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Mathematical Modeling and Numerical Simulation of Fabric Drape

The purpose of this article is to study the deformation of a fabric hanging over a two-dimensional obstacle and submitted to its own weight. Fabrics usually have a non-linear behaviour because of their flexibility. Furthermore, this problem is a large displacement one. In the first part, we establish the general equilibrium equations and we introduce two mathematical models. The first model is a non-linear membrane one, the mathematical analysis of which leads to the computation of the quasi-convex envelope of the associated energy density. We thus prove the existence of a generalised solution of this problem. The second model is a non-linear membrane-flexion model and is obtained when adding a regularising term to a non-coercive energy functional. Using the techniques of the Calculus of Variations, we prove the existence of at least one solution for this minimisation problem.