Unilateral contact problems with fractal geometry and fractal friction laws: Methods of calculation (Q1271708)

We deal with two interrelated subjects: the fractal geometry and the fractal behaviour in unilateral contact problems. More specifically, both the interfaces and the friction laws holding on these interfaces are modelled by means of the fractal geometry. According to the fractal model, the fractal law and the fractal interface are considered to be graphs of two different fractal interpolation functions which are ``fixed points'' of two contractive operators. Using this method, we approximate the fractal friction law by a sequence of nonmonotone possibly multivalued classical \(C^0\)-curves. The numerical treatment of the arising nonmonotone problem is accomplished by an advanced solution method which approximates the nonmonotone problem by a sequence of monotone subproblems. Numerical applications to cracked structures with a prescribed fractal geometry and fractal interface laws illustrate the theory.