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The nonlinear membrane energy: Variational derivation under the constraint “det∇u≠0”


Anza Hafsa, O; Mandallena, J P (2006). The nonlinear membrane energy: Variational derivation under the constraint “det∇u≠0”. Journal de Mathematiques Pures et Appliquees, 86(2):100-115.

Abstract

Acerbi, Buttazzo and Percivale gave a variational definition of the nonlinear string energy under the constraint “det∇u>0” (see [E. Acerbi, G. Buttazzo, D. Percivale, A variational definition of the strain energy for an elastic string, J. Elasticity 25 (1991) 137–148]). In the same spirit, we obtain the nonlinear membrane energy under the simpler constraint “det∇u≠0”.

Abstract

Acerbi, Buttazzo and Percivale gave a variational definition of the nonlinear string energy under the constraint “det∇u>0” (see [E. Acerbi, G. Buttazzo, D. Percivale, A variational definition of the strain energy for an elastic string, J. Elasticity 25 (1991) 137–148]). In the same spirit, we obtain the nonlinear membrane energy under the simpler constraint “det∇u≠0”.

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Additional indexing

Other titles:The nonlinear membrane energy: variational derivation under the constraint "det\nabla u>0"
Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > General Mathematics
Physical Sciences > Applied Mathematics
Uncontrolled Keywords:Dimensional reduction, Γ-convergence, Relaxation, Nonlinear membrane, Determinant constraint
Language:English
Date:2006
Deposited On:04 Jan 2010 15:17
Last Modified:21 Jan 2022 14:22
Publisher:Elsevier
ISSN:0021-7824
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1016/j.matpur.2006.01.004
Related URLs:http://arxiv.org/abs/math/0507310
  • Content: Accepted Version
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  • Description: Accepted manuscript, Version 1