Extended finite element method for strong discontinuity analysis of strain localization of non-associative plasticity materials

Abstract

The purpose of this paper is to propose a new development of the extended finite element method (XFEM) for carrying out the strong discontinuity analysis of strain localization of non-associative plasticity materials. The displacement is assumed to possess a Heaviside jump at the localization interface and the strain becomes bounded measure including a Dirac-delta function, but the traction must be continuous at the localization interface. First, the explicit expressions for the initiation condition and the slip direction and motion direction for the localization interface are derived from discontinuous bifurcation analysis. Second, the linearly and exponentially decreasing cohesive models are proposed respectively as the product of the combination of the continuum plasticity model and strong discontinuity kinematics, which relates the cohesive softening properties to the cohesive surface energy (or called cohesive fracture energy). Third, a linear cohesive/friction coupled model is proposed for the frictional contact interface based on the Mohr–Coulomb frictional law. The evolution of zero-thickness localization band (or called slip line) is shown to be equivalent to the crack initiation and propagation. Fourth, the finite element formulation is derived based on the XFEM to capture the displacement discontinuity. It is shown that numerical analysis for predicting the evolution of the localization interface ultimately falls into the framework of the XFEM with the embedded zero-thickness cohesive model or cohesive/friction coupled model. The cohesive segment method in the XFEM is used to simulate the initiation and propagation of the localization interface along the slip direction across the enriched elements. Numerical convergence due to cohesive/friction softening behaviors is solved by viscous regularization. Finally, numerical results on two typical cases including the single notched four-point bending model and the soil slope stability model under compression demonstrate the proposed methodology by studying the effects of the mesh size and cohesive surface energy on the evolutive localization interface and the load–displacement responses.