Nonlinear Solid Mechanics: Bifurcation Theory and Material Instability

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Davide Bigoni (Professor of Solid and Structural Mechanics, Università degli Studi di Trento, Italy)

Nonlinear Solid Mechanics

Bifurcation Theory and Material Instability

Davide Bigoni (Professor of Solid and Structural Mechanics, Università degli Studi di Trento, Italy)

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English

Cambridge University Press
30 July 2012

Non-linear science; Fluid mechanics; Engineering thermodynamics; Mechanics of solids; Mechanics of fluids

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.

By: Davide Bigoni (Professor of Solid and Structural Mechanics Università degli Studi di Trento Italy)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 254mm, Width: 178mm, Spine: 30mm
Weight: 1.170kg
ISBN: 9781107025417
ISBN 10: 1107025419
Pages: 554
Publication Date: 30 July 2012
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

Davide Bigoni is Professor of Solid and Structural Mechanics at the University of Trento, Italy, where he has been head of the Department of Mechanical and Structural Engineering for the past ten years. 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. He co-edited, with Deseri Luca, Recent Progress in the Mechanics of Defects (2011).

Reviews for Nonlinear Solid Mechanics: Bifurcation Theory and Material Instability

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