The purpose of this book is to present a research summary on solid mechanics at large strain, including the treatment of bifurcation and instability phenomena. The framework is crucial to the understanding of failure mechanisms in ductile materials, as connected to material instabilities, such as, shear banding.

I have employed Chapters 2 through 5 as a textbook for a graduate course on nonlinear elasticity that I have offered at the University of Trento since 1999, whereas Chapters 8, 10, 11 and 13 have been the basis for a course held at CISM (no. 414, ‘Material Instabilities in Elastic and Inelastic Solids’, H. Petryk, ed.). Chapters 6, 7, 9, 12, 14 and 15 have been added to present the elasticity and the yield critera in detail, including a treatment on elastic bifurcation and instability, wave propagation and multiple shear banding. This material has been taught during seminars for graduate students at various universities. Chapter 16 is devoted to the perturbative approach to material instability, developed by me in a series of articles in cooperation with D. Capuani, M. Brun, F. Dal Corso, M. Gei, A. Piccolroaz and J. R. Willis. Finally, I have to admit that the Introduction of the book is overlong; in fact, I have used it for a 20-hour graduate course on stability and bifurcation. The hope is to attract attention to the main topics presented in the book.