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We propose a novel approach for dynamically simulating articulated rigid bodies undergoing frequent and unpredictable contact and collision. Many practitioners solve these types of problems using reduced coordinate (or generalized coordinate) formulations that parameterize the degrees of freedom in a manner consistent with the constraints of articulation, effectively reducing the overall degrees of freedom, eliminating those that could violate the constraints. However, consistency conditions are required to ensure that closed loops are actually closed adding a nonlocal constraint to the system. Moreover, unpredictable contact and collision can pose serious difficulties. We have found it easier to design algorithms that treat closed loops and frequent contact and collision in maximal coordinates, and propose a novel maximal coordinates approach that builds on the previous work of [Guendelman et al. 2003]. Our approach works with any black box method for specifying valid joint constraints, and no special considerations are required for arbitrary closed loops and/or branching. Moreover, our technique is linear both in the number of bodies and in the number of auxiliary contact and collision constraints, unlike many other methods that are linear in the number of bodies but not in the number of auxiliary constraints.

We present an algorithm for the finite element simulation of elastoplastic solids which is capable of robustly and efficiently handling arbitrarily large deformation. In fact, our model remains valid even when large parts of the mesh are inverted. The algorithm is straightforward to implement and can be used with any material constitutive model, and for both volumetric solids and thin shells such as cloth. We also provide a mechanism for controlling plastic deformation, which allows a deformable object to be guided towards a desired final shape without sacrificing realistic behavior. Finally, we present an improved method for rigid body collision handling in the context of mixed explicit/implicit time-stepping.