Thermo-mechanical formulation of strain gradient plasticity for geomaterials

Constitutive formulation of strain gradient plasticity for geomaterials via a thermomechanical approach is investigated in this paper. It is demonstrated that, by defining two thermodynamical potentials (a free-energy function and a rate of dissipation function), the entire constitutive behavior of a decoupled strain-gradient-dependent material may be determined. The elastic relations are dependent on the free-energy function, while the plastic yielding and flow rule are determined by the dissipation function in conjunction with the free-energy function. Yield surfaces in both dissipative stress and true stress spaces may be derived without difficulty. Nonassociative flow rules and possible micromechanical mechanisms for the difference between plastic work and rate of plastic dissipation are interpreted for gradient-dependent materials. Using the obtained formulations and choosing appropriate thermodynamical functions, a wide variety of strain gradient plasticity models in the literature are recovered. Typical features associated with geomaterials, such as pressure and Lode-angle dependency, are addressed in detail. This paper provides a general thermodynamically-consistent framework of developing strain gradient plasticity models for geomaterials