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Publisher
Springer, Dordrecht
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Authors: Dominique François André Pineau André Zaoui
Publish Date: 2012
Volume: , Issue: , Pages: 83-154
Abstract
Chapter 2 begins with the definition of the elastic potential from the strain energy and discusses the thermodynamic definition Experimental observations concerning rubber elasticity are described followed by the explanation of models Discussion of the cohesion energy allows classifying the various types of atomic bonds Moduli and compliances in linear elasticity are described for anisotropic and then isotropic materials Stability of the equilibrium is discussed and field equations are described and illustrated by the example of the propagation of plane sine waves This is followed by the explanation of extremum theorems and an introduction to the finite elements methodChapter 2 continues with a discussion of homogenisation estimating and bounding for heterogeneous materials in linear elasticity with explanations about the effective moduli and compliances initial deformations thermoelasticity and the Voigt’s and Reuss’s bounds A section is devoted to the problems of inclusions ellipsoidal essentiallyLastly Chapter 2 is concerned with sharper bounds and improved estimates for the elastic moduli and compliances MoriTanaka model and HashinShtrikman bounds selfconsistent scheme Finally an outline of the theory of elastic random media is given
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