Plastic microstress for a defect energy dependent on Burgers tensor

This work presents an extended form of the Aifantis' strain-gradient plasticity theory through dependence of the plastic free energy on Burgers tensor. The constraints of codirectionality for the deviatoric stress and irrotationality of the plastic distortion are assumed. These provide the basis for expressing the workdone by the microstress conjugate to the Burgers tensor as, sum of the workdone by the microscopic hyperstress vector and scalar. The principle of virtual power is used to establish the microforce balance, which provides the relationship between the resolved shears, plastic microstress and the microscopic hyperstresses. The microforce balance, when augmented with relevant constitutive relations that are consistent with the free-energy imbalance, results in a non-local flow rule depicted as nonlinear second order partial differential equation in terms of the accumulated plastic strain with concomitant boundary conditions. It is shown in this work that, the plastic microstress is purely dissipative and cannot account for backstress whenever the defect energy is dependent on the Burgers tensor.