Nanomechanics of a screw dislocation in a functionally graded material using the theory of gradient elasticity

TL;DR

This paper extends the analysis of screw dislocations in functionally graded materials using second gradient elasticity, providing singularity-free analytical expressions for displacements, strains, and stresses.

Contribution

It introduces a displacement formulation and Fourier transform technique to derive new, explicit solutions within second gradient elasticity, expanding prior stress function method results.

Findings

Analytical expressions for displacements, strains, and stresses are obtained.

Results are free from singularities at the dislocation line.

Extends earlier work to second gradient elasticity.

Abstract

The modest aim of this short article is to provide some new results for a screw dislocation in a functionally graded material within the theory of gradient elasticity. These results, based on a displacement formulation and the Fourier transform technique, extends earlier findings (Lazar, M., 2007. On a screw dislocation in a functionally graded material, Mech. Res. Comm. 34, 305-311) obtained by the stress function method, to the case of the second gradient elasticity. Rigorous and easy-to-use analytical expressions for the displacements, the strains and the stresses are obtained which are free from singularities at the dislocation line.