A Concise Review of Gradient Models in Mechanics and Physics
Elias C. Aifantis
Abstract
The various mathematical models developed over the years to interpret the behavior\nof materials and corresponding processes they undergo were based on observations\nand experiments made at that time. Classical laws for solids (Hooke) and fluids\n(Navier–Stokes) form the basis of current technology. The discovery of new phenomena\nwith the aid of newly developed experimental probes have led to various modifications\nof these laws, especially at small scales. The emergence of nanotechnology is ultimately\nconnected with the design of novel tools for observation and measurements, as well\nas with the development of new methods and approaches for quantification and\nunderstanding. This paper first reviews the author’s previously developed weakly nonlocal\nor gradient models for elasticity, diffusion, and plasticity. It then proposes a similar\nextension for fluids and electrodynamics. Finally, it suggests a gradient modification of\nNewton’s law of gravity, with a possible connection to the strong force of elementary\nparticle physics.