| Description |
1 online resource |
| Contents |
Cover; Preface; Contents; 1 Concept of an elastic material; 2 Observers and invariance; 3 Mechanical power and hyperelasticity; 3.1 Elasticity and energy; 3.2 Work inequality; 4 Material symmetry; 4.1 Stress response; 4.2 Strain energy; 4.3 Isotropy; 5 Fiber symmetry; 6 Stress response in the presence of local constraints on the deformation; 6.1 Local constraints; 6.2 Constraint manifolds and the Lagrange multiplier rule; 6.3 Material symmetry in the presence of constraints; 7 Some boundary-value problems for uniform isotropic incompressible materials |
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7.1 Problems exhibiting radial symmetry with respect to a fixed axis7.1.1 Pressurized cylinder; 7.1.2 Azimuthal shear; 7.1.3 Torsion of a solid circular cylinder; 7.1.4 Combined extension and torsion; 7.2 Problems exhibiting radial symmetry with respect to a fixed point; 7.2.1 Integration of the equation; 7.2.2 Pressurized shells, cavitation; 8 Some examples involving uniform, compressible isotropic materials; 8.1 Spherical symmetry, revisited; 8.2 Plane strain; 8.3 Radial expansion/compaction; 9 Material stability, strong ellipticity and smoothness of equilibria |
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9.1 Small motions superposed on finitely deformed equilibrium states9.2 Smoothness of equilibria; 9.3 Incompressibility; 10 Membrane theory; 10.1 General theory; 10.2 Pressurized membranes; 10.3 Uniqueness of the director; 10.4 Isotropic materials; 10.5 Axially symmetric deformations of a cylindrical membrane; 10.6 Bulging of a cylinder; 11 Stability and the energy criterion; 11.1 The energy norm; 11.2 Instability; 11.3 Quasiconvexity; 11.4 Ordinary convexity; 11.4.1 Objections to ordinary convexity; 11.5 Polyconvexity; 11.6 Rank-one convexity |
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11.7 Equilibria with discontinuous deformation gradients11.8 The Maxwell-Eshelby relation; 11.8.1 Example: alternating simple shear; 12 Linearized theory, the second variation and bifurcation of equilibria; 13 Elements of plasticity theory; 13.1 Elastic and plastic deformations; 13.2 Constitutive response; 13.3 Energy and dissipation; 13.4 Invariance; 13.5 Yielding, the work inequality and plastic flow; 13.6 Isotropy; 13.7 Rigid-plastic materials; 13.8 Plane strain of rigid-perfectly plastic materials: slip-line theory; 13.8.1 State of stress, equilibrium; 13.8.2 Velocity field |
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Supplemental notes1 The cofactor; 2 Gradients of scalar-valued functions of tensors; 3 Chain rule; 4 Gradients of the principal invariants of a symmetric tensor; 5 Relations among gradients; 6 Extensions; 7 Korn's inequality; 8 Poincaré's inequality; Index |
| Summary |
This text is suitable for a first-year graduate course on non-linear elasticity theory. It is aimed at graduate students, post-doctoral fellows and researchers working in mechanics |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from HTML homepage (Oxford, viewed April 20, 2018) |
| Subject |
Elasticity.
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Mechanical engineering -- Mathematical models
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Elasticity
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SCIENCE -- Mechanics -- General.
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SCIENCE -- Mechanics -- Solids.
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Elasticity
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Mechanical engineering -- Mathematical models
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| Form |
Electronic book
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| ISBN |
0192528076 |
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9780192528070 |
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9780191746536 |
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0191746533 |
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