Bi-Penalty Stabilized Explicit Finite Element Algorithm For One-Dimensional Contact-Impact Problems

In this contribution, a stabilization technique for finite element modelling of contact-impact problems based on the bipenalty method and the explicit predictor-corrector time integration is presented. The penalty method is a standard method for enforced contact constrains in dynamic problems. This method is easily implemented but the solution depends on numerical value of the stiffness penalty parameter and also the stability limit for explicit time integration is effected by a choice of this parameter. The bipenalty method is based on penalized not only stiffness term but also mass term concurrently. By this technique with a special ratio of mass and stiffness penalty parameters, the stability limit of contact-free problem is preserved. In this contribution, we also present a modification of the explicit time scheme based on predictor-corrector form. By meaning of this approach, spurious contact oscillations are eliminated and the results do not depend on numerical parameters.