Nonlinear Solid Mechanics Bifurcation Theory and Material Instability [Hardcover]

Addresses behaviour of materials under extreme mechanical conditions and of failure in terms of non-linear continuum mechanics and instability theory.This book, written for researchers and graduate students, addresses the complex modeling of the behavior of materials under extreme mechanical conditions and of failure in terms of nonlinear continuum mechanics and instability theory. The theoretical framework presented is the key to understanding the failure conditions of materials, crucial for both the exploitation of traditional materials and the design of innovative materials.This book, written for researchers and graduate students, addresses the complex modeling of the behavior of materials under extreme mechanical conditions and of failure in terms of nonlinear continuum mechanics and instability theory. The theoretical framework presented is the key to understanding the failure conditions of materials, crucial for both the exploitation of traditional materials and the design of innovative materials.This book covers solid mechanics for nonlinear elastic and elastoplastic materials, describing the behavior of ductile material subject to extreme mechanical loading and its eventual failure. The book highlights constitutive features to describe the behavior of frictional materials such as geological media. On the basis of this theory, including large strain and inelastic behaviors, bifurcation and instability are developed with a special focus on the modeling of the emergence of local instabilities such as shear band formation and flutter of a continuum. The former is regarded as a precursor of fracture, while the latter is typical of granular materials. The treatment is complemented with qualitative experiments, illustrations from everyday life, and simple examples taken from structural mechanics.1. Introduction; 2. Elements of tensor algebra and analysis; 3. Solid mechanics at finite strains; 4. Isotropic nonlinear hyperelasticity; 5. Solutions of simple problems il'