Modelling Of Frictionless Contact/Impact Problems In Explicit Dynamics

Abstract

In this paper, a constitutive equation for frictionless contact to be used
in an explicit transient dynamic setting is derived. The use of standard penalty formulation
with high values of the penalty coefficients may lead to spurious oscillations in the
response of the system and consequent generation of fictitious energy within the system.
Thus, several issues related to the stability of the system, such as penalty selection, energy
conservation and contact force oscillation, among others, are addressed.
In the mathematical formulation of the problem, the momentum balance equations and
boundary conditions are imposed for each body separately, along with the constraints that
govern the interaction, i.e., the impenetrability and persistency condition. The constitutive
contact equation is derived from the first and the second laws of thermodynamics
which are carefully formulated with reference to the dynamic behaviour of the system. The
time integration of the constitutive contact equation is consistent with the global scheme.
Representative numerical simulations are finally given which illustrate the performance of
the proposed formulation.