Simulating Heterogeneity within Elastic and Inelastic Discrete Mechanical Models

Two approaches to incorporate heterogeneity in discrete models are compared. In the first, standard approach, the heterogeneity is dictated by geometrical structure of the discrete system. In the second approach, the heterogeneity is imposed by randomizing material parameters of the contacts between the rigid bodies. A similar randomization strategy is often adopted in continuous homogeneous models. The study investigates both the elastic and fracture behaviors of these model types, and compares their local and macroscale responses. It is found that the stress oscillations present in the standard discrete models built on heterogeneous geometric structures cannot be replicated by randomization of the elastically homogeneous discrete system. The marginal distributions and dependencies between the stress tensor components cannot be adequately matched. Therefore, there is a fundamental difference between these two views on discrete models. The numerical experiments performed in the paper showed that an identical response can be achieved at the macroscale by tuning the material parameters. However, the local behavior, fracturing, and internal dependencies are quite different. These findings provide insight into the potential for controlled random assignment of heterogeneity in homogeneous models. They also demonstrate the need for experimental data capable of verifying the correctness of such an approach.