Adaptive finite element analysis of fractal interfaces in contact problems

Structures involving interfaces with fractal geometry are referred here as a sequence of classical interfaces problems, which result from the consider ation of the fractal interfaces as the unique "fixed point" or the "determi nistic attractor" of a given Iterated Function System (IFS). On the interfa ce, unilateral contact conditions are assumed to hold. The approximations o f the fractal interfaces are combined with a penalty regularization based o n the minimization of the potential energy, after some appropriate transfor mations are performed. For this type of contact problems there often result singular points on the interfaces which lead to possible stress concentrat ions. Further-more, the convergence of finite element solution under a suff icient discretization can nor be determined from the outset. An adaptive fi nite element strategy appears to be suitable for such kind of contact probl ems in that it possesses the properties of adjusting automatically the mesh sizes both in the interior of the bodies and on the contact zone. In this spirit, both the goals of exactly determining the real contact areas, and o f enhancing the accuracy of finite element solution (meanwhile consuming re asonable computational costs) may be achieved. The error estimator based on the residual stress analysis is discussed. Numerical examples illustrate t he validity and effectiveness of the method proposed in this paper. (C) 200 0 Published by Elsevier Science S.A. All rights reserved.