Fracture in Disordered Brittle Media

This thesis consists of three main chapters, an introduction, and an appendix. The introduction (chapter 1) gives a general historical introduction to the problem of brittle fracture in disordered media. Chapters 2 and 4 are concerned with various aspects of fracture in disordered fuse networks. Chapter 2 investigates the asymptotic properties of fracture strength distributions, and explores their relation with extreme value statistics. Chapter 4 deals with critical phenomena in brittle fracture. This chapter introduces the concept of finite-sized critical-ity as a means to explain how fracture can have mixed properties of abrupt and continuous phase transitions. Chapter 3 describes the collective dynamics at the non equilibrium metal insulator transition. The phenomenon of dielec-tric breakdown at the metal insulator transition shares several characteristics with fracture, and provides a suitable build up to the development presented in chapter 4. The first three parts of the appendix provide an introduction to the various mathematical tools required in order to better appreciate the content of this thesis. Appendix A.1 discusses the basics of extreme value theory, while A.2 and A.3 provide a light introduction to linear elastic fracture mechanics. Appendix A.4 summaries some results on crack propagation in graphene that are not sufficiently well developed to merit a chapter, and yet are developed enough to merit a mention. iii To my parents, my teachers, and Preetha. iv ACKNOWLEDGEMENTS I acknowledge the help, support, and guidance of my advisor, Prof. James P. Sethna, with the utmost gratitude. He helped me become a better scientist and a better human. I am indebted to all my teachers, particularly, Mrs. for their enthusiasm and confidence in me. Alka Gohil and Aarti Jadhon – made my childhood memorable, and have been rock-solid in their support and love since then; for this I am deeply grateful. Finally, I would like to thank Preetha – the joy and soul of my life.