Finite element analysis of Voronoi cellular solids

Finite element analysis (FEA) was used to study the mechanical behavior of three idealized cellular solids: a regular hexagon, a two-dimensional non-periodic honeycomb, and a three-dimensional random network of struts. FEA results for uniaxial deformation of the hexagon with elastic-plastic cell walls were compared to analytical solutions for stiffness and strength. A plastic failure envelope was calculated for the two-dimensional non-periodic honeycomb under biaxial loading. Results were compared to the failure envelope for a regular hexagonal honeycomb. Finally, FEA results for a three-dimensional random structure under cyclic compression were compared to experimental results for fatigue of trabecular bone. The studies demonstrated the usefulness of the unit cell approach and the strengths of different finite element models for understanding mechanical response to uniaxial, biaxial, and cyclic loading. Thesis Supervisor: Loma J. Gibson Title: Matoula S. Salapatas Professor of Materials Science and Engineering Acknowledgements I once heard that graduate school is like being handed a small piece of the universe with the directive: "Solve this." Certainly, the thesis advisor's part in whether or not the student gets a solution is significant. But after sharing my own experiences with fellow students, I also recognize the critical role that an advisor plays in the overall quality of graduate school life. I was fortunate. I am very grateful to Professor Lorna Gibson for her guidance and enthusiastic support during my two years in the Department. A great big thanks to Ann Jacoby for suggesting her as an advisor. I am indebted to a number of people for assistance with the software programs used in chapters 3 and 4, specifically Dr. Matt Silva and Grant Schaffner for the mesh generation code for the two-dimensional Voronoi honeycomb; Drs. John Sullivan and Ken Brakke for help installing their programs; and most of all, Dr. Andy Kraynik and his colleagues at Sandia National Laboratories for the software to build the three-dimensional Voronoi meshes. Andy, thank you for your patient instruction and attention to detail. This research was supported by the Beinecke Brothers Memorial Scholarship, the Sperry Fund, and NIH grant #AR41894-0182. Special thanks to Dr. Tom Parkinson and Diego Gonzales for their assistance in administering these funds. I am grateful to everyone at the Beth Israel Deaconess Medical Center Orthopedic Biomechanics Laboratory-especially Jon Conta and Dave Rosler for listening to all my stories. A special thanks to Manan Trivedi, who always reminded me of the bigger picture, and to my brother Raghav, who warned me on the first day that FEM is a bad idea for a thesis topic. Finally, a note to my parents who always encouraged me to pursue my studies with passion and discipline: Your unconditional support of my personal and professional decisions has given me self-confidence and courage to embrace uncertainty. Thank you for the exciting opportunities that lie ahead. Table of