Description of plastic anisotropy effects at large deformations—part I: restrictions imposed by the second law and the postulate of Ilʹiushin

Phenomenologically, plastic anisotropy effects may be described by employing in the constitutive theory a set of internal variables suitable defined. These variables have to model the hardening response of the material under consideration as e.g. to describe the rotation of some symmetry axes. Such axes are imagined to be related with the development of the material substructure assumed, or, correspondingly, with the state variables characterizing this development. The objective of this paper is to present a thermodynamically consistent theory for plasticity (and viscoplasticity) which accounts for anisotropy effects. Important features of the theory are the use of the multiplicative decomposition of the deformation gradient tensor as well as the assumption of the validity of Ilʹiushinʹs postulate in the case of plasticity. For simplicity, apart from kinematic hardening effects, only orientational evolution of the underlying substructure is regarded. Care is taken that the theory is invariant with respect to rigid body rotations superposed to both, the current and the so-called plastic intermediate configuration.