|
ИСТИНА |
Войти в систему Регистрация |
ФНКЦ РР |
||
Applications of the Asymptotic Homogenization to Materials with Periodic and Non-Periodic Micro Structuresтезисы 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 15–19, 2021, Kassel, Germany, Book of Abstracts
- Тезисы
- Год издания: 2021
- Место издания: Universitat Kassel Kassel
- Первая страница: 304
- Последняя страница: 304
- Аннотация: Metamaterials are built so that they have non-classical properties at the macrolevel. The property of tension/compression/shear coupling with bending/torsion is studied using asymptotic homogenization method using microstructure periodicity. Asymptotic consideration gives an answer to the question whether the metamaterial is a material or a structure in relation to a particular physical property? The following definition is proposed. With respect to any property, an inhomogeneous medium is really a material at the macro level if this property is preserved when the number of the periodicity cells equals infinity.Asymptotic approach of the second order approximation has been applied to compressive/torsional coupling. Periodical structure allows getting the coupling moduli using computations for one periodicity cell only. It has to be noted that the application of the averaging leads to the macrolevel constitutive law of the non-classical type similar to the equations of the gradient elasticity.It was proved that the coupling moduli are inversely proportional to the number of cells (first order coupling). This conclusion is true for tension/bending and tension/torsion couplings if cells are stacked in Cartesian manner. Numerical examples support this theoretical conclusion.Finally, tension/torsion coupling is considered for cells stacked in the cylindrical manner. Zero order coupling is achieved in such a case, i.e., coupling moduli do not depend on the number of cells.The asymptotic homogenization is also applied for dispersed B4C/2024Al composite using its 3D micro structure images. The microstructure (structure at the level of inclusions) of such composites is complex due to the shape and random spatial arrangement of the inclusions. Model inclusions in the form of ellipsoids and other simple geometric shapes are often used. In our approach real 3D microstructure of the material was used to simulate the stress/strain state. This approach became possible because of the development of X-ray tomography and software for the reconstruction of 3D complex structure.The effective elastic moduli were calculated and verified by an experiment. The stress/strain concentration at the level of the structure was calculated in statics and dynamics. Loading diagrams for elastoplastic deformation are constructed. In particular, it was found that the diagram of von Mises stress intensity versus the intensity of deformations depends on the average hydrostatic pressure.Comparison with experiment shows that the currently available resolution of X-ray images seems to be sufficient. This makes it possible to partly replace real experiments with numerical ones.
- Добавил в систему: Артамонова Нина Брониславовна