The Direct Boundary Integral Approach To TheFrictional Unilateral Contact Problem In Cracks

Abstract

The paper presents a theory for the study of cracks having a given geometry by taking into account mechanical interactions like unilateral contact and friction between the crack sides. The interactions studied are of general monotone type. The arising problems are of non-classical nature, due to the interface conditions expressed it terms of non-differentiable convex superpotentials. The direct B.I.E.M. is extended appropriately in order to treat this type of problem. The developed method is illustrated by a numerical example concerning the calculation of strees fields with and without the contact consideration showing the influence of the ommision of this aspect of the phenomenon to the stress felds. INTRODUCTION Unilateral contact and friction produce a special kind of nonlinearity as the free boundaries between contact and noncontact regions can not be a priori known. These two phenomena have been extensively studied for deformable bodies both from the mathematical and the numerical point of view (c.f. Duvaut-Lions [7], Panagiotopoulos [11] and the references given therein). The inequalities describing unilateral contact and friction characterize the unilateral character of the corresponding mechanical problems, since for these problems the principle of virtual and of complementary virtual works hold in inequality from. Moreover, the problems no longer are expressed in terms of differential equations, but of multivalued differential equations, which are equivalent to variational inequalities expressing the principle of virtual, or of complementary virtual work. This nonclassical behaviour of cracks has not as yet been extensively studTransactions on Engineering Sciences vol 1, © 1993 WIT Press, www.witpress.com, ISSN 1743-3533