New lower bounds for the minimum M-eigenvalue of elasticity M-tensors and applications
作者： Haitao Che , Haibin Chen , Na Xu , Qingni Zhu
DOI: 10.1186/S13660-020-02454-1
关键词: Nonlinear elasticity 、 Eigenvalues and eigenvectors 、 Mathematics 、 Elasticity (economics) 、 Positive definiteness 、 Applied mathematics
摘要: M-eigenvalues of elasticity M-tensors play an important role in nonlinear and materials. In this paper, we present several new lower bounds for the minimum M-eigenvalue propose numerical examples to illustrate efficiency obtained results. As applications, provide checkable sufficient conditions strong ellipticity positive definiteness irreducible M-tensors.
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sci-hub.st 参考文章(32)
Cristina Padovani, Strong Ellipticity of Transversely Isotropic Elasticity Tensors Meccanica. ,vol. 37, pp. 515- 525 ,(2002) , 10.1023/A:1020946506754
Morton E. Gurtin, The Linear Theory of Elasticity Linear Theories of Elasticity and Thermoelasticity. pp. 1- 295 ,(1973) , 10.1007/978-3-662-39776-3_1
J. K. Knowles, Eli Sternberg, On the ellipticity of the equations of nonlinear elastostatics for a special material Journal of Elasticity. ,vol. 5, pp. 341- 361 ,(1975) , 10.1007/BF00126996
Jay R. Walton, J.Patrick Wilber, Sufficient conditions for strong ellipticity for a class of anisotropic materials International Journal of Non-linear Mechanics. ,vol. 38, pp. 441- 455 ,(2003) , 10.1016/S0020-7462(01)00066-X
J. K. Knowles, Eli Sternberg, On the failure of ellipticity of the equations for finite elastostatic plane strain Archive for Rational Mechanics and Analysis. ,vol. 63, pp. 321- 336 ,(1976) , 10.1007/BF00279991
S. Friedland, S. Gaubert, L. Han, Perron–Frobenius theorem for nonnegative multilinear forms and extensions Linear Algebra and its Applications. ,vol. 438, pp. 738- 749 ,(2013) , 10.1016/J.LAA.2011.02.042
Deren Han, H. H. Dai, Liqun Qi, Conditions for Strong Ellipticity of Anisotropic Elastic Materials Journal of Elasticity. ,vol. 97, pp. 1- 13 ,(2009) , 10.1007/S10659-009-9205-5
Yiju Wang, Liqun Qi, Xinzhen Zhang, A practical method for computing the largest M‐eigenvalue of a fourth‐order partially symmetric tensor Numerical Linear Algebra With Applications. ,vol. 16, pp. 589- 601 ,(2009) , 10.1002/NLA.633
Stan Chiriţă, Alexandre Danescu, Michele Ciarletta, On the Strong Ellipticity of the Anisotropic Linearly Elastic Materials Journal of Elasticity. ,vol. 87, pp. 1- 27 ,(2007) , 10.1007/S10659-006-9096-7
Yiju Wang, Louis Caccetta, Guanglu Zhou, Convergence analysis of a block improvement method for polynomial optimization over unit spheres Numerical Linear Algebra With Applications. ,vol. 22, pp. 1059- 1076 ,(2015) , 10.1002/NLA.1996