Modeling strong discontinuities at finite strains—A novel numerical implementation

In this paper, a finite element formulation suitable for the modeling of locally embedded strong discontinuities at finite strains is presented. Following the enhanced assumed strain concept (EAS), the proposed numerical model is based on an additive decomposition of the displacement gradient into a conforming and an enhanced part. The enhanced part is associated with the final failure kinematics of solids which are approximated by means of a discontinuous displacement field (strong discontinuities). Referring to the displacement jump, no special assumption, such as purely mode-I or mode-II failure, is made. The same holds for the class of interface laws considered which govern the evolution of the displacement discontinuity in terms of the traction vector, acting at the surface of strong discontinuities. Consequently, the suggested numerical framework can be applied to a broad range of different interface laws, including damage based models. In contrast to previous works, the presented finite element formulation does not require the static condensation technique to be employed. More precisely, instead of computing the conforming part of deformation and the displacement jump simultaneously from the weak form of equilibrium and the weak form of traction continuity, the different parts of the local deformation are decomposed according to a predictor–corrector algorithm. The proposed predictor and the corrector step are formally identical to that of classical computational plasticity models. Hence, subroutines designed for standard models (continuous deformation) can be applied with only minor modifications necessary. The applicability as well as the performance of the resulting finite element formulation are demonstrated by means of a fully three-dimensional analysis of shear band formation in a bar made of a ductile material.