A multiscale constitutive model for the elasticity of clay nanoparticle assemblies

Abstract

Due to its particulate nature, the mechanical properties of bulk clay are determined by interparticle forces and fabrics of particle assemblies. A thorough study of the connection between properties across length scales is crucial to a fundamental understanding of the mechanisms behind the complex mechanical behavior of clays and clayey soils. This paper demonstrates the development of a multiscale constitutive model for describing the small-strain elastic properties of illite, based on the results of coarse-grained mesoscale molecular dynamic simulations for monodisperse assemblies of illite primary particles. The formulation consists of a homogenization scheme linking the potential energy of the system with an optimal parameter set describing the mesoscale fabric of the particles, and a perturbation scheme describing the change of the parameters in response to infinitesimal strains applied to the systems. The small strain elastic stiffness tensors are calculated as the second-order derivative of the potential energy with respect to the infinitesimal strain. The results from model prediction are validated against the stiffness properties interpreted from numerical simulations as well as experimental findings from prior research studies. The multiscale constitutive model is able to effectively capture the elastic properties of illite in terms of magnitude and material symmetry purely based on the information of interparticle forces and fabrics.