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SUMMARYA common approach for the numerical simulation of non-linear multi-body contact problems is the use of Lagrange multipliers to model the contact conditions. The stability of standard algorithms is improved by introducing a modified mass matrix which assigns no mass to the potential contact nodes. By this, the spurious algorithmic oscillations in the multiplier do not occur any more, which facilitates the application of the primal-dual active set strategy to dynamical contact problems. The new mass matrix is calculated via a modified quadrature formula that needs no extra computational cost. In addition the conservation properties of the underlying algorithm are transferred to the modified mass version. Different numerical examples for frictional two-body contact problems illustrate the improvement in the results for the contact stresses.

In this paper, a new space-time discretization is proposed which is based on a modified mass matrix. The mass associated with a surface layer of elements is redistributed such that the inertia at the boundary is removed. This approach is motivated by the observation that standard space-time discretization schemes applied to dynamic contact problems yield spurious oscillations. A widely used approach for the numerical simulation of these problems is based on Lagrange multipliers which represent the contact stresses. But the algebraic contact conditions in combination with the inertia volume terms often yield nonphysical results for the contact stresses, and the stability of the algorithm can be lost. Our modified matrix is calculated via nonstandard quadrature formulas that require no extra computational effort. In addition, the conservation properties of the underlying algorithm are carried over to the modified method, and the standard optimal a priori estimates are still satisfied. Numerical examples confirm the optimality of the approach and its stabilization effect applied to contact problems.

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