December 7, 2025Open Access

Space‐Time FEM Solution of Dynamic Contact Problem With Discontinuous Velocity for Multiple Impact of Deformed Bar Using PDAS Method

Key Points

Energy conservation is maintained in the contact dynamics models, highlighting effective solution strategies.
The study leverages energy conservation to validate the dynamic models against existing methods like mass redistribution.
Iterative solution techniques involve a primal-dual active set algorithm, enhancing the numerical accuracy and performance in simulations.
The findings support the application of space-time FEM in capturing the dynamics of contact problems with non-smooth velocities.

Abstract

ABSTRACT A class of one‐dimensional impact and dynamic contact problems taking into account non‐smooth velocities is studied. The new space‐time finite element approximation of dynamic variational inequalities is suggested. The non‐smooth solution for the impact of an obstacle by an elastic bar and its energy conservation under persistency conditions is proved on partitions of the space‐time domain. The explicit solution of the double impact problem is taken as an analytical benchmark for numerical experiments. For an iterative solution, a primal‐dual active set (PDAS) algorithm stemming from semi‐smooth Newton methods is constructed. Numerical experiments compare the space‐time PDAS method with some other existing methods: a mass redistribution method, Paoli–Schatzman scheme, and a Nitsche‐based approximation, highlighting its advantages.

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