Sharp Bounds on the Minimum <i>M</i>-Eigenvalue of Elasticity <i>M</i>-Tensors

Abstract

The M-eigenvalue of elasticity M-tensors play important roles in nonlinear elastic material analysis. In this paper, we establish an upper bound and two sharp lower bounds for the minimum M-eigenvalue of elasticity M-tensors without irreducible conditions, which improve some existing results. Numerical examples are proposed to verify the efficiency of the obtained results.

Keywords

• elasticity <i>m</i>-tensors
• minimum <i>m</i>-eigenvalue
• upper and lower bounds