Integral equations and nonlocal damage theory: a numerical implementation using the BDEM

In this paper the integral equation approach is developed to describe elastic-damaging materials. An isotropic damage model is implemented to study nonlinear structural problems involving localisation phenomena. Especially for the cases that exhibit stress or strain concentrations, an integral approach can be recommended. Besides, the technique is able to represent well high gradients of stress/strain. The governing integral equations are discretised by using quadratic isoparametric elements on the boundary and quadratic continuous/discontinuous cells in the zone where the nonlinear phenomenon occurs. Two numerical examples are presented to show the physical correctness and efficiency of the proposed procedure. The results are compared with the local theory and they turn out to be free of the spurious sensitivity to cell mesh refinement.