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Hyperelasticity for crystals


Chipot, M (1990). Hyperelasticity for crystals. European Journal of Applied Mathematics, 1(2):113-129.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:lowest energy level; elastic crystal; Ericksen's subenergy
Language:English
Date:1990
Deposited On:18 Feb 2010 11:18
Last Modified:06 Dec 2017 21:13
Publisher:Cambridge University Press
ISSN:0956-7925
Publisher DOI:https://doi.org/10.1017/S0956792500000115
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0722.49006
http://www.ams.org/mathscinet-getitem?mr=1117347

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