NUMERICAL VALIDATION OF A CONSTITUTIVE THEORY FOR AN ARBITRARILY FRACTURED SOLID

We have developed a general constitutive theory that estimates the eff ective elastic moduli of a cemented granular material by applying stat istical mechanical averaging to a purely micromechanical model. We hav e also constructed a distinct element model of a cemented granular mat erial, based on the same micromechanical model, which accounts for the elastic forces due to bonding between pairs of spherical particles, a nd 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 patter ns of damage on the bonds of a randomly generated assembly of particle s. We then undertake numerical experiments, sending both p-waves and s -waves through the samples and measuring the wave velocities. The pred ictions of the theory for these velocities agree well with the results of the numerical model for a variety of damage patterns. We discuss t he implications of our theory, as well as potential applications.