| Methods for simulating frictional contact response are in high demand in robotics, graphics, biomechanics, structural engineering, and many other fields where the accurate modeling of interactions between solids are required. While techniques for accurately simulating structures and continua have advanced rapidly, methods for simulating the contact between solids have lagged behind. This thesis addresses the difficulties encountered in designing robust, accurate, and efficient computational methods for simulating frictional contact dynamics. We focus on understanding the fundamental sources of difficulty in frictional contact modeling, elucidating existing structures that can be leveraged to minimize them, and designing robust, accurate and efficient algorithms to simulate challenging frictional contact problems.;In this thesis a Coupled Principles formulation of discrete, time-continuous frictional contact is developed in depth. This is then applied as the basis for deriving novel, time-discrete, variational integrators that pose the discrete frictional contact problem as a system of coupled minimizations. Solutions to these systems are given by points that are optimal for both of the minimizations and avoid known issues with existing variational integration approaches for friction and contact. We then consider a specific two-step variant of these variational schemes that generalizes the popular Stewart-Trinkle model for frictional contact simulation. This is taken as a starting point for investigating the sources of difficulties found in solving these types of methods. We show that existing solution algorithms that have generally been presumed suitable for solving the contact-related optimization problems posed by these methods, fail entirely for many important examples of frictional contact and then address these limitations with our Staggered Projections algorithm. Applying a fixed-point scheme, derived from the Coupled Principles Formulation, we show that Staggered Projections efficiently obtains accurate solutions to optimization problems for many frictional contact problems that were previously impractical to solve. Finally, we also offer a detailed convergence analysis of the Staggered Projections algorithm, as well as simulations and instrumented examples that capture convincing and accurate frictional contact behaviors for both rigid and large deformation models. |
