A General Bipenalty Formulation for Explicit Contact-Impact Analysis With a Parameter Selection Criterion

A general bipenalty formulation with a parameter selection criterion is proposed for explicit contact-impact finite element analysis. In order to model the contact phenomenon using penalties, it is necessary to introduce an artificial contact stiffness that can increase the maximum natural frequency of the system. When a large stiffness penalty parameter is used, the stability condition forces to reduce the time step size, increasing at the same time the computational demands. A solution to avoid the small time step size requirement and possible instabilities is to include a mass penalty in addition to the stiffness penalty term, using a technique known as the bipenalty method. However, this method presents some other challenges, mainly related to the parameter selection criterion and its final accuracy. In this work, two important improvements for the bipenalty method are presented. (i) An element-type and dimension-independent criterion for the selection of penalty mass and stiffness parameters. (ii) A modified predictor-corrector scheme, specifically designed for the bipenalty method, that improves the accuracy of contact-impact problems. Different 1D, 2D, and 3D contact-impact examples are used to illustrate the stability, applicability to general contact cases, and reduction of the zigzag effect and spurious oscillations exhibited by the proposed methods.