Impact Simulations with Fracture. I. Method and Tests

We describe a new numerical tool based on the smooth particle hydrodynamics (SPH) method which is aimed at modeling impacts and collisions involving small solid objects. Our goal is to develop a suitable tool for the study of strength-dominated interactions between solid bodies. Although giant impacts have recently received most of the attention, collisions and/or impacts involving small (≤50 km) objects are (and have been) the most frequent ones. We intend to apply this model to such studies as the formation of asteroid families, the disruption of ringmoons, the accretion of planetesimals, and spallation from large cratering events. In this first paper in a series, we present all physical and numerical aspects of our model as well as a number of tests performed in order to validate our method. We adopt a strength model and implement a yon Mises yielding relation for stresses beyond the Hugoniot elastic limit. At the lower stresses associated with brittle failure, we use a rate-dependent strength based on the nucleation of Weibull flaws. Our model propagates statistical cracks at the subparticle scale based on the model of Grady and Kipp (1980) and resolves real cracks in a resolution-independent manner. Our method ensures that increases in resolution do not alter the fracture physics, only the accuracy. The resulting system predicts the shapes, locations, and velocities of the largest fragments in simulated laboratory impact events with unprecedented accuracy.