Gradients, Singularities and Interatomic Potentials

After a brief review on the ability of continuum gradient elasticity (GradEla) to eliminate singularities from dislocation lines and crack tips, we present an extension to its fractional counterpart by replacing the classical Laplacian in the gradient-enhanced Hooke's Law by a fractional one. Then, a discussion on implications of fractional gradient elasticity to eliminate stress/strain singularities from a screw dislocation is given, followed by the derivation of the fundamental solution of the governing fractional Helmholtz equation, for addressing more general problems. Finally, an elaboration is provided on using these ideas to revisit interatomic potentials used in materials science simulations.