A multifield variational formulation of viscoplasticity suitable to deal with singularities and non-smooth functions

In the present paper a multifield variational formulation of non-smooth viscoplasticity is illustrated which is well suited to deal with multivalued operators and non-smooth functions characterized by singularities. The adopted approach proves to be helpful in describing a geometrical framework of the non-smooth viscoplastic problem and in guiding to enhancements towards other kinds of plastic and viscoplastic material behavior. Alternative equivalent expressions of evolutive laws are discussed. The formulation shows to include Koiter’s theory as a special case. In addition, a multifield variational formulation of non-smooth viscoplasticity is illustrated. A procedure for deriving a parent potential in all the unknown variables is illustrated for non-smooth viscoplasticity problems. From the parent potential a set of associated multifield potentials is furtherly derived in one or more unknown fields and the relevant extremum properties are illustrated so that the non-smooth viscoplasticity structural problem is provided with a complete variational formulation suitable for developments in finite element applications.