With the emergence of nanoscience, nanotechnology, and nanoengineering, a need for mathematical modeling of various materials and processes that take place at the nanoscale has been advanced. One "top-down" approach was to extend classical continuum models at macro and micro scales down to nanoscales. Another "bottom-up" approach was to extend standard discrete models at the atomic and molecular scales up to nanoscales. A compromise between the two, the so-called Internal Length Gradient (ILG) approach, was proposed by the author to generate both classical elasticity and plasticity continuum models, as well as atomistic and molecular dynamics models for interpreting nanoscale materials and processes. Among these central results concern the elimination of singularities that do not exist at the nanoscale, as well as the description of size effects that abandon at the nanoscale.
Elias C. Aifantis is currently an Emeritus Professor of Mechanics at Aristotle University of Thessaloniki/Greece and Michigan Technological University/USA, as well as Mercator fellow at Friedrich-Alexander University/Germany and a Distinguished Professor at Beijing University of Civil Engineering and Architecture/China. Formerly, he has also been a Distinguished Faculty Advisor at King Abdulaziz University/Saudi Arabia, Distinguished Visiting Expert at ITMO University/Russia and Southwest Jiaotong University/China, as well as MegaGrant Director at Togliatti State University /Russia. He has promoted highly interdisciplinary work in mechanics of materials by bringing into the field of solid mechanics ideas from diffusion theory, chemical reactions, and nonlinear physics. He has coined the terms dislocation patterning, material instabilities, gradient plasticity/elasticity, chemo/nanomechanics, and pioneered internal length gradient (ILG) theories in these fields. Currently, he is extending the ILG framework to revisit electromagnetism and Maxwell’s equations, as well as gravitation and Newton’s Law. He has published over 640 articles and received about 14,360 citations with 58 h-index (Scopus); 13,280 citations with 57 h-index (Web of Science); 21,440 citations with 69 h-index (Google Scholar). He is included in the ISI Web of knowledge list of the world’s most highly cited authors in engineering