A computational model of interaction between material and interface cracks

Technical University of Košice, Faculty of Civil Engineering, Vysokoškolská 4, 042 00 Košice, Slovakia

^* Corresponding author: roman.vodicka@tuke.sk

Abstract

A quasi-static model for numerical solution of initiation and propagation of cracks along interfaces or inside materials is developed. The two types of cracks are modelled by the material damage theory with two independent damage parameters introduced. For cracks at the interface, in fact represented by contact of construction components, cohesive or adhesive contact is considered, for which several computational relationships based on energetic formulation exist. Accordingly, the appropriate modelling of bulk damage also includes energy consideration. In terms of cracks, it leads to so called diffuse cracks. The computational approach is referred to as phase field models. These will cause damage in a very narrow band representing the actual crack. The computational analysis provides stress-strain quantities and the damage variables to simulate both interface and material cracks. The proposed mathematical approach has a variational form based on an energetic formulation looking for a kind of weak solution. The solution is approximated by a time stepping procedure, a finite element code, and it utilizes quadratic programming algorithms.