An exact implementation of the Hoek–Brown criterion for elasto-plastic finite element calculations

Abstract

A simple stress update algorithm for generalised Hoek–Brown plasticity is presented. It is intended for use in elasto-plastic finite element computations and utilises the return mapping concept for computing the stress increment belonging to a given increment in strain at a material point. In the algorithm all manipulations are carried out in principal stress space, where the Hoek–Brown failure criterion has a very simple form compared to its formulation in general stress space. In principal stress space it is also simple to determine whether the stress should be returned to one of the edges or to the apex of the yield surface and to form the constitutive matrices. As opposed to earlier finite element implementations of Hoek–Brown plasticity the exact criterion is used, i.e. no rounding of the yield surface corners or edges is attempted. Numerical examples and a comparison with an often used method for dealing with the corner singularities indicates the efficiency of the presented.