A wedge disclination in a nonlinear elastic cylinder

Abstract

The stress and displacement fields and the energy of a wedge disclination in a nonlinear elastic cylinder under finite deformation are derived. A second-order elastic theory, which is based on the solutions of the first-order theory, is used for this purpose. It is found that the second-order Cauchy stresses are ratios of quadratic polynomials of ln(R/ρ), where R is the referential radial coordinate and ρ is the cylinder radius. The numerical results for steel suggest that the first-order theory is insufficiently accurate for disclinations with strength greater than 1°. Parametric studies of the elastic constants show that the second-order circumferential stress on the cylinder boundary is sensitive to the Lamé constants and one of the third-order elastic constants.