The nonlinear membrane model: A young measure and varifold formulation

Med Lamine Leghmizi , Christian Licht (1) , Gérard Michaille (2)

1 LMGC - Laboratoire de Mécanique et Génie Civil
2 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We establish two new formulations of the membrane problem by working in the space of W-Gamma o(1,p) (Omega, R-3)- Young measures and W-Gamma o(1,p) (Omega, 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.

Mots clés: membrane; Young measures; varifolds; gradients

Domaines: Matériaux et structures en mécanique [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]

Med Lamine Leghmizi, Christian Licht, Gérard Michaille. The nonlinear membrane model: A young measure and varifold formulation. ESAIM: Control, Optimisation and Calculus of Variations, 2005, 11, pp.449-472. ⟨10.1051/cocv:2005014⟩. ⟨hal-00574989⟩