Variational principles, FE and MPT for analysis of nonlinear impact-contact problems (Q1913272)

We present 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 which constitute the theoretical foundations of the ensuing numerical analysis. A general condition of non-interpenetration is suggested for general cases of two elasto-plastic 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 nonlinearities are considered; an eight node plane element is used to derive the finite element (FE) formulation in the problem.