Circular disclination loops in nonlocal elasticity

Abstract

Solutions for problems of circular twist and wedge disclination loops in an infinitely extended linear isotropic nonlocal elastic medium are obtained assuming an appropriate nonlocal modulus. The equilibrium equation is satisfied by introducing the Kröner’s stress function tensor. The Laplace and Hankel transforms are used to obtain the stress fields and the stored elastic energies. The oscillatory integrals containing Bessel functions are transformed into integrands which decay exponentially, thus producing a solution more amenable to numerical quadrature. It is found that maximum stresses are reached at some distance from the defect line. The obtained solutions lead to finite values of stresses at this line and reduce to the classical ones in the long wave-length limit.