Finite-Volume Method Implementation of the Modified Cam-Clay Constitutive Model

Abstract

This study addresses the challenge of numerically simulating nonlinear elastoplastic behavior in solid mechanics via the finite-volume method (FVM) that has not been traditionally dominant in the field. The study presents the implementation of a new FVM code tailored for nonlinear elastoplasticity of the modified Cam-clay model via OpenFOAM (version 2.3.0), an open-source C++ library primarily used for computational fluid dynamics, where OpenFOAM’s capabilities are extended to, unlike conventional fluid mechanics applications, model solid mechanics problems. This implementation utilizes an implicit–explicit split strategy to effectively handle nonlinearity and displacement coupling inherent in solid mechanics. Additionally, a novel single-cell correction procedure is proposed to, when plasticity occurs, adjust stress and plastic strain incrementally. Our results, validated against benchmark tests, demonstrate a good alignment with expected outcomes and show notable computational time savings compared to the traditional FEMs by Abaqus (version 6.14) simulations for the cases examined here. The insights gained in this study reveal the potential of FVMs not only for elastoplasticity modeling but also for more complex multiphysics simulations involving coupled fluid and solid dynamics. This capability positions FVMs as a promising tool for addressing a wide range of problems in geotechnical and subsurface engineering, highlighting the innovative integration of methodologies across disciplinary boundaries.