Size effects associated with skew symmetric Burgers tensor

This paper investigates size effect phenomena associated with the divergence of the transpose of plastic distortion in plastically deformed isotropic materials. The principle of virtual power, balance of energy, second law of thermodynamics, and codirectionality hypothesis are used to formulate the governing microforce balance and thermodynamically consistent constitutive relations for dissipative microscopic stresses associated with the plastic distortion and skew part of the Burgers tensor. It is obtained that the defect energy through the strictly skew Burgers tensor is converted to the defect energy via the divergence of the plastic distortion. The presence of material length scales in the obtained flow rule indicates that it is possible to apprehend size effects associated with the skew part of the Burgers tensor during the inhomogeneous plastic flow of solid material. Finally and amongst other things, it is shown that the dependency of the microscopic stress vector on the divergence of plastic distortion rate leads to weakening and strengthening effects in the flow rule.