Modeling the Inelastic Interphase in Unidirectional Composites

From a microscopic point of view, studying the influence of the interface on the mechanical behavior of a composite material leads to a contact problem between the reinforcement and the matrix, a problem initially studied by HERTZ-BOUSSINESQ [1]. Since then, several numerical approaches have been developed, such as the incremental methods [2], methods based on integral equations, methods which transform the mathematical formulation of the contact problem in a nonlinear optimization problem [3] [4]. In our study, we assume that there exists a contact surface between the two elastic bodies and that this surface is the limit of a thin layer of a "plastic" material. The resulting problem is a quadratic programming (QP) problem which can be handled by a variety of QP methods, among them Wolfe's algorithm. By applying the latter, we show that the obtained solution satisfies, within the elastic finite element approximation, all the conditions of the original problem. The method is applied to the case of an unidirectional composite under u'ansverse tensile test. Cracking of such a material is then studied and the results compared with experimental data.