Implicit yield function formulation for granular and rock-like materials

TL;DR

This paper introduces a general method to define an implicit convex yield function for granular and rock-like materials, enabling efficient and accurate numerical integration schemes despite complex yield surface features.

Contribution

It proposes a novel construction strategy for implicit convex yield functions from any convex yield surface, improving numerical integration in constitutive modeling.

Findings

The implicit yield function ensures convexity and numerical stability.

The return-mapping scheme performs accurately despite increased computational cost.

The method is applicable to elastic-plastic and damage models for granular materials.

Abstract

The constitutive modelling of granular, porous and quasi-brittle materials is based on yield (or damage) functions, which may exhibit features (for instance, lack of convexity, or branches where the values go to infinity, or false elastic domains) preventing the use of efficient return-mapping integration schemes. This problem is solved by proposing a general construction strategy to define an implicitly defined convex yield function starting from any convex yield surface. Based on this implicit definition of the yield function, a return-mapping integration scheme is implemented and tested for elastic-plastic (or -damaging) rate equations. The scheme is general and, although it introduces a numerical cost when compared to situations where the scheme is not needed, is demonstrated to perform correctly and accurately.