A new strain-gradient theory for an isotropic plastically deformed polycrystalline solid body

This study considers strain-gradient plasticity theory in the context of small deformations for an isotropic solid body with a view to investigating the distortion effects associated with the divergence of plastic strain through the Burgers tensor. The principle of virtual power is employed and the constraint of irrotationality is imposed on the plastic component of the gradient of the displacement vector. It is obtained that the gradient, curl, and divergence of the plastic strain in the body are mutually related. This relation establishes the existence of work done through the divergence of plastic strain as distinct from the work done through the gradient of the plastic strain. Consequently, a polycrystalline solid body undergoing distortion associated with the divergence of plastic strain exhibits new internal microstresses; and the obtained model, consisting of the microforce balance, constitutive relations, and plastic flow rule, extends the known Gurtin–Anand model in a natural fashion. Furthermore, in the governing flow rule, it is revealed that the internal microstresses associated with the divergence of plastic strain act as opposing agents to the internal microstresses associated with the gradient of the plastic strain via the length scales Q, L, and the gradient of the divergence of the plastic strain. This work shows the distortion effects associated with the divergence of plastic strain which the Gurtin–Anand strain-gradient plasticity theory in literature does not apprehend.