Two‐invariant modular implicit plasticity solver framework for geomechanical simulators

Abstract A modular, computationally efficient integration framework for two‐invariant‐based elastoplastic constitutive models is proposed. It is designed to allow a range of constitutive models to be incorporated with minimal programming effort. The development is intended for efficient numerical schemes in large‐scale geomechanical simulations. The modular format consists of four components: isotropic elastic relation, isotropic yield criterion, two‐invariant smooth flow potential plastic flow rule and isotropic hardening law. Linear and non‐linear bulk elasticity are considered. For the non‐linear case, a numerical assessment of the accuracy of bulk elasticity integration schemes is presented, where pure Euler and semi‐analytical integrators are compared. The deviatoric component of the elastic law considers both the constant shear modulus and constant Poisson's ratio models. The combination of the classic Terzaghi compaction law with different bulk elasticity models may lead to a physical inconsistency, which is removed by a straightforward modification of the hardening law. When used in conjunction with the proposed bulk elasticity models, it results in a family of compaction laws that significantly reshape the normal compaction line – a fact that seems to have been overlooked in the literature. The main contributions concerning the plasticity integrator are: a novel integration scheme that considers the variation of specific volume within each step; and a condensed system comprising two scalar return‐mapping equations. A Modified Cam‐Clay (MCC) model is used in the assessments. A comparison with an existing, well‐known algorithm is also provided and, in spite of its modularity/generality, the proposed scheme is shown to yield significant computational gains.