Bounds of M-eigenvalues and strong ellipticity conditions for elasticity tensors

ABSTRACT

Novel upper and lower bounds are derived for the M-eigenvalues of a fourth-order elasticity tensor by using the extreme eigenvalues of the symmetric matrices extracted from the given elasticity tensor. The new upper bound of the M-spectral radius is tighter than that given by S. Li et al. in [J Comput Appl Math. 2019;356]. Based on the new lower bound of the M-eigenvalues, a stronger sufficient condition is presented for the strong ellipticity of an elasticity tensor. Numerical examples are also given to demonstrate the results.

Keywords:

• Elasticity tensor
• M-eigenvalue
• WQZ-algorithm
• strong ellipticity condition

2010 Mathematics Subject Classifications:

• 15A42
• 15A69
• 65F15

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by National Natural Science Foundations of China (Grant No. 11671105) and Science and Technology Foundation of Guizhou Province ([2020]1Z002).