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Nonlinear Solid Mechanics
Bifurcation Theory and Material Instability

$206.00 (C)

  • Author: Davide Bigoni, Universit√† degli Studi di Trento, Italy
  • Date Published: July 2012
  • availability: Available
  • format: Hardback
  • isbn: 9781107025417

$ 206.00 (C)
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About the Authors
  • 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
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    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

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    Product details

    • Date Published: July 2012
    • format: Hardback
    • isbn: 9781107025417
    • length: 554 pages
    • dimensions: 254 x 178 x 30 mm
    • weight: 1.17kg
    • contains: 235 b/w illus. 18 colour illus. 10 tables
    • availability: 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.

  • Resources for

    Nonlinear Solid Mechanics

    Davide Bigoni

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  • Author

    Davide Bigoni, Università degli Studi di Trento, Italy
    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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