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Time-Integration Schemes for the Finite Element Dynamic Signorini Problem

A large variety of discretizations have been proposed in the literature for the numerical solution of the dynamic Signorini problem. We classify the different discretizations into four groups. The first three groups correspond to different ways of enforcing the contact condition: exact enforcement, enforcement with penalty, and enforcement with contact condition in velocity. The fourth approach is based on a modification of the mass matrix. Numerical simulations on two one-dimensional benchmark problems with analytical solutions illustrate the properties of representative methods within each class, focusing first on spurious oscillations triggered by contact and then on energy behavior after multiple impacts. Selected schemes are also tested on a two-dimensional benchmark.