On the gradient approach – Relation to Eringen’s nonlocal theory

A.C. Eringen has been a most active advocate of the nonlocal theory of continua finding many applications for it in solid, fluid, and electromagnetic media. His work is also used extensively for interpreting deformation and fracture phenomena at the micron and nano scales for which the gradient approach is also being used. The present paper is dedicated to Cemal’s memory. It provides an account of the author’s gradient approach as applied to elastic and plastic deformations with emphasis on ultrafine grain (ufg) and nanocrystalline (nc) polycrystals, also in comparison with the nonlocal theory. The results reported herein have been strongly motivated by Eringen’s works and vision, as well as by his example of endurance and kindness.