Nonlinear solid mechanics. Bifurcation theory and material instability. (Q2904659)

This monograph presents an extended overview of bifurcations and instabilities arising in nonlinear solid mechanics. After a detailed introduction, the author gives some elements of tensor algebra and analysis, in order to present essential facts from kinematics and dynamics of solid mechanics at finite strains. The present reviewer finds interesting the chapter on solutions for ``simple'' problems for finite-strain nonlinear elastic solids. This chapter plays an important role for understanding examples of the whole book. The domain of interest contains also the constitutive modelling of large-strain elastoplasticity. In this context, the author analyzes global and local conditions for uniqueness and stability of solutions. He explains incremental bifurcations of elastic solids, dynamic stability and bifurcation, post-critical behavior, and shear band formation. On balance, the monograph is a useful reference book in many fields of solid mechanics, addressing to mechanical engineers, researchers and students.