Elasticity M-tensors and the strong ellipticity condition

Weiyang Ding, Jinjie Liu, Liqun Qi and Hong Yan

Applied Mathematics and Computation, 2020, vol. 373, issue C

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.

Keywords: Elasticity tensor; Strong ellipticity; M-positive definite; S-positive definite; Alternating projection; M-tensor; Nonnegative tensor (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:373:y:2020:i:c:s0096300319309749

DOI: 10.1016/j.amc.2019.124982

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