MAE Seminar – E.C. Aifantis – Gradient Theory and Nanomechanics: A Journey from Mythology to the Present Era


4:00 pm-5:00 pm
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303 MAE-A
939 Sweetwater Drive
Gainesville, FL 32611-6250


Gradient Theory and Nanomechanics:
A Journey from Mythology to the Present Era

E.C. Aifantis
Aristotle University of Thessaloniki, Thessaloniki 54124, Greece,
Michigan Technological University, Houghton MI 49931, USA
Beijing Univ of Civil Engr and Architecture, Beijing 100044, China
ITMO University, St. Petersburg 197101, Russia
Togliatti State University, Togliatti 445020, Russia


Since its birth at MTU in mid-1980’s for plasticity and dislocation dynamics and in mid-1990’s for elasticity, gradient theory has grown to emerge as a primary tool for material instabilities and size effects in macro/meso and micro/nano mechanics. Applications range from shear bands and cracks in metals to disintegration of rocks and earthquakes; from nanotubes and nanotechnology to lithium batteries and nanoenergy; and from understanding pattern formation and morphogenesis in biology to modeling cancer growth in oncology and Alzheimer disease in neurology.

The talk will review the structure of gradient theory for various classes of behavior (diffusion, deformation, mechanochemistry) and show its ability to eliminate singularities from dislocations and cracks; predict size-dependent fracture and phase diagrams; interpret the inverse Hall-Petch relation in nanopolycrystals and intermittent plasticity in micro/nanopillars; and, finally, transfer these ideas on self-organization in “non-living” materials to model the proliferation/migration of “living” cells in the brain.

In addition to standard continuum mechanics techniques easy-to-use tools from stochastic processes, non-extensive thermodynamics and Tsallis q-statistics, as well as fractional calculus and fractals will be employed.


Elias Aifantis was born on October 10, 1950 in Greece. Graduated from National Technical Univ. of Athens in 1973 with a diploma in Mining and Metallurgy, awarded a PhD in 1975 from Chemical Engineering and Materials Science of the University of Minnesota (the fastest PhD without a Master’s ever in that Department). He became an Assistant Professor of Theoretical and Applied Mechanics at the University of Illinois at Urbana-Champaign in 1976, which was dissolved soon after his resignation in 1980, when he went back to University of Minnesota as a visiting Professor. He joint Michigan Tech in 1982 as a Full Professor with tenure (the youngest ever appointed as such in Michigan). In 1990 he accepted a special honorary invitation/metaklisi to join Aristotle University of Thessaloniki where he is at present. Since 2010 he is an Emeritus Professor of Michigan Tech. Currently he is also a Distinguished Visiting Professor at Beijing Univ. of Civil Engineering and Architecture (formerly also at Southwest Jiaotong University) and Togliatti State University (formerly also at ITMO).

He has advised a number of PhDs and postdocs of whom 7 and 9 hold academic positions, respectively, throughout the world.

He is included in the ISI Web of knowledge list of the world’s most highly cited authors in engineering. He has published >600 articles and received ~10370 citations and 50 h-factor (SCOPUS).

He has been supported with funds from NSF, ARMY/ARO/NATO, US Academy of Sciences, European Commission, Greece, Japan, China and Russia.

The terms “dislocation patterning”, “gradient plasticity, “gradient elasticity”, “material instabilities”, “chemomechanics” and “nanomechanics”, first appeared in the scientific literature through his articles with his students and collaborators.


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Katerina Aifantis