A generalized differential scheme for the effective conductivity of percolating microinhomogeneous materials with the Hall effect

IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY International Journal of Engineering Science Pub Date : 2024-11-06 DOI:10.1016/j.ijengsci.2024.104175
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Abstract

In this paper, we propose a self-consistent scheme for the calculation of the components of the effective electrical conductivity tensor. The calculations were fulfilled for a microinhomogeneous material, the components of which have the Hall effect. The presence of the Hall effect leads to appearance of asymmetry of the components of the conductivity tensor and to dependence of these components on the magnitude of the magnetic field applied to the material. Our approach is based on the Generalized Differential Effective Medium (GDEM) method. This method generalizes the classical differential scheme (DEM) for the case of several inclusion types instead of one. In this case, the GDEM scheme leads to a system of matrix differential equations that were solved numerically. This solution was obtained for materials containing spherical or cylindrical inclusions (3D and 2D-problems). In the case of cylindrical inclusions, the results were obtained for inclusions with the symmetry axes orthogonal to the magnetic field. The application of the GDEM method allows us to consider the percolation effect for 2D and 3D-microheterogeneous materials. The results obtained are compared to the experimental data and the calculation results obtained by other self-consistent schemes.
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利用霍尔效应计算渗流微均质材料有效电导率的广义微分方案
在本文中,我们提出了一种计算有效电导张量成分的自洽方案。计算是针对具有霍尔效应的微均质材料进行的。霍尔效应的存在导致电导张量的分量出现不对称性,并且这些分量取决于施加到材料上的磁场大小。我们的方法基于广义微分有效介质(GDEM)方法。该方法是对经典微分方案(DEM)的概括,适用于包含多种类型而非一种类型的情况。在这种情况下,GDEM 方案会产生一个矩阵微分方程系统,并通过数值方法求解。这种解法适用于含有球形或圆柱形夹杂物的材料(三维和二维问题)。在圆柱形夹杂物的情况下,得到的结果是对称轴与磁场正交的夹杂物。应用 GDEM 方法,我们可以考虑二维和三维微均质材料的渗滤效应。我们将所得结果与实验数据和其他自洽方案的计算结果进行了比较。
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来源期刊
International Journal of Engineering Science
International Journal of Engineering Science 工程技术-工程:综合
CiteScore
11.80
自引率
16.70%
发文量
86
审稿时长
45 days
期刊介绍: The International Journal of Engineering Science is not limited to a specific aspect of science and engineering but is instead devoted to a wide range of subfields in the engineering sciences. While it encourages a broad spectrum of contribution in the engineering sciences, its core interest lies in issues concerning material modeling and response. Articles of interdisciplinary nature are particularly welcome. The primary goal of the new editors is to maintain high quality of publications. There will be a commitment to expediting the time taken for the publication of the papers. The articles that are sent for reviews will have names of the authors deleted with a view towards enhancing the objectivity and fairness of the review process. Articles that are devoted to the purely mathematical aspects without a discussion of the physical implications of the results or the consideration of specific examples are discouraged. Articles concerning material science should not be limited merely to a description and recording of observations but should contain theoretical or quantitative discussion of the results.
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