Bi-penalty stabilized technique with predictor–corrector time scheme for contact-impact problems of elastic bars

This paper presents a stabilization technique for the finite element modelling of contact-impact problems of elastic bars via a bi-penalty method for enforcing contact constraints while employing an explicit predictor–corrector time integration algorithms. The present proposed method combines three salient features in carrying out explicit transient analysis of contact-impact problems: the addition of a penalty term associated with a kinetic energy expression of gap constraints, in addition to the conventional internal energy penalty term of the gap constraints; an explicit integration method that alleviates spurious oscillations; and, a judicious selection of two penalty parameters such that the stable time steps of the resulting explicit method is least compromised. Numerical experiments have been carried out with three explicit methods: the standard central difference method, the stabilized predictor–corrector method (Wu, 2003 [50]) and a method for mitigating spurious oscillations (Park et al., 2012 [44]) as applied to simulate one-dimensional contact-impact problems of the Signorini problem and the impact of two elastic bars. Results indicate that the proposed method can maintain the contact-free stability limit of the central difference and yield improved accuracy compared with existing bi-penalty methods.