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Springer, Dordrecht

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Elastic Behaviour

Authors: Dominique François, André Pineau, André Zaoui,

Publish Date: 2012
Volume: , Issue:, Pages: 83-154
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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 method.Chapter 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, thermo-elasticity and the Voigt’s and Reuss’s bounds. A section is devoted to the problems of inclusions, ellipsoidal essentially.Lastly, Chapter 2 is concerned with sharper bounds and improved estimates for the elastic moduli and compliances: Mori-Tanaka model and Hashin-Shtrikman bounds, self-consistent scheme. Finally an outline of the theory of elastic random media is given.



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