A simple but rigorous versions of Mindlin’s first gradient elasticity, with one material length (gradient coefficient), was considered. By using the stress function method, modified stress functions were found for all 6 types of Volterra defect (dislocations and disclinations) situated in an isotropic and infinitely extended medium. By means of these stress functions, exact analytical solutions were obtained for the stress and strain fields of dislocations and disclinations. One advantage of these solutions for the elastic strain and stress was that they had no singularities at the defect line. They were finite and had maxima or minima in the defect core region. The stresses and strains were either zero, or had a finite maximum value at the defect line. The maximum value of the stresses could serve as a measure of the critical stress level at which fracture and failure might occur. Stress and elastic strain singularities were both removed in this simple gradient theory.

Non-Singular Stress and Strain Fields of Dislocations and Disclinations in First Strain Gradient Elasticity. M.Lazar, G.A.Maugin: International Journal of Engineering Science, 2005, 43[13-14], 1157-84