Pergamon Mechanics Research Communications, Vol. 22, No. 6, pp. 561-570, 1995 Copyright © 1995 Elsevier Science Ltd Printed in the USA. All rights reserved 0093-6413/95 $9.50 + .00 0093-6413(95)00062-3 MODELING THE INELASTIC INTERPHASE IN UNIDIRECTIONAL COMPOSITES C. Disdier, E. Loute* and J. Pastor Laboratoire Matrriaux Composites, ESIGEC, Universit6 de Savoie, 73376 Le Bourget-du-Lac, France, *EU.S.L., Bruxelles and CORE, UCL, Louvain-la-Neuve, Belgique. (Received 15 December 1994; accepted fi)r print 15 September 1995) Introduction 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. Fo~anulation We consider an elastic body of volume f2, made of two homogeneous and isotropic parks referred to as l and 2 with a common contact surface denoted by I'~_2 . This surface is delined as the limit of a thin zone in a way similar to what is done in Limit Analysis to define the velocity jump. Consequently, the associated mechanical variables are the stress vector on the facet which is tangent to 1'~_2 and the con'esponding displacement jump vector, Iv] v2 - v ~ ; according to the convention of positive tensile stress, the normal n to the facet is oriented from first to second material. The truncated Tresca domain [ llll oi" the admissible stress vectors on a contact facet, depicted by the figure 1 in the present isotropic plane case with ::,~ c:~, and the HILL maximum work principle define the isotropic contact law. Hence the unsticking of the two elastic parts is possible whenever the stress vector leaches the domain D frontier, since in the present case the two materials adjacen 561