Non-local boundary integral formulation for softening damage

A strongly non-local boundary element method (BEM) for structures with strain-softening damage treated by an integral-type operator is developed. A plasticity model with yield limit degradation is implemented in a boundary element program using the initial-stress boundary element method with iterations in each load increment. Regularized integral representations and boundary integral equations are used to avoid the di culties associated with numerical computation of singular integrals. A numerical example is solved to verify the physical correctness and e ciency of the proposed formulation. The example consists of a softening strip perforated by a circular hole, subjected to tension. The strainsoftening damage is described by a plasticity model with a negative hardening parameter. The local formulation is shown to exhibit spurious sensitivity to cell mesh re nements, localization of softening damage into a band of single-cell width, and excessive dependence of energy dissipation on the cell size. By contrast, the results for the non-local theory are shown to be free of these physically incorrect features. Compared to the classical non-local nite element approach, an additional advantage is that the internal cells need to be introduced only within the small zone (or band) in which the strain-softening damage tends to localize within the structure.