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DOI: 10.5445/IR/1000080589
Veröffentlicht am 28.02.2018

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]

Herrmann, H.; Beddig, M.

Abstract:
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.


Zugehörige Institution(en) am KIT Fakultät für Mathematik (MATH)
Publikationstyp Zeitschriftenaufsatz
Jahr 2018
Sprache Englisch
Identifikator ISSN: 1736-6046, 1736-7530
URN: urn:nbn:de:swb:90-805898
KITopen ID: 1000080589
Erschienen in Proceedings of the Estonian Academy of Sciences
Band 67
Heft 1
Seiten 73-92
Schlagworte fibre orientation, tensor series, spherical surface harmonics, constitutive equations, alignment tensors, orientation tensors
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