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.

中文翻译：

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弹性M张量的最小M特征值的新下界及其应用

弹性的M特征值M张量在非线性弹性和材料中起重要作用。在本文中，我们为弹性M张量的最小M特征值提出了几个新的下界，并提供了数值示例来说明所获得结果的效率。作为应用程序，我们为不可约弹性M张量的强椭圆率和正定性提供了几个可检查的充分条件。