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

TL;DR

This paper introduces a subdifferential-based implicit return-mapping scheme for Mohr-Coulomb plasticity that improves stress analysis accuracy and simplifies tangent operator construction, enhancing Newton-like methods in elastoplastic problems.

Contribution

It presents a novel subdifferential approach for implicit return-mapping in Mohr-Coulomb plasticity, eliminating guesswork and enabling better analysis of the constitutive operator.

Findings

The scheme accurately detects stress states on the yield surface.

It simplifies the construction of the consistent tangent operator.

Numerical experiments demonstrate improved slope stability analysis.

Abstract

The paper is devoted to a 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 closed form. This fact eliminates blind guesswork from the scheme, enables to analyze properties of the constitutive operator, and simplifies construction of the consistent tangent operator which is important for the semismooth Newton method applied on the incremental boundary value elastoplastic problem. The incremental problem in Mohr-Coulomb plasticity is combined with the limit load analysis. Beside a conventional direct method of the 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.