Corotational rates in constitutive modeling of elastic-plastic deformation

The principal axes technique is used to develop a new hypoelastic constitutive model for an isotropic elastic solid in finite deformation. The new model is shown to produce solutions that are independent of the choice of objective stress rate. In addition, the new model is found to be equivalent to the isotropic finite elastic model; this is essential if both models describe the same material.

The new hypoelastic model is combined with an isotropic flow rule to form an elastic-plastic rate constitutive equation. Use of the principal axes technique ensures that the stress tensor is coaxial with the elastic stretch tensor and that solutions do not depend on the choice of objective stress rate. The flow rule of von Mises and a parabolic hardening law are used to provide an example of application of the new theory. A solution is obtained for the prescribed deformation of simple rectilinear shear of an isotropic elastic and isotropic elastic-plastic material.