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International Journal for Multiscale Computational Engineering

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GRADIENTS AND INTERNAL LENGTHS IN SMALL SCALE PROBLEMS OF MECHANICS

Volume 20, Issue 6, 2022, pp. 89-110
DOI: 10.1615/IntJMultCompEng.2022043377
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Avraam A. Konstantinidis
Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
Elias C. Aifantis
Aristotle University of Thessaloniki, Thessaloniki 54124, Greece; Michigan Technological University, Houghton, MI 49931, USA; Mercator Fellow, Friedrich-Alexander University, Erlangen-Nuremberg, 90762 Fürth, Germany

ABSTRACT

Mechanics has been a fundamental tool and principal motivation for the development of basic sciences and engineering. Its use has recently been extended from macroscopic to microscopic and nanoscopic scales and phenomena. A particular methodology in this direction is the generalization of classical theories of elasticity, plasticity, and failure through the introduction of higher order gradients of the pertinent variables and corresponding internal lengths. This article, written in honor of a charismatic contributor in the field of generalized continuum mechanics, Professor Patrizia Trovalusci, begins with a simple paradigm of how to extend standard thermoelasticity theory to its gradient counterpart. It then provides a number of other examples ranging from strength of materials and stress concentrations to plastic flow and failure.

KEY WORDS: gradient thermomechanics, internal lengths, GradEla beams, GradEla dislocations and cracks, stress concentrations, size effects, gradient-stochastic models
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