Importance of numerical algorithm for stress integration in the application of elastoplastic soil models for geotechnical problems

Abstract

The mathematical formulation of the constitutive equations is expressed through a set of differential nonlinear equations. The incrementally-iterative procedures are mainly used for solving material nonlinear problems by the finite element method. It is necessary to calculate the current stresses based on the known deformations. The accuracy of stresses determination directly affects the accuracy of the results, which implies the importance of finding the most efficient methods for the numerical integration of the constitutive relations of the model. The first part of the paper describes several classes of algorithms that successfully solve the problem of stress integration for elastoplastic models, in the sense that they meet three basic requirements: consistency with constitutive relations, numerical stability and incremental condition of plastic consistency. The second part presents the original procedure for applying the implicit Governing Parameter Method for the Modified Cam Clay constitutive model, as well as an assessment of the accuracy of the method.