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Интеллектуальная Система Тематического Исследования НАукометрических данных |
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Two Applications of the Asymptotic Homogenization Methodтезисы доклада
- Авторы: Sheshenin S.V., Artamonova N.B., Klementyev P.D.
- Сборник: 91st Annual Meeting of the International Association of Applied Mathematics and Mechanics, March 16–20, 2020, Kassel, Germany, Book of Abstracts
- Тезисы
- Год издания: 2020
- Место издания: Universitat Kassel Kassel
- Первая страница: 331
- Последняя страница: 331
- Аннотация: Two applications of the asymptotic homogenization are considered. In the first part the paper presents an application of the asymptotic homogenization for determining the effective moduli and stress concentration in B4C/2024Al composite, using 2D and 3D internal structure images. A specific feature of the applied multi scale method was three scales used. The values of the Young's modulus calculated for plane-strain and plane-stress almost coincide with each other for the same volume rations of B4C. 3D structure was used to compare the effective moduli computed using 3D problem formulation with the moduli calculated in plane problems. Thus, the calculations confirm the possibility of using twodimensional images of the micro structure to calculate effective moduli of the macro level isotropic composite. Comparison of the effective moduli with experimental data shows an agreement. The second study concerns an application of asymptotic multi scale method to metamaterials. Such materials have several distinctive properties: negative Poisson's ratio, tension/bending coupling and tension/torsion coupling. There is a fundamental question regarding the number of cells. If some property remains to be true for infinite number of cells, then we treat such a metamaterial as real material. On contrary, the metamaterial must be treated just as a structural element, if the same property is valid only for finite number of cells and vanishes when the number of cells approaches infinity. A specific feature of such materials is the periodicity of the structure, i.e. entire material is composed of the same cells stacked to each other. Due to periodicity there exists asymptotic representation in terms of small parameter, which is inversely proportional to the number of cells along any coordinate axis. Averaging technique up to the second approximation order leads to constitutive relations of a nonclassical type similar to gradient elasticity theory. It is proved that the coupling moduli are proportional to the small parameter (coupling of the first order). This conclusion is true for tension/bending and tension/torsion couplings, if cells are stacked in Cartesian coordinate system manner. Numerical examples are given to support this theoretical conclusion. Finally, tension/torsion coupling is considered for cells stacked in the manner of the cylindrical coordinates. On contrary to Cartesian stacking style zero order coupling is achieved for cylindrical style stacking, i.e. coupling moduli do not depend on the number of cells. Supported by RFBR (projects 19-51-53006/08).
- Добавил в систему: Артамонова Нина Брониславовна