Modelling of frictionless contact/impact problems in explicit dynamics

M. LUEGE, D. R. J. OWEN, J. YU Y B. LUCCIONI

Parana, Santa Fe

Congreso; VII Congreso Argentino de Mecanica Computacional MECOM'02; 2002

Asociación Argentina de Mecánica Computacional (AMCA)

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.