Non-singular solutions of GradEla models for dislocations: An extension to fractional GradEla

Abstract

An account of non-singular solutions of gradient elasticity (GradEla) models for dislocations, along with clarifications of certain issues raised on previously published results, is given. Then, an extension to fractional GradEla solutions is pursued and certain preliminary results on this emerging topic are listed.

A Note on Gradient/Fractional One-Dimensional Elasticity and Viscoelasticity

“…Other definitions of a fractional Laplacian are possible, and a detailed discussion is provided in [10]. In any case, it is beneficial to express the fractional Laplacian operator as the convolution of the integer-order Laplacian with an appropriate power-law kernel [11] (see also [12]). In the one-dimensional case, the above process provides…”

Construction of Nonsingular Stress Fields for Non-Euclidean Model in Planar Deformations

“…The research cycle presented in [5][6][7][8][9][10] is devoted to the development of a nonsingular model for describing the field of elastic stresses and strains for dislocations and disclinations in the framework of a Mindlin's gradient theory. It should be noted that research groups motivated by Aifantis [11][12][13][14], also built nonsingular solutions of gradient elasticity for dislocations and cracks.…”