On the stress update algorithm of an advanced critical state elasto-plastic model and the effect of yield function equation

Mohammad Rezania,Nallathamby Sivasithamparam,Mohaddeseh Mousavi Nezhad

doi:10.1016/j.finel.2014.06.009

Abstract

This paper investigates the computational performance of S-CLAY1S constitutive model by varying its yield function equation. S-CLAY1S is an advanced anisotropic elasto-plastic model that has been developed based on the extension of conventional critical state theory. In addition to modified Cam-Clay׳s hardening law, S-CLAY1S also accounts for inherent and evolving plastic anisotropy, interparticle bonding and degradation of bonds during plastic straining. A modified Newton–Raphson stress update algorithm has been adopted for the implementation of the model and it was found that the algorithm׳s convergence performance is sensitive to the expression of the yield function. It is shown that for an elasto-plastic model which is developed based on the critical state theory, it is possible to improve the performance of the numerical implementation by changing the form of the yield function. The results of this work can provide a new perspective for computationally cost-effective implementation of complex constitutive models in finite element analysis that can yield in more efficient boundary value level simulations.

Highlights

Initial anisotropy is assumed to be cross-anisotropic, which is a realistic assumption for normally consolidated clays deposited along the direction of consolidation
The robustness of a modified Newton–Raphson algorithm applied to the S-CLAY1S model has been evaluated using different forms of its yield function
The proposed stress update scheme is generally very robust, and impartial in terms of accuracy; its convergence performance is found to be considerably sensitive to the yield function equation as well as acceptable tolerances

Summary

Introduction

Initial anisotropy is assumed to be cross-anisotropic, which is a realistic assumption for normally consolidated clays deposited along the direction of consolidation. The main issue in an explicit algorithm is that its success largely relies on the size of the incremental load steps, the results at boundary value level, can be load step dependant This problem usually results in limiting the application of an advanced constitutive model at practical level. In the implicit or so-called return mapping algorithm [15] the constitutive model's governing equations are treated nonlinearly and are solved in an iterative manner until the drift from the yield surface is small enough [16] In this method the computed stress state automatically satisfies the yield condition. Through model performance comparisons the most suitable formulation of the advanced anisotropic model is identified for its implementation

S-CLAY1S model

S-CLAY1S implementation

Computational performance

At stress point level

At boundary value level

Conclusion