Identification of higher-order elastic constants for grain assemblies based upon granular micromechanics

Abstract

Macroscale behavior of granular media is characterized by the significant effects of grain-pair interactions and the microstructure of each grain neighborhood. From a continuum viewpoint, granular materials may be modeled as micromorphic media to account for their complex grain-scale (microscale) kinematics. To this end we express the grain displacement in terms of the neighboring grain displacements utilizing the Taylor series expansion. The introduced gradients in the Taylor series are identified in terms of the macroscale deformation measures introduced in microstructural elasticity and micromorphic mechanics. As a result, a continuum model of the granular media is derived enriched by nonclassical terms, including terms that model grain displacement fluctuations and higher gradients of displacements. In the derived model, the continuum stiffness tensors are obtained in terms of grain-pair stiffness coefficients and fabric parameters defining the geometry of grains and their contacts. To identify the elastic constants of the enhanced continuum model, we perform numerical experiments on grain assemblies using discrete simulations subjected to relevant boundary conditions. The need for additional macroscale deformation measures for the continuum modeling of granular materials becomes evident in this identification process. The obtained elastic constants are then used to determine the microscale (or grain-pair) stiffness coefficients applicable to the continuum model. These grain-scale stiffness coefficients are found to be affected by the heterogeneity of microstructure.