Micromechanics-Based Continuum Constitutive Modeling of Isotropic Non-Cohesive Particulate Materials, Informed and Validated by the Discrete Element Method.

摘要

We apply homogenization methods from the field of micromechanics to obtain the macroscale effective elastic moduli and the macroscale effective material friction angle for a statistically isotropic non-cohesive particulate material, such as gravel, sand, or powder, in terms of the microscale properties of the particulate material, such as the inter-particle normal and tangential contact stiffnesses (which can be derived from the mechanical properties of the material constituting the individual particles in the particulate material), the inter-particle static friction coefficient, and the geometric properties of the local particle packing structure. In this way, we obtain macroscale information that can be used in elastoplastic continuum constitutive models for general statistically isotropic non-cohesive particulate materials, based on micromechanics. All of our theoretical results are informed and validated by numerical simulations of quasi-static true triaxial and simple shear tests on multiple randomly packed material specimens of roughly 3,000-30,000 spherical particles, performed using the discrete element method (DEM). Using the discrete element method, and performing simulations with particle rotation either allowed or prohibited, we are able to isolate the effect of particle rotation in a particulate material in both the elastic and plastic ranges. Our theoretical analyses improve previous theoretical analyses in the literature, which are typically based on the principle of minimum potential energy, and are thus unable to capture the effects of mechanisms or zero-energy strains due to particle rotation in a particulate material. In contrast, our direct micromechanics derivations are based on force and moment equilibrium for individual particles, and are thus able to capture the effects of mechanisms or zero-energy strains due to particle rotation in a particulate material. We prove, both analytically and by our discrete element simulations, that mechanisms due to particle rotation can and do exist in a particulate material on the microscale, and we demonstrate how these local mechanisms affect the overall behavior of a particulate material on the macroscale.