Fractal interfaces with unilateral contact and friction conditions

Abstract

Structures involving interfaces with fractal geometry are analyzed here as a sequence of classical interface subproblems. On the interface, unilateral contact and friction boundary conditions are assumed to hold. These classical subproblems result from the consideration of the fractal interface as the ‘fixed point’ (or the ‘deterministic attractor’) of a given transformation. This approximation of the fractal is combined with a two-level contact-friction algorithm based on the optimization of the potential and of the complementary energy, after some appropriate transformations relying on the singular value decomposition of the equilibrium matrix are performed. Numerical examples illustrate the theory.