A continuum and variationally consistent damage plastic model based on granular micromechanics towards critical state simulations

The presentation aims to report a continuum theory for materials having granular microstructure and accounting for some dissipative phenomena like damage and plasticity. The continuum description is constructed by means of purely mechanical concepts, assuming expressions of elastic and dissipation energies as well as postulating a hemi-variational principle, without incorporating any additional postulates, like flow rules, that are generally used in a standard theory. Karush–Kuhn–Tucker (KKT)-type conditions, providing evolution equations for damage and plastic variables associated with grain–grain interactions, are derived solely from the fundamental postulates and higher order gradient components in the elastic energy induce a system of Partial Differential Equations (PDEs) and Boundary Conditions (BCs) that are derived by the same hypotheses. Numerical experiments have been performed to investigate the applicability of the model. Cyclic loading–unloading histories have been considered to elucidate the material hysteretic features of the continuum. We also assess the competition between damage and plasticity, each having an effect on the other. Further, the evolution of the load-free shape is shown not only to assess the plastic behavior, but also to make tangible the point that, in the proposed approach, plastic strain is found to be intrinsically compatible with the existence of a placement function. Finally an application for critical state simulations within the present continuum model will be addressed. The critical state concept characterizes the mechanical behavior of sheared granular materials, in which deformation occurs without change of material volume and it is worth to be noted that it has been achieved in the literature only within the computationally onerous Discrete Element Method (DEM).