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Sharp bounds on the minimum M-eigenvalue of elasticity Z-tensors and identifying strong ellipticity
Gang Wang,Linxuan Sun,Xueyong Wang
Keywords:Elasticity Z-tensors, elasticity M-tensors, minimum M-eigenvalue, upper and lower bounds
Abstract:
      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.