Nonlinear Solid Mechanics
Nonlinear Solid Mechanics
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.
- Addresses complex modelling of the behaviour of materials under extreme mechanical conditions
- Deals with failure in terms of nonlinear continuum mechanics and instability theory
- Subject matter is explained with qualitative experiments, illustrations from everyday life and simple examples taken from structural mechanics
Reviews & endorsements
"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
Product details
July 2014Paperback
9781107699502
554 pages
254 × 178 × 29 mm
0.95kg
235 b/w illus. 18 colour illus. 10 tables
Available
Table of Contents
- 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.
