Nonlinear Solid Mechanics
Bifurcation Theory and Material Instability

Addresses behaviour of materials under extreme mechanical conditions and of failure in terms of non-linear continuum mechanics and instability theory.

Davide Bigoni (Author)

9781107025417, Cambridge University Press

Hardback, published 30 July 2012

554 pages, 235 b/w illus. 18 colour illus. 10 tables
25.4 x 17.8 x 3 cm, 1.17 kg

"The book will be useful to engineers who want to be acquainted with an up-to-date presentation of nonlinear materials. It will also be useful to mathematicians who are interested in comprehensive and realistic modelling of such non linear materials." -Mathematical Reviews

This book covers solid mechanics for non-linear elastic and elastoplastic materials, describing the behaviour of ductile material subject to extreme mechanical loading and its eventual failure. The book highlights constitutive features to describe the behaviour of frictional materials such as geological media. On the basis of this theory, including large strain and inelastic behaviours, bifurcation and instability are developed with a special focus on the modelling 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 in finitely deformed nonlinear elastic solids
6. Constitutive equations and anisotropic elasticity
7. Yield functions with emphasis on pressure-sensitivity
8. Elastoplastic constitutive equations
9. Moving discontinuities and boundary value problems
10. Global conditions of uniqueness and stability
11. Local conditions for uniqueness and stability
12. Bifurcation of elastic solids deformed incrementally
13. Applications of local and global uniqueness and stability criteria to non-associative elastoplasticity
14. Wave propagation, stability and bifurcation
15. Post-critical behaviour and multiple shear band formation
16. A perturbative approach to material instability.

Subject Areas: Mechanics of fluids [TGMF], Mechanics of solids [TGMD], Engineering thermodynamics [TGMB], Mechanical engineering & materials [TG], Fluid mechanics [PHDF], Nonlinear science [PBWR]