A variational principle for dynamic contact with large deformation

Dynamic contact between a deformable body with either large or small deformation and a rigid obstacle can be modeled with Signorini contact condition stated in terms of the normal component of the displacement – as long as the relative positions are clearly defined. The geometrical relation, however, is unpredictable when large motion or large deformation and complex surface geometry are involved. The use of normal velocity is more suitable. A variational inequality is proposed for the dynamic contact problem. The penalty method is introduced and implemented in explicit finite element software. Numerical examples are presented to demonstrate the robustness of the algorithm.