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BL
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| Record Number
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873739
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| Main Entry
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Steigmann, David J.
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| Title & Author
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Finite elasticity theory /\ David J. Steigmann.
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| Edition Statement
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First edition.
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| Publication Statement
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Oxford :: Oxford University Press,, 2017.
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, ©2017
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| Page. NO
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1 online resource
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| ISBN
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0191746533
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: 0192528076
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: 9780191746536
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: 9780192528070
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0198567782
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9780198567783
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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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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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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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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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.
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| Abstract
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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.
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| Subject
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Elasticity.
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| Subject
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Mechanical engineering-- Mathematical models.
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Elasticity.
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Mechanical engineering-- Mathematical models.
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SCIENCE-- Mechanics-- General.
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| Subject
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SCIENCE-- Mechanics-- Solids.
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| Dewey Classification
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531.382
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| LC Classification
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QA931
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