The B-bar method and the limitation principles

The generalized elastic material provides a reference model to cast in a unitary framework many structural models which are based on nonlinear monotone multivalued relations such as viscoelasticity\ plasticity and unilateral models[ The modi_ed forms of the Hu Washizu and Hellinger Reissner principles and the displacement!based variational formulation are recovered for the generalized elastic material starting from a functional in the complete set of state variables[ The related limitation principles are derived and their specialization to elasticity and elastoplasticity with mixed hardening are provided[ It is shown that the interpolating _elds for the pressure and the volumetric strain usually adopted in the B!bar method lead to a limitation principle[ Accordingly the same elastic and elastoplastic solutions can be obtained by means of an approximate mixed displacement:pressure variational principle[ A second application is concerned with the conditions ensuring the coincidence of the solutions between an approximate two!_eld mixed formulation and the displacement!based method[ Numerical examples are provided to show the coincidence of the solutions obtained from di}erent mixed _nite element formulations\ in elasticity or elastoplasticity\ under the validity of the limitation principles