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Nanoscience and Technology: An International Journal

ISSN Print: 2572-4258
ISSN Online: 2572-4266

Nanoscience and Technology: An International Journal

Formerly Known as Nanomechanics Science and Technology: An International Journal

DOI: 10.1615/NanomechanicsSciTechnolIntJ.v7.i4.10
pages 261-295

DO NANOSIZED RODS HAVE ABNORMAL MECHANICAL PROPERTIES? ON SOME FALLACIOUS IDEAS AND DIRECT ERRORS RELATED TO THE USE OF THE GRADIENT THEORIES FOR SIMULATION OF SCALE-DEPENDENT RODS

Sergey A. Lurie
Dorodnicyn Computing Centre, Federal Research Center "Computer Science and Control", Institute of Applied Mechanics Russian Academy of Sciences, Moscow, Russian Federation; Tomsk Polytechnic University, 30 Lenin Ave., Tomsk, Russia
Dmitriy B. Volkov-Bogorodsky
Institute of Applied Mechanics of the Russian Academy of Sciences, Moscow, Russia
P. A. Belov
Scientific Innovative Center "Institute of Research, Development and Transfer of Technologies", Moscow, Russia; Institute of Applied Mechanics, Russian Academy of Sciences, Moscow, Russia
E. D. Lykosova
Institute of Applied Mechanics, Russian Academy of Sciences, Moscow, Russia

ABSTRACT

The problem of improved simulation of ultrathin rods, arising because of the need of explaining the known experimental data about a substantial dependence of the flexural rigidity of such ultrathin structures on their thickness when the thickness becomes commensurable with characteristic parameters of the material microstructure, is discussed. In order to simulate such effects in the theory of thin rods the gradient theories are used. The question of whether ultrathin structures really implement the scale effects that result in substantial modification of effective rigidity properties is considered. The analysis is made using correct applied versions of gradient theories as well as different approaches in formulating the applied theories of bending of rods, beginning with the variational and semi-inverse methods and ending with the asymptotic method. It is shown that the assertion on a hyperbolic dependence of effective rigidity of ultrathin rods on the thickness, actively discussed in the recent years, is fallacious.