Towards a constitutive model for cemented granular materials

For several years we have been embarked on a program to understand the response of cemented granular materials to large deformations at high strain rates. A typical problem of interest is the formation of a crater in alluvium by a nuclear explosion (Margolin, et al., 1988). Our goal is to construct a constitutive model that represents the complex behavior of such materials and yet is simple enough to use in large scale calculations based on computer programs that model solid continuum dynamics. The purpose of this paper is to describe the process of creating the analytic model. We will derive an expression for the effective elastic moduli expressed as integrals over the configurations of the average grain. These integrals depend on probability distributions for the number of bonds, their lengths, and their relative orientations. The form of these probability distributions will vary for different materials and depends on the process by which the material was formed. We do not discuss this point in this paper. Instead, we will make some reasonable assumptions for the probability distributions and go on to evaluate the qualitative dependencies of the effective moduli. Our final results show that the Youngs' modulus of the granular assemblymore » should vary linearly with the area of the bond, the number of bonds per grain (i.e., the coordination number), the expected length of the bond, and the Youngs' modulus of the bonding material. Also, Poisson's ratio should be 0.25. We verify these dependencies numerically with calculations in our modified TRUBAL code. 5 refs., 4 figs., 1 tab.« less