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Finite elasticity theory

Author: David J Steigmann
Publisher: Oxford : Oxford University Press, 2017. ©2017
Edition/Format:   eBook : Document : English : First editionView all editions and formats
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.
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Genre/Form: Electronic books
Electronic book
Additional Physical Format: Print version:
Steigmann, David J.
Finite elasticity theory.
Oxford, United Kingdom : Oxford University Press, 2017
(DLC) 2017932403
(OCoLC)982092883
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: David J Steigmann
ISBN: 0192528076 9780192528070 9780191746536 0191746533
OCLC Number: 1002189281
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. 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. 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. 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. 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.
Responsibility: David J. Steigmann.

Abstract:

A graduate-level text on Finite Elasticity, suitable for graduate students, post-doctoral associates and researchers. Introduces the reader to the basic elements of this central topic, which serves  Read more...

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There are many textbooks and treatises on finite elasticity, but Finite Elasticity Theory by David J. Steigmann is special. First, it is at the same time concise and deep, without any dogmatism. Read more...

 
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