Micromechanically informed constitutive model and anisotropic damage characterization of Cosserat continuum for granular materials

Abstract

The microstructures of granular materials are represented by Voronoi cells generated with a Voronoi tessellation of discrete particle assembly. A Voronoi cell model including not only the reference particle laid inside the Voronoi cell but also its intermediate neighboring particles is presented to formulate micromechanically based macroscopic constitutive relations and constitutive modular tensors of effective Cosserat continuum. The anisotropy of effective Cosserat continuum due to intrinsic characters and deformation-induced evolutions of microstructure of granular materials of the Voronoi cell is quantitatively demonstrated. The derived micromechanically informed macroscopic constitutive relation of effective Cosserat continuum reveals that the Cauchy stresses are not only constitutively related to the strains but also to the curvatures defined in Cosserat continuum, likewise, the couple stresses are not only constitutively related to the curvatures but also to the strains. The derived modular tensors are verified by comparisons of them with those given for classical isotropic Cosserat continuum and are used to identify the elastic constitutive parameters of isotropic Cosserat continuum. The micromechanically informed macroscopic damage factor tensor to characterize anisotropic material damage of effective Cosserat continuum is formulated with no need specifying macroscopic phenomenological damage criterion and damage evolution law. The principal directions and values of the derived damage factor tensor along with numerical results reveal the microscopic mechanisms of macroscopic damage phenomenon, i.e. loss of contacts, re-orientation of contacts of the reference particle with its intermediate neighboring particles and concomitant volumetirc dilatation of the Voronoi cell.