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Hyperelasticity for crystals

Published online by Cambridge University Press:  16 July 2009

Michel Chipot
Michel Chipot
Affiliation:
Université de Metz, Département de Mathématique, Ile du Saulcy, 57045 Metz – Cedex, France
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Abstract

The goal of this note is to explain the process of computing the lowest energy level achieved by an elastic crystal subject to homogeneous boundary deformation. This analysis follows mainly the lines of Chipot and Kinderlehrer or Fonesca but we expect that it will lead to some new results for some other energy functional having different invariance properties. The mathematical interest of the result also lies in the fact that the lowest energy level computed this way coincides with the relaxed energy functional (see Fonesca). This relaxed energy is determined by a known thermodynamic quantity, Ericksen' subenergy. Within this review we will also analyse some of the mathematical and physical aspects of these highly oscillatory problems.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 1 , Issue 2 , June 1990 , pp. 113 - 129
Copyright
Copyright © Cambridge University Press 1990

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