The elasto-plastic bulk model for compact cohesionless materials in continuum mechanics

Abstract

An orthotropic bulk model is proposed for cohesionless materials. The internal energy is defined as half the square of the product of the strain tensor and the bulk tensor. Strain tensors which leave the value of the internal energy unchanged are called orthotropic deviators and constitute a degree of freedom. The shape of the bulk tensor is variable, but is controlled by the Mohr-Coulomb friction limit. This gives rise to two basic modes: the isotropic mode where deviators are prevented by friction, and the deviatoric mode where deviators cause new voids in the material. A third mode occurs when volume is conserved through plastic recompaction of these voids. Elastic stress formulae are derived for each domain of strain tensors. The bulk model has potential for describing elasto-plastic behaviour of dense soils. When it is combined with a cohesion model it describes the behaviour of brittle rock as discussed elsewhere.