Material modeling for micromorphic continua (in the sense of Eringen and Suhubi [IJES, 1964]) of combined viscoelastic-viscoplastic constitutive nonlinearity is developed for the first time – e.g., applicable to asphaltic and polymer-bonded granular matter – and, in so doing, is recast in a compact energetic formulation via “granular micromechanics.” Under that novel homogenization paradigm, potentials and pseudo-potentials for viscoelastic viscoplasticity are scale-bridged by averaging discrete grain-contact interactions over a representative granular assemblage. As a critical feature of the multiscale method, higher-order kinematics are considerably simplified by employing a microstructural length scale in conjunction with Taylor-series expansion. In distinction to prior granular micromorphic micromechanics, our discrete-to-continuum modeling embeds a volume constraint to weakly enforce mean-field definitions in the representative assemblage by the method of Lagrange multipliers: analogous to the classical three-field reformulation of a mixed interpolation space for nonlinear finite elements. It is further demonstrated that volume-constrained reformulation renders micromorphic constitutive modeling constitutively appropriate for viscous-binder-bonded particulate materials. As a consequence, coupled pressure- and rate-sensitive dissipative phenomena (combined viscoelasticity and Drucker-Prager viscoplasticity) become both microstructurally sensitive and algorithmically straightforward. A key practical upshot is that computational implementation relies on non-custom methods in numerical optimization with examples provided.
2025-04-09 09:00:00
