  Contact phenomena are essential in understanding the behavior of mechanical
systems. Existing computational approaches for simulating mechanical contact
often encounter numerical issues, such as inaccurate physical predictions,
energy conservation errors, and unwanted oscillations. We introduce an
alternative technique, rooted in the non-overlapping Schwarz alternating
method, originally developed for domain decomposition. In multi-body contact
scenarios, this method treats each body as a separate, non-overlapping domain
and prevents interpenetration using an alternating Dirichlet-Neumann iterative
process. This approach has a strong theoretical foundation, eliminates the need
for contact constraints, and offers flexibility, making it well-suited for
multiscale and multi-physics applications.
  We conducted a numerical comparison between the Schwarz method and
traditional methods like Lagrange multiplier and penalty methods, focusing on a
benchmark impact problem. Our results indicate that the Schwarz alternating
method surpasses traditional methods in several key areas: it provides more
accurate predictions for various measurable quantities and demonstrates
exceptional energy conservation capabilities. To address the issue of unwanted
oscillations in contact velocities and forces, we explored various algorithms
and stabilization techniques, ultimately opting for the naive-stabilized
Newmark scheme for its simplicity and effectiveness. Furthermore, we validated
the efficiency of the Schwarz method in a three-dimensional impact problem,
highlighting its innate capacity to accommodate different mesh topologies, time
integration schemes, and time steps for each interacting body.
