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

Lurie, S. A.; Volkov-Bogorodsky, Dmitriy B.; Belov, P. A.; Lykosova, Elena D.

doi:10.1615/nanomechanicsscitechnolintj.v7.i4.10

Cited by 4 publications

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“…Тем более неожиданной является возможность уточнения классических решений вследствие учёта градиентных эффектов, которым в данных задачах удаётся дать чёткую физическую трактовку. Приведённые в сообщении результаты получены на основе корректных градиентных моделей стержней, широко обсуждаемых в последнее время [8][9][10].…”

Section: Introductionunclassified

On the refined stress analysis in the applied elasticity problems accounting of gradient effects

Ломакин

Lurie

Lur'e³

et al. 2019

Доклады Академии наук

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The paper proposes an extension of the approaches of gradient elasticity of deformable media, which consists in using the fundamental property of solutions of the gradient theory - the smoothing of singular solutions of the classical theory of elasticity, converting them into a regular class not only for the problems of micromechanics, where the length scale parameter is of the order of the materials characteristic size, but for macromechanical problems. In these problems, the length scale parameter, as a rule, can be found from the macro-experiments or numerical experiments and does note have an extremely small values. It is shown, by attracting numerical three-dimensional modeling, that even one-dimensional gradient solutions make it possible to clarify the stress distribution in the constrained zones of the body and in the area of the loads application. It is shown that additional length scale parameters of the gradient theory are related with specific boundary effects and can be associated with structural geometric parameters and loading conditions that determine the features of the classical three-dimensional solution.

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Section: Introductionunclassified