It was noted that, in the presence of plastic slip gradients, compatibility required gradients in the elastic rotation and stretch tensors. In a crystal, the gradient in elastic rotation could be related to bond-angle changes at the cores of so-called geometrically necessary dislocations. The corresponding continuum strain energy density could be obtained from an interatomic potential that included 2- and 3-body terms. The 3-body terms induced restoring moments that led to a couple stress tensor in the continuum limit. The resultant stress and couple stress jointly satisfied a balance law. Boundary conditions were obtained for stress, couple stress, strain and strain-gradient tensors. This higher-order continuum theory had been formulated by Toupin. The latter’s theory was extended here so as to incorporate constitutive relations for the stress and couple stress under multiplicative elasto-plasticity. It was demonstrated that certain slip-dominated deformation mechanisms increased the compliance of nanostructures in bending-dominated situations.

Couple Stresses in Crystalline Solids - Origins from Plastic Slip Gradients, Dislocation Core Distortions and Three-Body Interatomic Potentials. K.Garikipati: Journal of the Mechanics and Physics of Solids, 2003, 51[7], 1189-214