An enhanced cutting plane algorithm of elastoplastic constitutive models for geomaterials

Abstract

Integration of the nonlinear stress–strain relationship plays a critical role in the application of constitutive models to engineering practice. Aiming at the nonlinear integration problems commonly existing in elastoplastic constitutive models for geomaterials, we herein present a robust enhanced cutting plane algorithm (ECPA). This algorithm is based on the traditional cutting plane algorithm (CPA) with a new adaptive substepping technique. The accuracy of the CPA is first investigated via a series of numerical examples on a unified hardening/softening elastoplastic model with different nonlinearity degrees of yield functions and plastic potential functions. An intriguing observation is that the accuracy of CPA cannot be guaranteed as long as the plastic flow direction (i.e., ∂G/∂σ ) is not a constant during loading. To overcome this deficiency, a substepping technique for adaptively restricting substep increments solely related to the plastic flow direction was originally proposed and embedded into CPA. The robustness, including the accuracy and efficiency of the proposed ECPA, is evaluated by setting different increment steps and error tolerances. Finally, the ECPA is applied to the Modified Cam Clay (MCC) model, and the robustness of the ECPA is further assessed in element scale tests and a boundary value problem.