Micromechanical formulation of stress dilatancy and its implications on the flow rule

The paper presents micromechanical formulations of stress dilatancy and their use as a flow rule in classical elasto-plasticity calculations. We explore two different micromechanical approaches that both arrive at a stress dilatancy expression endowed with micromechanical information. One is based on energy calculations at both micro- and macro-scales, while the other on a micro-directional formulation of contact forces and displacements in a representative elementary volume. The nature of the flow rule that results from such formulations is discussed in relation to the dependence of the plastic strain increment vector on the loading (stress increment) direction. Interestingly, it is shown that in general three dimensional conditions, the ratios of the components of plastic strain increment are functions of not only the current stress, but also of the stress increment direction. The flow rule, commonly postulated in classical plasticity where the plastic strain increment depends solely on the current stress state, is in fact restricted to only two dimensional conditions, i.e. axi-symmetric or plane strain/plane stress.