Materials with elastic range and plastic change of volume

Following the lines of previous papers of Lucchesi and Podio-Guidugli and Lucchesi and Silhavý, we sketch a theory of materials with elastic range that, unlike the treatment in those papers, places no restrictions on plastic changes of volume or on related quantities. We then describe with some detail the constitutive behavior of two important classes of materials with elastic range that, by analogy with the terminology used in classical plasticity, we call v. Mises materials and ideally plastic materials. Finally, for a specific ideally plastic v. Mises material, we present a numerical computation that shows how, when plastic change of volume is allowed, the shear stress maintaining a simple shear flow need not have constant value.