Normal elastic-plastic impact in plane strain

A quasi-static theory of local two-dimensional elastic-plastic indentation is used to calculate energy dissipation during transverse impact between hard cylindrical bodies with parallel axes. Finite-element calculations are used to verify compliance relations derived analytically for both loading and unloading; these in turn are used to evaluate the work done during the compression and restitution stages of impact. The final relative motion between the colliding bodies is dependent on transformation of energies in the impact system. For impact between bodies which differ significantly in size, there will be energy lost through elastic waves propagating through the colliding bodies and this must be accounted for when calculating the final kinetic energy of relative motion at separation. For higher speed impacts there is energy lost to plastic deformation also. The work done in plastically deforming the contact region depends on hysteresis of the compliance of the contact region during compression and restitution phases of the contact period.