The widely used method for solution of impacts of bodies, called the penalty method, is based on the contact force proportional to the length of the interpenetration of bodies. This method is regarded as unsatisfactory by the authors of this contribution, because of an inaccurate fulfillment of the energy conservation law and violation of the natural demand of impenetrability of bodies. Two non-traditional methods for the solution of impacts of bodies satisfy these demands exactly, or approximately,...
A summary of recent results concerning the modelling as well as the variational and numerical analysis of frictionless contact problems for viscoplastic materials are presented. The contact is modelled with the Signorini or normal compliance conditions. Error estimates for the fully discrete numerical scheme are described, and numerical simulations based on these schemes are reported.
In this work, we consider the quasistatic frictionless contact problem between a
viscoelastic piezoelectric body and a deformable obstacle. The linear electro-viscoelastic
constitutive law is employed to model the piezoelectric material and the normal compliance
condition is used to model the contact. The variational formulation is derived in a form
of a coupled system for the displacement and electric potential fields. An existence and
uniqueness result is recalled. Then, a fully discrete scheme...
Wilkins' method has been successfully used since early 60s for numerical
simulation of high velocity contact elastic-plastic flows. The present work
proposes some effective modifications of this method including more
sophisticated material model including the Baushinger effect; modification of
the algorithm based on correction of the initial configuration of a solid; a
contact algorithm based on the idea of a mild contact.