The nonlinear membrane model: a Young measure and varifold formulation

We establish two new formulations of the membrane problem by working in the space of $W^{1,p}_{\Gamma_0}(\Omega,\mathbf R^3)$-Young measures and $W^{1,p}_{\Gamma_0}(\Omega,\mathbf R^3)$-varifolds. The energy functional related to these formulations is obtained as a limit of the 3d formulation of the...

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Published inESAIM. Control, optimisation and calculus of variations Vol. 11; no. 3; pp. 449 - 472
Main Authors Leghmizi, Med Lamine, Licht, Christian, Michaille, Gérard
Format Journal Article
LanguageEnglish
Published Les Ulis EDP Sciences 01.01.2005
Subjects
35B05
49J45
74K15
Deformation
Energy
Engineering Sciences
Equilibrium
Materials and structures in mechanics
Mechanics
Membrane
Physics
varifolds
Young measures
varifolds
membrane
Young measures
gradients
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Summary:We establish two new formulations of the membrane problem by working in the space of $W^{1,p}_{\Gamma_0}(\Omega,\mathbf R^3)$-Young measures and $W^{1,p}_{\Gamma_0}(\Omega,\mathbf R^3)$-varifolds. The energy functional related to these formulations is obtained as a limit of the 3d formulation of the behavior of a thin layer for a suitable variational convergence associated with the narrow convergence of Young measures and with some weak convergence of varifolds. The interest of the first formulation is to encode the oscillation informations on the gradients minimizing sequences related to the classical formulation. The second formulation moreover accounts for concentration effects.
Bibliography:publisher-ID:cocv0411
PII:S129281190500014X
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ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1292-8119
1262-3377
DOI:10.1051/cocv:2005014