Internal spring distribution for quasi brittle fracture via Symmetric Boundary Element Method

Abstract

In this paper the symmetric boundary element formulation is applied to the fracture mechanics problems for quasi brittle materials. The basic aim of the present work is the development and implementation of two discrete cohesive zone models using Symmetric Galerkin multi-zone Boundary Elements Method. The non-linearity at the process zone of the crack will be simulated through a discrete distribution of nodal springs whose generalized (or weighted) stiffnesses are obtainable by the cohesive forces and relative displacements modelling. This goal is reached coherently with the constitutive relation that describes the interaction between mechanical and kinematical quantities along the process zone. The cracked body is considered as a solid having a “particular” geometry whose analysis is obtainable through the displacement approach employed in (Panzeca et al., 2000; 2002-b) by some of the present authors in the ambit of the Symmetric Galerkin Boundary Elements Method (SGBEM). In this approach the crack edge nodes are considered distinct and the analysis is performed by evaluating all the equation system coefficients in closed form (Guiggiani, 1991; Gray, 1998; Panzeca et al., 2001; Terravecchia, 2006).