A new model to simulate impact breakup

We have developed a preliminary version of a new type of code to simulate the outcomes of impacts between solid bodies, which we plan to further refine for application to both asteroid science and space debris studies. In the current code, colliding objects are modeled as two-dimensional arrays of finite elements, which can interact with each other in both an elastic and a shock-wave regime. The finite elements are hard spheres with a given value for mass and radius. When two of them come into contact the laws of inelastic scattering are applied, thus giving rise to the propagation of shock waves. Moreover each spherical element interacts elastically with its nearest neighbours. The interaction force corresponds to that of a spring having an equilibrium length equal to the lattice spacing, and results into the propagation of elastic waves in the lattice. Dissipation effects are modeled by means of a dissipative force term proportional to the relative velocity, with a given characteristic time of decay. The possible occurrence of fractures in the material is modeled by assuming that when the distance of two neighbouring elements exceeds a threshold value, the binding force between them disappears for ever. This model requires finding a plausible correspondence between the input parameters appearing in the equations of motion, and the physical properties of real solid materials. Some of the required links are quite obvious (e.g., the relationship between mass of the elements and elastic constant on one side, and material density and sound velocity on the other side), some others a priori are unclear, and additional hypotheses on them must be made (e.g., on the restitution coefficient of inelastic scattering). Despite the preliminary character of the model, we have obtained some interesting results, which appear to mimic in a realistic way the outcomes of actual impacts. For instance, we have observed the formation of craters and fractures, and (for high impact energies) the occurrence of catastrophic breakup. The masses and velocities of the fragments resemble those found in laboratory impact experiments.