Emerging Spatial and Temporal Discretization Methods in Contact and Impact Mechanics

The focus of this discussion will be the recent evolution of both spatial and temporal discretization techniques in contact and impact mechanics. With regard to spatial discretization, attention will be focused on the movement from traditional “node to surface” methodologies for description of contact interaction, to new “surface to surface” algorithms that in most cases have their motivation in the mortar method. While an anticipated result of this evolution was the increased numerical accuracy produced by integral forms of the contact constraints, it has also been seen that considerable robustness in large sliding applications results from the non-local character of the formulation. In this discussion both of these advantages of the surface to surface framework will be demonstrated, as will recent extensions that enable reliable simulation of self-contact phenomena.

When extending computational contact formulations to the transient regime, the consideration of reliable time integrators for impact phenomena is of interest. Accordingly, we examine some of the issues associated with time stepping in semidiscrete formulations of contact/impact, with particular emphasis on the energy-momentum paradigm as applied to impact mechanics. We consider a form of the energy-momentum approach which encompasses dissipative phenomena (such as inelasticity and friction), and focus on a numerical approach that allows for velocity discontinuities to be incorporated into the contact updating scheme.