High-fidelity-generalized-method-of-cells micromechanical analysis of damage evolution in viscoelastic composites

The effect of time-delayed stress response, typical for viscoelastic materials, on the evolution of damage in porous soft materials and fiber-reinforced soft-matrix composites is studied by employing the material-sink gradual damage evolution theory and the micromechanical finite strain high-fidelity generalized method of cells (HFGMC). In the material-sink approach, damage and crack locations are not postulated in advance, but are instead predicted by the solution of a two-way coupled system of mechanistically derived differential equations, which include the intact-material balance law, in addition to stress equilibrium. The viscoelastic response is based on a rheological model of the generalized Maxwell type, typical for biological tissues. The viscoelastic constitutive relation is generalized to incorporate evolving damage, resulting in loading-rate sensitive time-dependent response. The finite strain HFGMC micromechanics analyzes composite materials that possess periodic microstructure and are comprised of constituents characterized by complex response, with a viscous part, a hyperelastic part and a degradation part, described by a phase-field like approach, albeit derived mechanistically. In the framework of HFGMC micromechanics, the repeating unit cell of the periodic composite is divided into numerous subcells. The resulting coupled system of equations is enforced in the subcell in strong form in the volume-averaged sense and the internal (continuity) and global (periodic) boundary conditions are imposed in the surface-averaged sense. Subcell equilibrium is algorithmically attained prior to fields continuity. Applications are presented for the prediction of the stress response and damage evolution history in porous soft viscoelastic materials and fiber-reinforced viscoelastic composites.