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Contact phenomena are essential in understanding the behavior of mechanicalsystems. Existing computational approaches for simulating mechanical contactoften encounter numerical issues, such as inaccurate physical predictions,energy conservation errors, and unwanted oscillations. We introduce analternative technique, rooted in the non-overlapping Schwarz alternatingmethod, originally developed for domain decomposition. In multi-body contactscenarios, this method treats each body as a separate, non-overlapping domainand prevents interpenetration using an alternating Dirichlet-Neumann iterativeprocess. This approach has a strong theoretical foundation, eliminates the needfor contact constraints, and offers flexibility, making it well-suited formultiscale and multi-physics applications.  We conducted a numerical comparison between the Schwarz method andtraditional methods like Lagrange multiplier and penalty methods, focusing on abenchmark impact problem. Our results indicate that the Schwarz alternatingmethod surpasses traditional methods in several key areas: it provides moreaccurate predictions for various measurable quantities and demonstratesexceptional energy conservation capabilities. To address the issue of unwantedoscillations in contact velocities and forces, we explored various algorithmsand stabilization techniques, ultimately opting for the naive-stabilizedNewmark scheme for its simplicity and effectiveness. Furthermore, we validatedthe efficiency of the Schwarz method in a three-dimensional impact problem,highlighting its innate capacity to accommodate different mesh topologies, timeintegration schemes, and time steps for each interacting body.

Fundamentally New Coupled Approach to Contact Mechanics via the Dirichlet-Neumann Schwarz Alternating Method