An elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor

doi:10.1007/s10483-021-2718-9

Applied Mathematics and Mechanics (English Edition) ›› 2021, Vol. 42 ›› Issue (5): 747-754.doi: https://doi.org/10.1007/s10483-021-2718-9

• 论文 • 上一篇

An elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor

Tianbo WANG, Dinglin YANG, Chen LI, Diwei SHI

Department of Engineering Mechanics, School of Aerospace Engineering, Tsinghua University, Beijing 100084, China

收稿日期:2021-01-05 修回日期:2021-01-29 出版日期:2021-05-01 发布日期:2021-04-22
通讯作者: Diwei SHI, E-mail:sdw17@mails.tsinghua.edu.cn

An elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor

Tianbo WANG, Dinglin YANG, Chen LI, Diwei SHI

Department of Engineering Mechanics, School of Aerospace Engineering, Tsinghua University, Beijing 100084, China

Received:2021-01-05 Revised:2021-01-29 Online:2021-05-01 Published:2021-04-22
Contact: Diwei SHI, E-mail:sdw17@mails.tsinghua.edu.cn

摘要/Abstract

摘要： Based on the Cayley-Hamilton theorem and fixed-point method, we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional (3D) inner-product space, which avoids introducing the generating function and Taylor series expansion. The proof is also extended to any finite-dimensional inner-product space.

关键词: representation theorem, analytic tensor function, fixed-point method

Abstract: Based on the Cayley-Hamilton theorem and fixed-point method, we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional (3D) inner-product space, which avoids introducing the generating function and Taylor series expansion. The proof is also extended to any finite-dimensional inner-product space.

Key words: representation theorem, analytic tensor function, fixed-point method

中图分类号:

53A45

Tianbo WANG, Dinglin YANG, Chen LI, Diwei SHI. An elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(5): 747-754.

[1]	Zhenyu MING, Liping ZHANG, Yannan CHEN. An irreducible polynomial functional basis of two-dimensional Eshelby tensors[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(8): 1169-1180.
[2]	阎大桂;徐军;严尚安;付诗禄. FIfth-ORDER ISOTROPIC DESCARTES TENSOR[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(4): 395-398.

An elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor

An elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor

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