Couple stresses in crystalline solids: origins from plastic slip gradients, dislocation core distortions, and three-body interatomic potentials

摘要: Abstract In the presence of plastic slip gradients, compatibility requires gradients in elastic rotation and stretch tensors. a crystal lattice gradient can be related to bond angle changes at cores so-called geometrically necessary dislocations. The corresponding continuum strain energy density obtained from an interatomic potential that includes two- three-body terms. terms induce restoring moments lead couple stress tensor limit. resulting jointly satisfy balance law. Boundary conditions are upon stress, This higher-order theory was formulated by Toupin (Arch. Ration. Mech. Anal. 11 (1962) 385). Toupin's has been extended this work incorporate constitutive relations for under multiplicative elastoplasticity. is exploited solve boundary value problem relevance single polycrystalline nano-devices. It demonstrated certain slip-dominated deformation mechanisms increase compliance nanostructures bending-dominated situations. significance these ideas context plasticity models also dwelt upon.