Published 4 issues per year
ISSN Print: 2572-4258
ISSN Online: 2572-4266
Indexed in
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
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.
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Lomakin E. V., Lurie S. A., Rabinskiy L. N., Solyaev Y. O., Semi-Inverse Solution of a Pure Beam Bending Problem in Gradient Elasticity Theory: The Absence of Scale Effects, Doklady Physics, 63, 4, 2018. Crossref
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Lurie S., Solyaev Y., Revisiting bending theories of elastic gradient beams, International Journal of Engineering Science, 126, 2018. Crossref
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Charalambopoulos Antonios, Gortsas Theodore, Polyzos Demosthenes, On Representing Strain Gradient Elastic Solutions of Boundary Value Problems by Encompassing the Classical Elastic Solution, Mathematics, 10, 7, 2022. Crossref