2009 SCAIM Seminar - 03

Numerical methods for the solution of multibody, frictional contact problems are in demand in a wide variety of application areas that include structural engineering, robotics, computer animation, interactive medical simulation, biomechanics, and granular flow. While pioneering research in applied mathematics, mechanics, and graphics have helped us to understand many of the unique challenges imposed by contacting systems, robust, accurate and efficient methods for solving frictional contact problems have remained elusive. In particular, classical complementarity formulations of frictional contact, when discretized for numerical integration, generally lead to challenging optimization problems. We've found that, in practice, standard optimization methods such as Lemke's algorithm, Projected Gauss-Seidel, and interior point methods, that have generally been presumed suitable for solving these contact-related optimization problems, fail entirely for many important examples of frictional contact. To address and understand these difficulties we present a generalized approach for formulating numerical methods to solve frictionally contacting systems. This leads us to an investigation of the properties of both rigid and elastic contacting systems which cause difficulties and to propose principled methods for obtaining and approximating their solutions in practical settings. Finally, we validate the proposed methods by obtaining accurate solutions to a wide range of frictionally contacting systems that were previously impractical to solve, as well as robust and stable simulations of elastic-frictional composites, friction-dependent masonry, stick-slip oscillation, and other complex frictional contact behaviors.