Asymptotic modeling of thin curved martensitic films

Article type: Research Article

Authors: Le Dret, Hervé | Zorgati, Hamdi

Affiliations: Université Pierre et Marie Curie-Paris 6, UMR 7598 LJLL, Paris, F-75005 France and CNRS, UMR 7598 LJLL, Paris, F-75005 France E-mail: ledret@ccr.jussieu.fr | CEREMADE, CNRS UMR 7534, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris, France and Institüt Für Mathematik, Universität Zürich, Winterthurerstr. 190, CH-8057 Zürich, Switzerland E-mail: hamdi.zorgati@math.unizh.ch

Abstract: We consider a thin curved film made of a martensitic material. The behavior of the film is governed by a free energy composed of a bulk energy term and an interfacial energy term. We show that the minimizers of the free energy converge to the minimizers of an energy depending on a two-dimensional deformation and one Cosserat vector field when the thickness of the curved film goes to zero using $\varGamma$-convergence arguments.

Journal: Asymptotic Analysis, vol. 48, no. 1-2, pp. 141-171, 2006