On the fractal fracture in brittle structures Numerical approach

Abstract

The aim of the present paper is to study the influence of the irregular fracture of structures, consisting of brittle materials, on the arising stress and strain fields. This type of fracture, depends strongly on the microstructure of the body and on the loading applied on the structure. In this paper brittle fracture phenomena are modelled by means of fractal geometry, which describes with great accuracy the arising fracture patterns. Not only the fractality of the form of the arising cracks but also the fractality of the induced friction law at the interface is considered here. This fact takes into account the radomness of the interface asperities causing the friction forces. According to the fractal model introduced in this paper, the fractal interface of a crack or the fractal stress-strain or reaction-displacement law is considered to be the unique ‘fixed point’ of a given Iterative Function System (I.F.S.) or the graph of a fractal interpolation function (F.I.F.). On the fractal interface nonmonotone contact and friction conditions are assumed to hold. The methods developed here extend the classical FEM to the case of fractal interfaces and to the case of fractal nonmonotone stress-strain laws. Numerical applications from the static analysis of brittle structures with prescribed crack geometry and crack interface laws are included in order to illustrate the theory.