Numerical integration of elasto-plastic constitutive models using the extrapolation method

Stress-strain integration algorithms are an important component of finite element codes. When they are robust, accurate and fast, the performance of a finite element code significantly improves, especially when advanced elasto-plastic constitutive models are used. This paper introduces a novel algorithm for the stress-strain integration of elasto-plastic soil models with automatic control of the integration error. The proposed algorithm is based on the extrapolation method used for the solution of ordinary differential equations. In this work the algorithm has been coded for the Barcelona Basic Model (a classic elasto-plastic volumetric hardening constitutive model for unsaturated soils) but its application can be easily extended to other categories of models. The efficiency and error properties of the extrapolation algorithm are assessed by integrating stresses over strain increments of different sizes and with different error tolerances. The performance of the algorithm is compared against alternative Runge-Kutta integration schemes with control of integration error.