Incorporation of internal state variables and plastically-induced anisotropy into a constitutive model involving scalar, conjugate, stress/strain base pairs

In a previous study from the author and his co-worker, a constitutive model for isotropic, elastic perfectly-plastic materials was developed using scalar, conjugate, stress/strain base pairs. These stress/strain base pairs result from a Gram–Schmidt decomposition of the deformation gradient. A limitation of this prior work is that we assumed the microscopic structures of such elastic–plastic materials would remain constant throughout a deformation process, i.e., there would be no change in the resulting microstructural properties. Typically, internal state variables are used to represent macroscopic manifestations of these microstructural properties. In this paper, we incorporate internal state variables into our previously developed constitutive model, and as a consequence, plastically-induced anisotropy shows up naturally in the developed model. These are, however, different from the typically used internal state variables and are introduced only for this purpose.