In this paper BEM formulations applied to localization problems are discussed. The formulation is particularly dedicated to analysis of elastoplastic two-dimensional bodies for which the formulation has successfully implemented. First, we discuss the capability of BEM to deal with the localization phenomena. The proposed algorithms are formulated as usual by assuming an initial stress or strain field applied over the domain area where plastic strains take place. The initial stress integrals are approximated over triangular and quadrangular cells. The regularization of the plastic zone is achieved by following the gradient plasticity approach. The plastic multiplier integral representation is derived and several alternatives to obtain the corresponding algebraic equations are discussed. A simple numerical example is shown to illustrate the capability of the BEM technique to obtain regularized solutions in the context of gradient plasticity.
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