Numerical validation of a constitutive theory for an arbitrarily fractured solid

Abstract

We have developed a general constitutive theory that estimates the effective elastic moduli of a cemented granular material by applying statistical mechanical averaging to a purely micromechanical model. We have also constructed a distinct element model of a cemented granular material, based on the same micromechanical model, which accounts for the elastic forces due to bonding between pairs of spherical particles, and which allows for the possibility of anisotropic damage to the bonds. In this paper, we use a model based on the distinct element method (DEM) to validate the predictions of the theory for various prescribed patterns of damage. In particular we impose several anisotropic patterns of damage on the bonds of a randomly generated assembly of particles. We then undertake numerical experiments, sending both p‐waves and s‐waves through the samples and measuring the wave velocities. The predictions of the theory for these velocities agree well with the results of the numerical model for a variety of damage patterns. We discuss the implications of our theory, as well as potential applications.