Subdifferential-based implicit return-mapping operators in Mohr-Coulomb plasticity

The paper is devoted to the numerical solution of an elastoplastic constitutive initial value problem containing the Mohr-Coulomb yield criterion, a nonassociative plastic flow rule, and a nonlinear isotropic hardening. The constitutive problem is discretized by the implicit Euler method. Instead of the conventional Koiter formulations, we define the plastic flow rule using the subdifferential of the plastic potential to keep just one plastic multiplier and derive some formulas regardless a type of the return to the yield surface. This idea simplifies the solution scheme so that one can a priori decide about the return type even if the nonlinear hardening is introduced. Moreover, one can easily analyze the mathematical properties of the stress-strain operator and consequently simplify construction of the consistent tangent operator. These operators are used for solving the corresponding incremental boundary-value problem by the semismooth Newton method. The remaining part of the paper is focused on incremental limit analysis. The direct and also indirect controls of the loading process are considered and used in 2D and 3D numerical experiments on slope stability. The related Matlab codes are available.