examples - p. page_321 23. 7: Conclusions - p. page_353 24. Appendices - p. page_356 25. Appendix B: Constitutive models - p. page_361 26. Appendix C: An alternative CPDI derivation - p. page_368 27. Appendix D: Moving least square approximations - p. page_370 28. Appendix E: Utilities - p. page_373 29. Appendix F: Explicit Lagrangian finite elements - p. page_376 30. Acknowledgments - p. page_381
