Conditions for embedding Casagrande's critical states into hypoplasticity

Conditions for a consistent description of stationary states within the framework of a certain class of hypoplastic constitutive models are presented. The constitutive equation is of the rate type and incrementally non-linear. Casagrande's critical state concept is embedded in the model, which is also apt to describe contractant and dilatant behaviour. The adaptation of various predefined limit conditions with smooth and conical critical stress surfaces is outlined in detail. For large deformations with rotations of the principal axes, the objective stress rate given by Green and Naghdi is proposed instead of the objective stress rate given by Zaremba and Jaumann. Finally, the response of the constitutive equation for large shearing is compared with experimental results.