Nonlinear Solid Mechanics: Bifurcation Theory and Material Instability

ISBN-13: 9781107025417 / Angielski / Twarda / 2012 / 554 str.

Davide Bigoni

Opis

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.

Recenzje

"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

Spis treści

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.