Tensor series expansion of a spherical function for the use in constitutive theory of materials containing orientable particles

Estonian Academy of Sciences. Proceedings

Heiko Herrmann¹ 

关键词: fibre orientation;    tensor series;    spherical surface harmonics;    constitutive equations;    alignment tensors;    orientation;    tensors.;   

DOI  :  10.3176/proc.2018.1.04

学科分类：化学（综合）

来源: Teaduste Akadeemia Kirjastus

【 摘 要 】

This paper presents a didactical introduction to a tensor series expansion of a spherical function for the use in constitutivetheory 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 apossible choice for a basis. Then, the connection between spherical harmonics and symmetric traceless tensors is explained. Thisis the basis for introducing and understanding orientation and alignment tensors as well as their connection to the orientationdistribution function. The style of presentation was chosen to be more on the didactical side, differently from the theorem–proofstyle found elsewhere, which directly starts from symmetric tensors.

【 授权许可】

CC BY-NC