MESO-MECHANICALLY INFORMED MACROSCOPIC CHARACTERIZATION OF DAMAGE-HEALING-PLASTICITY FOR GRANULAR MATERIALS

The multiscale characterization of coupled damage-healing and plasticity for granular materials is presented in the frame of second-order computation homogenization. The structure composed of granular materials is modeled as Cosserat continuum at the macroscale. The representation volume element (RVE) possessing the meso-structure of discrete particle assembly is assigned at each of the integration points of the finite element mesh generated in the macroscopic continuum. The incremental non-linear constitutive relation for the discrete particle assembly of RVE is established. The incremental forces and couple moments applied to the peripheral particles on the boundary of the RVE from the medium outside the RVE are expressed in terms of the incremental translational and rotational displacements of peripheral particles of the RVE, the elastic stiffness of the current deformed meso-structural RVE, and the incremental dissipative frictional forces condensed to the peripheral particles of the RVE. Based on the average field theory and the Hill’s lemma, meso-mechanically informed macroscopic incremental nonlinear constitutive relation is derived for the gradient-enhanced Cosserat continuum. The tensorial damage, healing factors, and the tensorial net damage factor combining the effects of both the damage and the healing and the plastic strain to characterize anisotropic damage-healing and plasticity of granular materials are defined in the isothermal thermodynamic framework. In addition, densities of damage and plastic dissipative energies, the density of healing energy are defined so that the damage, the healing and the plastic effects on the failure of granular material are quantitatively comparable. The results of the example problem of strain localization demonstrate validity of the proposed method for characterizing the damage-healing-plasticity occurring in granular materials.