Variational principles, FE and MPT for analysis of non-linear impact-contact problems Original Research Article

This paper presents an analysis of the impact-contact problems between elasto-plastic bodies without friction. Three pairs of extended variational complementary functionals for the impact-contact problems are presented and constitute the theoretical foundations of the ensuing numerical analysis. A general condition of non-interpenetration is suggested for general cases of two elastoplastic solids in contact. In fact, the extended variational principles are equivalent to a stationarity of the potential energy with constraints on displacements which may be reduced to a particular case of the mathematical programming techniques (MPT). The present analysis is limited to a two-dimensional time dependent case where both geometrical and material non-linearities are considered. With the incremental form of the functional II2, an eight node plane element is used to derive to finite element (FE) formulation in the problem. The resulting equations are solved by an extended Wilson-θ scheme and the Lamker method. To verify the suitability of the method, two numerical examples are calculated and the results are compared with the corresponding experimental ones. The comparison demonstrates that the present model is capable of modelling the non-linear impact-contact problems.