Thermodynamic framework for damage-healing-plasticity of granular materials and net damage variable

Based on the meso-structured Voronoi cell model for discrete particle assembly and the derived meso-mechanically informed constitutive relations of anisotropic Cosserat continuum, thermodynamic framework of isothermal meso-mechanically informed damage-healing and plastic process for granular materials is presented. The accumulated net (effective) damage factor tensor combining both material damage and healing effects is defined in terms of the initial (undamaged) and current (damaged) elastic moduli tensors of the meso-structured Voronoi cell attributed to the material point. According to the non-negativity of thermodynamic energy dissipations, the net damage variable is separated into the two component internal state variables; i.e. the damage and healing variables, which are accumulated in terms of incremental damage and healing variables, respectively. The meso-mechanically informed macroscopic damage-healing and plastic characterization are achieved without the need to specify macroscopic phenomenological damage, healing and plastic criteria, and their evolution laws. The merit of the proposed tensorial net damage and healing variables in modeling healing effects on initial weakened elastic stiffness (i.e. initial material defects) is demonstrated in terms of their isotropic scalar forms and integrated into the continuum damage-healing mechanics. The numerical results conceptually illustrate the performance of the proposed definitions of meso-mechanically informed net damage, damage, and healing variables. The coupled damage-healing and plastic process in anisotropic Cosserat continuum for granular materials is characterized in terms of densities of thermodynamic dissipations that make effects of the damage-healing and the plastic component processes on the material failure quantitatively comparable.