An internal variable variational formulation of viscoplasticity Original Research Article

In the paper evolutive processes and variational principles in viscoplasticity are examined in detail. The treatment is faced by the recourse to an internal variable formulation and by taking advantage of the appropriate tools in order to deal with multivalued operators. This general framework enables the development of a consistent variational formulation for viscoplastic models. For this purpose the problem at hand is set in operational form by encompassing into a unique expression the field equations and the constitutive equations. The viscoplastic structural operator in all variables is accordingly integrated, a family of viscoplastic potentials is deduced and the relevant sequence of extremum properties in one or more unknown variables is derived.