Non-Linear Elastic Deformations
This meticulous and precise account of the theory of finite elasticity fills a significant gap in the literature. The book is concerned with the mathematical theory of non-linear elasticity, the application of this theory to the solution of boundary-value problems (including discussion of bifurcation and stability) and the analysis of the mechanical properties of solid materials capable of large elastic deformations. The setting is purely isothermal and no reference is made to thermodynamics. For the most part attention is restricted to the quasi-static theory, but some brief relevant discussion of time-dependent problems is included.
Especially coherent and well written, Professor Ogden's book includes not only all the basic material but many unpublished results and new approaches to existing problems. In part the work can be regarded as a research monograph but, at the same time, parts of it are also suitable as a postgraduate text. Problems designed to further develop the text material are given throughout and some of these contain statements of new results.
Widely regarded as a classic in the field, this work is aimed at research workers and students in applied mathematics, mechanical engineering, and continuum mechanics. It will also be of great interest to materials scientists and other scientists concerned with the elastic properties of materials.
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applied arbitrary axial basis vectors Biot stress body forces boundary conditions boundary-value problem Cauchy elastic Cauchy stress coaxial compression configuration conjugate constitutive law constraint contravariant coordinate corresponding covariant current conﬁguration cylinder deduce deﬁned deformation gradient denote differential discussion divergence theorem e-mode edition elastic moduli elastic solid equivalent Eulerian example ﬁrst ﬁxed follows given Grad hence homogeneous incompressible material incremental deformation independent inequality inverse isochoric isotropic isotropic materials line elements linear mathematical Mechanics moduli motion nominal stress normal notation Note obtain orthonormal orthonormal basis physical plane polar decomposition principal axes principal stretches proper orthogonal properties rectangular Cartesian reference conﬁguration relative respectively restriction rotation satisﬁed second-order tensor Section simple shear sinh solution speciﬁc strain tensor strain-energy function stress tensor stress-deformation relation strong ellipticity sufﬁcient surface symmetry group tensor ﬁeld theorem theory traction Truesdell two-point tensor unconstrained material uniqueness values