IDENTIFYING STRONG ELLIPTICITY VIA BOUNDS ON THE MINIMUM M -EIGENVALUE OF ELASTICITY Z -TENSORS

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