Elasticity M-tensors and the strong ellipticity condition
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
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Detail(s)
Original language | English |
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Article number | 124982 |
Journal / Publication | Applied Mathematics and Computation |
Volume | 373 |
Online published | 14 Jan 2020 |
Publication status | Published - 15 May 2020 |
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Abstract
In this paper, we establish two sufficient conditions for the strong ellipticity of any fourth-order elasticity tensor and investigate a class of tensors satisfying the strong ellipticity condition, the elasticity M-tensor. The first sufficient condition is that the strong ellipticity holds if the unfolding matrix of this fourth-order elasticity tensor can be modified into a positive definite one by preserving the summations of some corresponding entries. Second, an alternating projection algorithm is proposed to verify whether an elasticity tensor satisfies the first condition or not. Besides, the elasticity M-tensor is defined with respect to the M-eigenvalues of elasticity tensors. We prove that any nonsingular elasticity M-tensor satisfies the strong ellipticity condition by employing a Perron-Frobenius-type theorem for M-spectral radii of nonnegative elasticity tensors. Other equivalent definitions of nonsingular elasticity M-tensors are also established.
Research Area(s)
- Alternating projection, Elasticity tensor, M-positive definite, M-tensor, Nonnegative tensor, S-positive definite, Strong ellipticity
Citation Format(s)
Elasticity M-tensors and the strong ellipticity condition. / Ding, Weiyang; Liu, Jinjie; Qi, Liqun et al.
In: Applied Mathematics and Computation, Vol. 373, 124982, 15.05.2020.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review