Cracks of fractal geometry with unilateral contact and friction interface conditions

Abstract

Structures involving cracks of fractal geometry are studied here, on the assumption that at the interface unilateral contact and friction boundary conditions hold. Approximating the fractal by a sequence of classical surfaces or curves and combining this procedure with a two-level contact-friction algorithm based on the optimization of the potential and of the complementary energy, we get the solution of the problem after some appropriate transformations relying on the S.V.D.-decomposition of the equilibrium matrix. Numerical examples, using singular elements for the consideration of the crack singularity, illustrate the theory.