On the effects of plastic rotation in the finite deformation of anisotropic elastoplastic materials

Using the notions of intermediate configuration firstly introduced by Eckart (1948) and of vector directors due to E. and F. Cosserat (1909), we obtain constitutive equations for an anisotropic solid subject to finite strains. This study closely follows Mandel's ideas (1971, 1982) although it differs in presentation and in the way of deriving the final equations. In a second part we establish the form of constitutive equations for some particular anisotropic materials by applying representation theorems. As an application, we show that the introduction of plastically induced rotations suppresses oscillations of Cauchy stress for a material with kinematic hardening submitted to simple shear test: in fact our method consists in defining a new stress rate which is physically motivated. It provides an alternative to the more phenomenological approach of Nagtegaal and de Jong (1980/1982). Furthermore, in contrast to other recent methods, it can be applied to a wide range of anisotropic materials.