A direct elimination algorithm for quasi-static and dynamic contact problems

• A new direct elimination algorithm for full stick and frictionless quasi-static and dynamic contact problems has been developed and implemented.
• Conserving time stepping algorithms have been used within the framework of the new contact formulation.
• A selected number of quasi-static and dynamic numerical examples has been chosen to show the performance of the new contact formulation.
• The performance of the conserving time stepping algorithm has been shown for a frictionless case.

This paper deals with the computational modeling and numerical simulation of contact problems at finite deformations using the finite element method. Quasi-static and dynamic problems are considered and two particular frictional conditions, full stick friction and frictionless cases, are addressed. Lagrange multipliers and regularized formulations of the contact problem, such as penalty or augmented Lagrangian methods, are avoided and a new direct elimination method is proposed. Conserving algorithms are also introduced for the proposed formulation for dynamic contact problems. An assessment of the performance of the resulting formulation is shown in a number of selected benchmark tests and numerical examples, including both quasi-static and dynamic contact problems under full stick friction and frictionless contact conditions. Conservation of key discrete properties exhibited by the time stepping algorithm used for dynamic contact problems is also shown in an example.