Emergence of critical state in granular materials using a variationally-based damage-elasto-plastic micromechanical continuum model

The mechanical response of granular materials, exemplified by frictional grain interactions, is characterized by a critical state in which deformation occurs without change of material volume or stresses when subjected to large shear deformation. In this work, a granular micromechanics approach (GMA) based continuum model is used to investigate the emergence of such a critical state. The continuum description is constructed through mechanical concepts based upon elastic and dissipation energies defined for a generic grain-pair interaction. A hemivariational principle provides the basis for considering the evolution of damage and plasticity phenomena comprising grain-pair contact loss and irreversible deformation. As a consequence, the Karush–Kuhn–Tucker (KKT)-type conditions are derived, which give the evolution equations for the irreversible phenomena. Notably, in this derivation there is no invocation of flow rules and other similar assumptions of classical phenomenological continuum damage and plasticity. Further, Piola's ansatz is elaborated to kinematically connect granular micromechanics of grain-pair to the continuum description. While the concept of critical state analysis has been handled with either phenomenological approaches or discrete numerical frameworks, in the present paper this concept is examined within a micromechanics-based continuum description. The constitutive model is established and the coupled damage and plastic irreversible quantities are assessed. The critical state is shown to emerge as grain-pair related damage and plastic evolution in a competitive/collaborative manner during the imposed loading path.