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.

中文翻译：

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确定有效扩散磁导率时的不完美接触建模

摘要

这项工作开发了一种通用方法来解释不完美接触，以确定各种性质的有效属性，即有效扩散率以及导热率和导电率。当微观层面的场不连续时，就会出现不完美的接触。创建统一方法的可能性是由于控制方程的相似性。同时，不完美接触的出现可能是由微观结构特征和工艺本身的细节引起的。对于具体而言，确定有效扩散渗透率，因为可以考虑出现不完美接触的各种原因。原因可能与结构缺陷的形成和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美接触的方法。在第一种情况下，设置了字段跳转。在第二种情况下，引入了具有极端特性的薄涂层的不均匀性。以具有球形不均匀性的材料为例进行了综合分析。得到了等效非均匀性贡献张量的解析表达式，从而简化了各种均匀化方法的推广。