A Stabilized Bipenalty Formulation Using a Predictor-Corrector Scheme for Explicit Contact-Impact Analysis

Abstract

This work presents a novel stabilized bipenalty formulation for explicit contact-impact analysis, aiming to enhance traditional bipenalty methods and resolve issues associated with a large mass penalty parameter. To address this challenge, two key contributions are introduced. First, a new formulation integrates the bipenalty method with a predictor-corrector scheme, enabling a more accurate penetration estimation by dividing the computational process into prediction and correction phases. This separation ensures that the mass penalty affects only the contact forces, thereby eliminating undesirable mass effects on internal forces when a large mass penalty parameter is used. Second, new criteria tailored to the predictor-corrector scheme are proposed for two types of contact problems: the flexible-rigid case and the flexible-flexible case. Unlike traditional bipenalty methods, which rely on stability conditions for explicit time integrators, the proposed criteria focus on enforcing the kinematic constraints. As a result, any predicted penetration is eliminated during the correction phase, leading to zero penalty energy. Stability analysis confirms that the computation of the gap within the correction phase maintains stability. Contact impact examples are performed in 1D, 2D, and 3D and demonstrate that the proposed method provides improved stability and superior performance compared to the penalty and traditional bipenalty methods for various contact scenarios, including extremely large penalty parameter cases.