Energy-Momentum Approaches to Impact Mechanics

Abstract

This chapter deals specifically with dynamic impact problems, exploring in particular the interaction of contact constraint enforcement schemes with the globally observed behavior of temporal integration schemes such as those introduced in Section 2.4.2. Specifically, we focus our interest now on the sort of numerical issues that arise when one simulates potentially inelastic impact events in large deformations, as might be typified by the Taylor impact results obtained using classical Newmark methods in Section 5.5.1.3. In particular, the “bouncing” phenomenon depicted for the Taylor problem in Figure 5.19 provides good motivation for the issues considered in this chapter. As can be seen in that figure, use of the trapezoidal rule from the Newmark family, in conjunction with the contact constraints considered to this point in the monograph, gives rise to alternating states of contact/no contact for nodes on the interface, representing obviously spurious behavior. The bouncing can be eliminated through introduction of numerical damping, but at the cost of a loss of numerical accuracy. Furthermore, in the most general case, the introduction of numerical damping may stabilize a solution (or eliminate oscillations as in the bar impact problem), but often leaves the analyst wondering whether some physically meaningful behavior may also be erroneously affected by this remedy.