A novel algorithmic framework for the numerical implementation of locally embedded strong discontinuities Original Research Article

In this paper, a novel algorithmic framework for the numerical modeling of locally embedded strong discontinuities suitable for the analysis of material failure such as cracking in brittle structures or shear bands in soils is proposed. Based on the enhanced assumed strain (EAS) concept, the final failure kinematics of solids, approximated by discontinuous displacement fields, are incorporated into the finite element formulation. In contrast to previous works, the discontinuous part of the deformation mapping is condensed out at the material level without employing the standard static condensation technique. As a consequence, the resulting constitutive equations are formally identical to those of standard plasticity models. Hence, the return-mapping algorithm is applied to the numerical implementation. Only slight modifications of this, by now classical, algorithm are necessary. The proposed framework is applicable to any constitutive equation characterizing the inelastic part of deformation. Referring to the yield (failure) function and the evolution equations, no special assumption has to be made. Despite the differences between the presented numerical framework and the original implementation of the strong discontinuity approach (SDA), it is shown that both finite element models are completely equivalent. The applicability of the novel algorithmic formulation and its numerical performance are investigated by means of two two-dimensional as well as by means of a fully three-dimensional numerical analysis of shear band formation.