Data-driven modeling of granular matter’s elastic nonlinearity by volume constraint

Abstract

Traditional analytic homogenization methods of granular micromechanics limit the maximum predicted effective Poisson’s ratio to at most 1/4 for strain-driven constitutive models. However, this prediction disagrees with both the experimental evidence and discrete element method (DEM) simulations of many granular materials. To resolve this problem, a novel data-driven and volume-constrained homogenization of nonlinear granular elasticity is proposed with only the incompressible-limit upper bound on Poisson’s ratio of 1/2. Due to the volume constraint, the proposed formulation bears similarity to techniques in state-based peridynamics and, likewise, classical mixed finite elements. The new multiscale model is designed to be particularly advantageous for machine learning of effective moduli from DEM simulations (and other data sources) informed by the packings’ topology, specifically the average number of intergranular contacts per grain (the coordination number). Self-consistent elastic solutions for structured granular packings supplement DEM data in model training in order to cover a larger parameter space, demonstrating the flexibility of the method. The homogenization approach is further developed to capture glass bead packs’ semi-Hertzian nonlinearity. The designed utility for data-driven modeling is exemplified in the training of a micromechanically-sensitive input-convex neural network (ICNN) constitutive model applied in finite element analysis of an illustrative boundary value problem.