UNILATERAL CONTACT PROBLEMS WITH FRACTAL GEOMETRY AND FRACTAL FRICTION LAWS - METHODS OF CALCULATION

The present paper deals with two interrelated subjects: the fractal ge ometry and the fractal behaviour in unilateral contact problems, More specifically, throughout this paper both the interfaces and the fricti on laws holding on these interfaces are modelled by means of the fract al geometry. It is important to notice here that the fractality of the induced friction laws takes into account the randomness of the interf ace asperities causing the friction forces. According to the fractal m odel introduced in this paper, both the fractal law and the fractal in terface are considered to be graphs of two different fractal interpola tion functions which are the ''fixed points'' of two contractive opera tors. Using this method, the fractal friction law is approximated by a sequence of nonmonotone possibly multivalued classical C-0-curves. Th e numerical treatment of each arizing nonmonotone problem is accomplis hed by an advanced solution method which approximates the nonmonotone problem by a sequence of monotone subproblems. Numerical applications from the static analysis of cracked structures with a prescribed fract al geometry and fractal interface laws are included in order to illust rate the theory.