An irreducible polynomial functional basis of two-dimensional Eshelby tensors

doi:10.1007/s10483-019-2502-6

Applied Mathematics and Mechanics (English Edition) ›› 2019, Vol. 40 ›› Issue (8): 1169-1180.doi: https://doi.org/10.1007/s10483-019-2502-6

An irreducible polynomial functional basis of two-dimensional Eshelby tensors

Zhenyu MING¹, Liping ZHANG¹, Yannan CHEN²

1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China;
2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China

收稿日期:2018-09-27 修回日期:2019-01-28 出版日期:2019-08-01 发布日期:2019-08-01
通讯作者: Liping ZHANG E-mail:lipingzhang@tsinghua.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11271221, 11771244, 11571178, and 11771405)

An irreducible polynomial functional basis of two-dimensional Eshelby tensors

Zhenyu MING¹, Liping ZHANG¹, Yannan CHEN²

1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China;
2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China

Received:2018-09-27 Revised:2019-01-28 Online:2019-08-01 Published:2019-08-01
Contact: Liping ZHANG E-mail:lipingzhang@tsinghua.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11271221, 11771244, 11571178, and 11771405)

摘要/Abstract

摘要： The two-dimensional (2D) Eshelby tensors are discussed. Based upon the complex variable method, an integrity basis of ten isotropic invariants of the 2D Eshelby tensors is obtained. Since an integrity basis is always a polynomial functional basis, these ten isotropic invariants are further proven to form an irreducible polynomial functional basis of the 2D Eshelby tensors.

关键词: relative motion, inertial force, generalized force, invariance, representation theorem, Eshelby tensor, isotropic invariant, irreducible functional basis

Abstract: The two-dimensional (2D) Eshelby tensors are discussed. Based upon the complex variable method, an integrity basis of ten isotropic invariants of the 2D Eshelby tensors is obtained. Since an integrity basis is always a polynomial functional basis, these ten isotropic invariants are further proven to form an irreducible polynomial functional basis of the 2D Eshelby tensors.

Key words: relative motion, inertial force, generalized force, invariance, Eshelby tensor, representation theorem, irreducible functional basis, isotropic invariant

中图分类号:

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.

参考文献 34

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An irreducible polynomial functional basis of two-dimensional Eshelby tensors

An irreducible polynomial functional basis of two-dimensional Eshelby tensors

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