New lower bounds for the minimum M-eigenvalue of elasticity M-tensors and applications

Abstract

Abstract M-eigenvalues of elasticity M-tensors play an important role in nonlinear elasticity and materials. In this paper, we present several new lower bounds for the minimum M-eigenvalue of elasticity M-tensors and propose numerical examples to illustrate the efficiency of the obtained results. As applications, we provide several checkable sufficient conditions for the strong ellipticity and positive definiteness of irreducible elasticity M-tensors.

Keywords

• M-eigenvalue
• Elasticity M-tensors
• Strong ellipticity
• M-positive definiteness