Conditions of strong ellipticity and calculations of M-eigenvalues for a partially symmetric tensor

Jianxing Zhao

Applied Mathematics and Computation, 2023, vol. 458, issue C

Abstract: Strong ellipticity condition (SE-condition) of the equilibrium equations for general nonlinear elastic materials can be equivalently transformed into the SE-condition of a partially symmetric tensor. Qi et al. in 2009 proved that the SE-condition of a partially symmetric tensor holds if and only if its smallest M-eigenvalue is positive. In this paper, a criterion for the SE-condition of a partially symmetric tensor is first given. And then, an alternative method to compute all M-eigentriples of a partially symmetric tensor is presented. Finally, two numerical examples show the effectiveness of the proposed criterion and the calculation of M-eigenvalues in judging the SE-condition of the equilibrium equations.

Keywords: Strong ellipticity conditions; Equilibrium equations; Partially symmetric tensors; M-eigenvalues (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:458:y:2023:i:c:s0096300323004149

DOI: 10.1016/j.amc.2023.128245

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