Abstract
<i>M</i>-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 <i>M</i>-eigenvalue via extreme eigenvalue of the symmetric matrices extracted from elasticity <i>Z</i>-tensors without irreducible conditions, which improves some existing results. Based on the lower bound estimations for the minimum <i>M</i>-eigenvalue, we provide some checkable sufficient or necessary conditions for the strong ellipticity of elasticity <i>Z</i>-tensors. Numerical examples are given to demonstrate the proposed results.
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