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

Abstract

AbstractThe paper is devoted to constitutive solution, limit load analysis and Newton‐like methods in elastoplastic problems containing the Mohr‐Coulomb yield criterion. Within the constitutive problem, we introduce a self‐contained derivation of the implicit return‐mapping solution scheme using a recent subdifferential‐based treatment. Unlike conventional techniques based on Koiter's rules, the presented scheme a priori detects a position of the unknown stress tensor on the yield surface even if the constitutive solution cannot be found in a closed form. This eliminates blind guesswork from the scheme and enables to analyze properties of the constitutive operator. It also simplifies the construction of the consistent tangent operator, which is important for the semismooth Newton method when applied to the incremental boundary‐value elastoplastic problem. The incremental problem in Mohr‐Coulomb plasticity is combined with limit load analysis. Beside a conventional direct method of incremental limit analysis, a recent indirect one is introduced and its advantages are described. The paper contains 2D and 3D numerical experiments on slope stability with publicly available Matlab implementations.