Multifield variational principles and computational aspects in rate-plasticity

In the present paper multifield variational formulations and extremum principles in rate plasticity are investigated. A suitable strategy is presented for the formulation of variational principles by casting the non-linear field equations and the constitutive multivalued equations into a structural operator governing the rate plasticity model problem. By following a consistent procedure a multifield potential is derived and the relevant multifield variational principle is presented in all the unknown variables of the problem. In addition, it is shown that the present procedure allows the consistent derivation of other variational principles in rate plasticity. In order to illustrate such capability of the procedure two variational principles are derived which represent the extensions to rate plasticity of the Greenberg and the Prager Hodge principles holding in rate-independent plasticity. The presented extremum formulations are able to providing the support for variationally consistent developments of numerical algorithms in computational applications. Accordingly, a computational procedure for rate plasticity is illustrated and an integration algorithm is described for an efficient numerical solution of structural problems in rate plasticity. The considered algorithmic procedure is suitable for different rate plasticity constitutive models by properly specializing the flow function of the adopted constitutive model and it is useful with respect to other procedures which are specifically related to a given constitutive model. Numerical results are finally reported in order to illustrate the effects of different constitutive models and the influence of different prescribed loading rates on the non-linear behavior of rate plastic materials.