Hybrid discrete-to-continuum viscoelastic viscoplasticity by volume constraint

Abstract

Material modeling for micromorphic continua (in the sense of Eringen and Suhubi [IJES, 1964]) of combined viscoelastic-viscoplastic constitutive nonlinearity is developed, for application to some geomaterials and other granular materials, and is recast in a compact energetic formulation via “granular micromechanics.” Under the granular mechanics 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 proposed multiscale method, higher-order kinematics are considerably simplified by employing a microstructural length scale in conjunction with Taylor-series expansion. In distinction to prior micromorphic micromechanics, our discrete-to-continuum scale-bridging 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’ selective integration. As subsequently demonstrated, volume-constrained reformulation renders micromorphic modeling constitutively appropriate for viscoelastic viscoplastic particulate materials. As a consequence, coupled pressure- and rate-sensitive dissipative phenomena - i.e., of combined viscoelasticity and Drucker–Prager viscoplasticity– -become microstructurally sensitive and algorithmically advantageous, utilizing numerical methods in bound-constrained optimization.