IDENTIFYING STRONG ELLIPTICITY VIA BOUNDS ON THE MINIMUM <i>M</i>-EIGENVALUE OF ELASTICITY <i>Z</i>-TENSORS

Gang Wang; Chong Wang; Lixia Liu

doi:10.11948/20210284

2023 Volume 13 Issue 2

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Gang Wang, Chong Wang, Lixia Liu. IDENTIFYING STRONG ELLIPTICITY VIA BOUNDS ON THE MINIMUM M-EIGENVALUE OF ELASTICITY Z-TENSORS[J]. Journal of Applied Analysis & Computation, 2023, 13(2): 609-622. doi: 10.11948/20210284

Citation:

Gang Wang, Chong Wang, Lixia Liu. IDENTIFYING STRONG ELLIPTICITY VIA BOUNDS ON THE MINIMUM M-EIGENVALUE OF ELASTICITY Z-TENSORS[J]. Journal of Applied Analysis & Computation, 2023, 13(2): 609-622. doi: 10.11948/20210284

IDENTIFYING STRONG ELLIPTICITY VIA BOUNDS ON THE MINIMUM M-EIGENVALUE OF ELASTICITY Z-TENSORS

1.
School of Management Science, Qufu Normal University, Rizhao 276800, China
2.
School of Mathematics and Statistics, Xidian University, Xian 710071, China

Corresponding author: Email address: wgglj1977@163.com(G. Wang)
Fund Project: The authors were supported by the Natural Science Foundation of Shandong Province (ZR2020MA025), the Natural Science Basic Research Program of Shaanxi Province (2023JCYB056), the Natural Science Foundation of China (12071250, 11801430) and High Quality Curriculum of Postgraduate Education in Shandong Province (SDYKC20109)

Abstract

Abstract

$M$-eigenvalues of fourth-order partially symmetric tensors play an important role in the nonlinear elastic material analysis. In this paper, we establish sharp upper and lower bounds on the minimum $M$-eigenvalue via extreme eigenvalue of the symmetric matrices extracted from elasticity $Z$-tensors without irreducible conditions, which improves some existing results. Based on the lower bound estimations for the minimum $M$-eigenvalue, we provide some checkable sufficient or necessary conditions for the strong ellipticity of elasticity $Z$-tensors. Numerical examples are given to demonstrate the proposed results.
- Elasticity Z-tensors /
- minimum M-eigenvalue /
- upper and lower bounds /
- strong ellipticity
MSC: 15A18, 15A42, 15A69

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References

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