Nonlinear springs with dynamic frictionless contact
This paper focuses on mathematical and numerical approaches to dynamic frictionless contact of nonlinear viscoelastic springs. This contact model is formulated by a nonlinear ordinary differential equation system and a pair of complementarity conditions. We propose three different numerical schemes in which each of them consists of several numerical methods. As a result, three groups of time-discrete numerical formulations are established. We use the coefficient of restitution to prove convergence of numerical trajectories, passing to the limit in the time step size. The Banach-fixed point theorem is applied to show the existence of global solutions satisfying all conditions. A new form of energy balance is derived, which is verified theoretically and numerically. All of the three schemes are implemented and their numerical results are compared with each other.
Publisher URL: https://link.springer.com/article/10.1007/s00030-018-0544-4