Bigoni D. Nonlinear Solid Mechanics. Bifurcation Theory and Material Instability

New York, Cambridge University Press, 2012, 550 pages.
This book covers solid mechanics for nonlinear elastic and elastoplastic materials, describing the behavior of ductile materials subjected to extreme mechanical loading and their 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, whereas 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.
Davide Bigoni is a professor in the faculty of engineering at the University of Trento, where he has been head of the Department of Mechanical and Structural Engineering. He was honored as a Euromech Fellow of the European Mechanics Society. He is co-editor of the Journal of Mechanics of Materials and Structures (an international journal founded by C. R. Steele) and is associate editor of Mechanics Research Communications.Elements of tensor algebra and analysis
Solid mechanics at finite strains
Isotropic non-linear hyperelasticity
Solutions of simple problems in finitely deformed non-linear elastic solids
Constitutive equations and anisotropic elasticity
Yield functions with emphasis on pressure sensitivity
Elastoplastic constitutive equations
Moving discontinuities and boundary value problems
Global conditions of uniqueness and stability
Local conditions for uniqueness and stability
Incremental bifurcation of elastic solids
Applications of local and global uniqueness and stability criteria to non-associative elastoplasticity
Wave propagation, stability and bifurcation
Post-critical behaviour and multiple shear band formation
A perturbative approach to material instability