Mixed Finite Element for Cracked Interface

Abstract

Several disorders observed in an existing work on civil engineering may have their origin in local phenomena which reveal the weak points of this work. These critical zones are located, on the one hand in the links between materials or interfaces, on the other hand in singularly formed areas such as cavities, angles and cracks, seats of strong stress concentrations. In this paper, the finite element method (mixed formulation) is used for the study of the interfacial cracks in bimaterials. A special finite element based on the mixed formulation, able to take into account the continuity of the interface on the coherent part (mechanical and geometrical continuity), and the discontinuity of this one on the cracked part (edge effect), is used to model at best this type of interface. This element was developed by H. Bouzerd using a direct formulation: the shape functions of the displacement and stress fields are built directly starting from the real configuration of the element in a reference (x, y). In this purpose, this element was reformulated starting from a reference element in a natural plan (ζ,η). This formulation presents, in addition to the simplification of calculations, the enormous advantage of modelling the types of cracks and their orientations. This interface element was associated with the virtual extension—crack to evaluate the energy release rates using only one meshing by finite elements. Several numerical examples concerning the interfacial cracks are analysed to assess the validity of this element by comparing with an available analytical solution or numerical ones obtained from others finite elements.