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

In this paper, we establish an upper bound and sharp lower bounds on the minimum M-eigenvalue of elasticity Z-tensors without irreducible conditions. Based on the lower bound estimations for the minimum M-eigenvalue, we provide some checkable sufficient conditions for the strong ellipticity. Numerical examples are given to show the efficiency of the proposed results.

Automated summary

This paper establishes upper and lower bounds on the minimum M-eigenvalue of elasticity Z-tensors without irreducible conditions. It provides sufficient conditions for strong ellipticity based on the lower bound estimations for the minimum M-eigenvalue. Numerical examples are used to demonstrate the efficiency of the proposed results.