Strength evaluation of retrofit shear wall elements with interfaces of fractal geometry

Structures involving rough interfaces, with irregularities of all scales, are simulated with the help of fractal geometry. More specifically, the approach followed is the multilevel hierarchical approach. This approach has a multiscale self-affine structure appropriate for the simulation of rough interfaces. In the sequence, the problems resulting from the consideration of a fractal interface as a profile with a hierarchical structure are analyzed, with the assumption that, on the interface, nonmonotone adhesive contact and friction conditions hold. The method developed consists of an extension of the classical finite element method to the case of fractal interfaces. The case of nonconvex energy problems is investigated, and some results from static analysis of concrete shear walls with prescribed fractal cracks are included in order to illustrate the theory.