VARIATIONAL-PRINCIPLES, FE AND MPT FOR ANALYSIS OF NONLINEAR IMPACT CONTACT PROBLEMS

This paper presents an analysis of the impact-contact problems between elasto-plastic bodies without friction. Three pairs of extended varia tional complementary functionals for the impact-contact problems are p resented and constitute the theoretical foundations of the ensuing num erical analysis. A general condition of non-interpenetration is sugges ted 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 techniqu es (MPT). The present analysis is limited to a two-dimensional time de pendent case where both geometrical and material non-linearities are c onsidered. With the incremental form of the functional II2, an eight n ode plane element is used to derive the finite element (FE) formulatio n in the problem. The resulting equations are solved by an extended Wi lson-theta 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 demo nstrates that the present model is capable of modelling the non-linear impact-contact problems.