Modeling of Imperfect Contacts in Determining the Effective Diffusion Permeability

IF 0.4 Q4 MATHEMATICS Vestnik St Petersburg University-Mathematics Pub Date : 2024-01-24 DOI:10.1134/s1063454123040088

K. P. Frolova, E. N. Vilchevskaya, V. A. Polyanskiy

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Abstract

The work develops a universal approach to accounting for imperfect contacts in determining effective properties of various nature, namely, effective diffusivity and thermal and electrical conductivity. Imperfect contacts appear when fields at the microlevel are not continuous. The possibility of creating a unified approach is due to the similarity of the governing equations. At the same time, the appearance of imperfect contacts may be caused by microstructural features and by the specifics of the process itself. For concreteness, the effective diffusion permeability is determined, since various reasons for the appearance of imperfect contacts can be considered. The reasons can be associated both with the formation of structural defects and with the presence of the specific segregation effect. The paper generalizes and compares two approaches to accounting for imperfect contacts. In the first case, a field jump is set. In the second case, an inhomogeneity with a thin coating possessing extreme properties is introduced. A comprehensive analysis is carried out on the example of a material with spherical inhomogeneities. Analytical expressions for the contribution tensor of the equivalent inhomogeneity are obtained, which results in simplification of the generalization of various homogenization methods.

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在确定有效扩散渗透率时建立不完全接触模型

摘要这项工作开发了一种通用方法，在确定各种性质的有效特性（即有效扩散率、热导率和电导率）时考虑不完全接触。当微观层面的场不连续时，就会出现不完全接触。由于控制方程的相似性，可以创建一种统一的方法。同时，不完全接触的出现可能是由微观结构特征和工艺本身的特殊性造成的。为了具体化，可以确定有效扩散渗透率，因为可以考虑出现不完全接触的各种原因。这些原因既可能与结构缺陷的形成有关，也可能与特定偏析效应的存在有关。本文概括并比较了两种解释不完全接触的方法。第一种情况是设置场跃。在第二种情况下，引入了具有极端特性的薄涂层不均匀性。以具有球形不均匀性的材料为例进行了全面分析。得到了等效非均质性贡献张量的分析表达式，从而简化了各种均质化方法的一般化。

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来源期刊

Vestnik St Petersburg University-Mathematics MATHEMATICS-

CiteScore

0.70

自引率

50.00%

发文量

期刊介绍： Vestnik St. Petersburg University, Mathematics is a journal that publishes original contributions in all areas of fundamental and applied mathematics. It is the prime outlet for the findings of scientists from the Faculty of Mathematics and Mechanics of St. Petersburg State University. Articles of the journal cover the major areas of fundamental and applied mathematics. The following are the main subject headings: Mathematical Analysis; Higher Algebra and Numbers Theory; Higher Geometry; Differential Equations; Mathematical Physics; Computational Mathematics and Numerical Analysis; Statistical Simulation; Theoretical Cybernetics; Game Theory; Operations Research; Theory of Probability and Mathematical Statistics, and Mathematical Problems of Mechanics and Astronomy.