Rate-Dependent Hyperplasticity with Internal Functions

This paper extends previous work reported by Houlsby and Puzrin in 2001 in which a thermomechanical framework was set out for the derivation of rate-dependent plasticity theory with internal variables. A key feature of the earlier formalism is that the entire constitutive response is determined by the knowledge of two scalar potential functions. In this paper, we extend the concept of internal variables to that of internal functions, which represent infinite numbers of internal variables. In this case, the thermodynamic functions are replaced by functionals. This work also extends previous work on rate-independent materials reported by Puzrin and Houlsby in 2001a. The principal advantages of this development are that it can provide realistic modeling of kinematic hardening effects and smooth transitions between elastic and elastic-viscoplastic behavior. The ability of a model developed within this new framework to capture realistically various aspects of rate dependent undrained triaxial behavior of saturated clays has been verified against experimental data.