Modelling Limit States Within the Framework of Hypoplasticity

Abstract

The focus of this paper is on modelling limit stress states or so‐called critical states in which a cohesionless granular body can be deformed continuously at a constant stress and a constant volume. The constitutive equations are based on the framework of hypoplasticity, which is an alternative concept to elasto‐plasticity. The requirements for modelling limit stress states are studied for both a standard and a micro‐polar hypoplastic model. As in a micro‐polar description the stress tensor is usually non‐symmetric, the question arises as to whether the result for the limit stress ratio based on the symmetric Cauchy stress tensor in the standard continuum is the same as the one obtained from the micro‐polar continuum description. To this end the limit stress state is analysed under plane shearing of a lateral infinite granular strip located between parallel rough platens under a constant normal stress. It is shown that the stress ratio in the limit state obtained from the micro‐polar hypoplastic model can only be the same as for the standard hypoplastic continuum model under certain conditions on the centre line of the shear band.