This volume is a thorough introduction to contemporary research in elasticity, and may be used as a working textbook at the graduate level for courses in pure or applied mathematics or in continuum mechanics. It provides a thorough description (with emphasis on the nonlinear aspects) of the two competing mathematical models of three-dimensional elasticity, together with a mathematical analysis of these models. The book is as self-contained as possible.
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Geometrical and other preliminaries
The equations of equilibrium and the principle
The boundary value problems of threedimensional
addition applied arbitrary associated assume assumption axiom Ball Banach space body boundary condition boundary value problem bounded called Chapter closed compute consequence consider constants constitutive contains continuous converges convex corresponding defined definition deformed configuration denote density derivative differentiable direction displacement domain elasticity element equations equivalent established example Exercise exists expression extended formula given Hence holds hyperelastic implies inequality injective instance isotropic linear Lipschitz-continuous mapping material mathematical matrix mean value theorem means method minimizer models natural nonlinear normed vector notation observation obtain open subset operator orthogonal matrix partial particular Piola-Kirchhoff stress problem proof prove pure reference configuration relation Remark respect response function result satisfies Sect sense sequence Show smooth solution stored energy function strain symmetric Theorem unit vector vector space weak