Non-Coaxiality and Energy Dissipation in Granular Materials

Abstract

The paper presents a theoretical and experimental study of the effects of non-coaxiality or non-coincidence of the principal stress and the principal plastic strain increment directions on the behaviour of granular materials. Experimental results from hollow cylindrical tests on sand involving principal stress rotation which support previously published results on non-coaxiality are presented. These results imply that constitutive relations cannot be sufficiently formulated in the principal stress space unless the deviations between the principal stress and plastic strain increment directions are taken into consideration. It is shown that plasticity formulations with plastic potentials that are scalar functions of the stress invariants alone implicitly assume coaxiality and cannot be used for loading involving principal stress rotation. The paper presents a comprehensive analysis of the effects of non-coaxiality on the energy dissipation of sand. The paper shows that energy dissipation calculated from the principal stresses and the principal plastic strain increments or from the stress and plastic strain increment invariants, would be erroneous and would over-estimate the amount of dissipated energy during loading in the case of non-coaxial flow. A non-coaxiality factor is introduced in order to account for the effects of non-coaxiality on the energy dissipation equation and in a stress-dilatancy relation for granular materials. Explicit expressions of the non-coaxiality factor for two-and three-dimensional loading conditions are given at the end of the paper. Experimental results are presented to show the validity of the proposed energy dissipation and stress-dilatancy equations.