Existence de solutions pour un modèle de drapé d'un tissu

Abstract

In this Note we establish the existence of minimizer of a nonconvex energy functional. This functional is an energy of deformation of a woven fabric subject only to his own weight and fixed on a part of its boundary. A typical example is the case of a tablecloth on a table. We make the hypothesis that the fabric is inextensible in the direction of the fibers but can undergo membrane shear and flexion deformations. We use technics introduced in [3], in the no membrane shear case. The studied energy involves tensors analog to those of [7] and [5] to which we added a regularizing term accounting for shear angle variation.