Programmable behavior of the metamaterial by kind unit cells connection

Author details

L.R.[1] Smolin I.Yu. Akhmetshin
National Research Tomsk State University, Tomsk, Russian Federation

https://doi.org/10.15593/perm.mech/2023.1.03

The paper is devoted to the numerical analysis of uniaxial loading of a sample of the mechanical metamaterial. The structure of the mechanical metamaterial is constructed of a ring and four ligaments, which make up a tetrachiral structure. The peculiarity of such a structure consists in torsion of the sample under the force load. Two methods of connecting cells in the metamaterial are considered adjoining and overlapping. The adjoining method of joining cells increases the thickness of the internal structure of the sample, which allows us to consider it as a topological defect of the metamaterial. The overlapping method saves the base material from which the tetrachiral structure is constructed. Differences in the structure when constructing a three-dimensional sample result in a significant change in the characteristics of the sample. Numerical solution of the problem is performed in a three-dimensional formulation using the finite element method. The constitutive relation describing the behavior of the model corresponds to Hooke's law. Numerical simulation of uniaxial loading made it possible to obtain the results of mechanical response and to analyze the effective properties of metamaterials. A topological defect in the form of a thickening of the internal structure elements led to a difference in the linear dimensions of the two samples. The increased thickness of the unit cell connection elements resulted in a decrease in the effective density of the metamaterial sample. The same sample showed a triple increase in the value of the elastic modulus. The greater ability to resist deformation resulted in a reduced twist effect compared to the sample whose cells were joined by the overlapping method. The results obtained will make it possible to program the mechanical behavior and properties of the metamaterial sample.

Keywords

mechanical metamaterialcell structurecell connectionchiralitynumerical simulationfinite element methodelastic deformationstructure-properties relationshiptwisteffective properties.

ПРОГРАММИРУЕМОЕ ПОВЕДЕНИЕ МЕТАМАТЕРИАЛА ПРИ ИЗМЕНЕНИИ СПОСОБА СОЕДИНЕНИЯ ЭЛЕМЕНТАРНЫХ ЯЧЕЕК

Работа посвящена численному анализу одноосного нагружения образца из механического метаматериала. Структура механического метаматериала построена из кольца и четырех связок, составляющих тетрахиральную структуру. Особенность подобной структуры заключена в скручивании образца под силовой нагрузкой. Рассмотрены два метода соединения ячеек в метаматериале «присоединение» и «внахлест». Метод соединения ячеек «присоединение» увеличивает толщину некоторых элементов внутренней структуры образца, что позволяет рассматривать это как топологический дефект метаматериала. Соединение методом «внахлест» позволяет экономить базовый материал, из которого построена тетрахиральная структура. Различия в структуре при построении трехмерного образца приводят к существенному изменению его характеристик. Численное решение задачи осуществляется в трехмерной постановке с использованием метода конечных элементов. Определяющее соотношение, описывающее поведение модели, соответствует закону Гука. Численное моделирование одноосного нагружения образцов позволило получить результаты их механического отклика и проанализировать эффективные свойства метаматериалов. Топологический дефект в виде утолщения элементов внутренней структуры приводит к различию линейных размеров образцов. Увеличенная толщина в местах соединения элементарных ячеек также привела к уменьшению эффективной плотности образца из метаматериала. Этот же образец продемонстрировал тройное увеличение значения модуля упругости. Большая способность к сопротивлению деформированию привела к уменьшению эффекта скручивания по сравнению с образцом, ячейки которого соединялись методом «внахлест». Полученные результаты позволят программировать механическое поведение и свойства образцов из метаматериала.

Ключевые слова

механический метаматериалячеистая структурасоединение ячеекхиральностьчисленное моделированиеметод конечных элементовупругое деформированиесоотношение структура – свойстваскручиваниеэффективные характеристики.

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Article information

Published: 29 May 2023
Issue date: 29 May 2023
Issue: No. 1 (2023)