AN IMPLICIT TIME-STEPPING METHOD FOR QUASI-RIGID MULTIBODY SYSTEMS WITH INTERMITTENT CONTACT

We recently developed a time-stepping method for simulating rigid multi-body systems with intermittent contact tha t is implicit in the geometric information [1]. In this paper, we ex tend this formulation to quasi-rigid or locally compliant objec ts, i.e., objects with a rigid core surrounded by a compliant layer, si milar to Song et al. [2]. The difference in our compliance mode l from existing quasi-rigid models is that, based on physicalmotivations, we assume the compliant layer has a maximum possibl e normal deflection beyond which it acts as a rigid body. Therefore, we use an extension of the Kelvin-Voigt (i.e. linear springdamper) model for obtaining the normal contact forces by incorporating the thickness of the compliant layer explicitl y in the contact model. We use the Kelvin-Voigt model for the tangent ial forces and assume that the contact forces and moment satisfy an ellipsoidal friction law. We model each object as an intersection of convex inequalities and write the contact constraint as a complementarityconstraint between the contact force and a distance function de pendent on the closest points and the local deformation of the bo dy. The closest points satisfy a system of nonlinear algebraic e quations and the resultant continuous model is a Differential C omplementarity Problem (DCP). This enables us to formulate a g eometrically implicit time-stepping scheme for solving theDCP which is more accurate than a geometrically explicit scheme . The discrete problem to be solved at each time-step is a mixed nonlinear complementarity problem.