The formulation of stable time-stepping algorithms for dynamic contact problems, both frictionless and frictional, is presented. Special attention is given to the properties of the underlying continuum problem to serve as guidelines for the development of the algorithms. The proposed method conserves linear and angular momenta, and, in the frictionless case, conserves the energy by means of a restoration potential. Coulomb's friction law is used to model the friction phenomenon; the scheme presented herein is unconditionally dissipative, just as the physical system is.; The scheme has been enhanced by the enforcement of a constraint on the velocities, in addition to the unilateral (impenetrability) constraint imposed on the displacements; this enhancement does not disturb the conservation/restoration properties. Numerical dissipation may also be added to stabilize the scheme for problems with high frequency energy modes.; A multibody implementation is presented to show the versatility of the algorithm. In this implementation, the contact detection scheme includes an efficient sorting procedure which makes large scale simulations possible.; Lastly, various numerical examples show the stability and robustness of the scheme.
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