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Simulating multi-body dynamics with both rigid and flexible parts and with frictional contacts is a hard problem. We solve this by expressing the couplings between the bodies as position level constraints. The implicit treatment of the constraint directions gives us improved stability over velocity based methods. Then by employing regularization of nonlinear constraints and a convex minimization formulation, we bridge constraint-based methods to traditional force-based methods. In fact, the former are just a dual variables formulation of the latter. We solve this dual problem using position based dynamics (PBD). We show how PBD is a completely valid modeling technique and we extend it with an accurate contact and Coulomb friction model. We further show for the first time how the same solver can be used to simulate both rigid and deformable solids with two way coupling. For the soft bodies we introduce a novel form of linear finite elements expressed as constraints, that is more accurate than PBD mass-spring systems. More of our results include the energy conserving Newmark integrator and the accelerated Jacobi solver suitable for parallel architectures. Note that this paper is an extended and revised version of the conference paper published in [1]. [ABSTRACT FROM AUTHOR]

This paper deals with the computational modeling and numerical simulation of contact problems at finite deformations using the finite element method. Quasi-static and dynamic problems are considered and two particular frictional conditions, full stick friction and frictionless cases, are addressed. Lagrange multipliers and regularized formulations of the contact problem, such as penalty or augmented Lagrangian methods, are avoided and a new direct elimination method is proposed. Conserving algorithms are also introduced for the proposed formulation for dynamic contact problems. An assessment of the performance of the resulting formulation is shown in a number of selected benchmark tests and numerical examples, including both quasi-static and dynamic contact problems under full stick friction and frictionless contact conditions. Conservation of key discrete properties exhibited by the time stepping algorithm used for dynamic contact problems is also shown in an example. [ABSTRACT FROM AUTHOR]