Nonlinear Solid Mechanics: Bifurcation Theory and Material Instability

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Cambridge University Press, 30 lug 2012 - 532 pagine
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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.
 

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Indice

Elements of tensor algebra and analysis
91
Solid mechanics at finite strains
125
Isotropic nonlinear hyperelasticity
152
Solutions of simple problems in finitely deformed nonlinear
162
Constitutive equations and anisotropic elasticity
188
Elastoplastic constitutive equations
251
decomposition of the deformation gradient
265
Moving discontinuities and boundary value problems
275
Incremental bifurcation of elastic solids
338
Applications of local and global uniqueness and stability criteria
385
Wave propagation stability and bifurcation
403
Postcritical behaviour and multiple shear band formation
427
A perturbative approach to material instability
444
nonsymmetric constitutive equations
457
References
507
Index
527

Global conditions of uniqueness and stability
293
Local conditions for uniqueness and stability
310

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Informazioni sull'autore (2012)

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).

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