Shear band static evolution by spatially mobilized plane criterion based Drucker-Prager model and numerical manifold method

Abstract

The shear band due to strain localization is deemed a strong discontinuous plane in this study, and simulated by the numerical manifold method (NMM). The SMP (Spatially Mobilized Plane) criterion is incorporated into the Drucker-Prager (DP) model by the transformed stress (TS) method. The constitutive integration of plasticity is carried out on the new yielding surface with the tensile part being cut off, leading to a mixed complementarity problem (MiCP). The Gauss-Seidel based projection contraction (GSPC) algorithm is invoked to solve the MiCP. In NMM, the cohesion is a constant when the contact is in slipping state. This study modifies the cohesion so that the decaying of cohesion could be reflected with the growth of the sliding. To accelerate the convergence, the contact stiffness matrix in open state is proposed to be constructed in a new way in this paper. The NMM formulation for solving the strain localization problem is derived in this study. The displacement controlled method is extended to the material nonlinearity accompanied with contact problem. Two examples, including the soil block and soil slope under compression, have been studied to verify the efficiency of the proposed method in simulating the process of shear band evolution.