Tensor series expansion of a spherical function for the use in constitutive theory of materials containing orientable particles [Sfäärilise funktsiooni tensorrea kasutamine orienteeritud osakesi sisaldava materjali olekuvõrrandi teoorias]
Tensor series expansion of a spherical function for the use in constitutive theory of materials containing orientable particles [Sfäärilise funktsiooni tensorrea kasutamine orienteeritud osakesi sisaldava materjali olekuvõrrandi teoorias]
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球函数的张量级数展开，用于含可定向颗粒材料的本构理论
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
M. Beddig
中科院分区：
文献类型：
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作者：
H. Herrmann;M. Beddig
本文介绍了一种用于含定向粒子材料本构理论的球函数张量级数展开式。在几个应用领域中，两个角度的函数，例如取向（密度）分布函数，被展开成一系列对称的不可约张量。本文将解释这一系列的扩展，开始审查的代表性的功能定义在一个单位球的球谐函数，这是一个可能的选择的基础。然后，球谐函数和对称无痕张量之间的联系进行了解释。这是介绍和理解取向和排列张量以及它们与取向分布函数的联系的基础。呈现的风格被选择为更多的教学方面，不同于其他地方发现的理论证明风格，直接从对称张量开始。
This paper presents a didactical introduction to a tensor series expansion of a spherical function for the use in constitutive theory of materials containing orientable particles. In several application areas a function of two angles, e.g. an orientation (density) distribution function, is expanded into a series of symmetric irreducible tensors. This paper will explain this series expansion, starting with reviewing the representation of a function defined on a unit sphere in terms of spherical harmonics, which are a possible choice for a basis. Then, the connection between spherical harmonics and symmetric traceless tensors is explained. This is the basis for introducing and understanding orientation and alignment tensors as well as their connection to the orientation distribution function. The style of presentation was chosen to be more on the didactical side, differently from the theorem–proof style found elsewhere, which directly starts from symmetric tensors.