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.

开发了组合粘弹性-粘塑性本构非线性的微形态连续体（Eringen 和 Suhubi [IJES，1964] 意义上的）材料建模，用于某些地质材料和其他颗粒材料，并通过“颗粒”重新构建为紧凑的能量公式。微观力学。”在颗粒力学均质化范式下，粘弹性粘塑性的势和赝势通过在代表性颗粒组合上平均离散颗粒接触相互作用来进行尺度桥接。作为所提出的多尺度方法的一个关键特征，通过采用微观结构长度尺度与泰勒级数展开相结合，高阶运动学得到了显着简化。与之前的微形态微力学不同，我们的离散到连续尺度桥接嵌入了体积约束，通过拉格朗日乘子的方法在代表性组合中弱化平均场定义：类似于混合插值的经典三场重构非线性有限元选择性积分空间。正如随后所证明的，体积约束的重新配制使得微形态建模本质上适合粘弹性粘塑性颗粒材料。因此，在边界约束优化中利用数值方法，耦合压力和速率敏感的耗散现象（即粘弹性和德鲁克-普拉格粘塑性的组合）变得具有微观结构敏感性和算法优势。