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Zbl 1094.74010
Moakher, Maher
On the averaging of symmetric positive-definite tensors. (English)
[J] J. Elasticity 82, No. 3, 273-296 (2006). ISSN 0374-3535; ISSN 1573-2681/e

Summary: We present properly invariant averaging procedures for symmetric positive-definite tensors which are based on different measures of nearness of symmetric positive-definite tensors. These procedures intrinsically account for the positive-definite property of the tensors to be averaged. They are independent of the coordinate system, preserve material symmetries, and more importantly, they are invariant under inversion. The results of these averaging methods are compared with the results of other methods including that proposed by {\it S. Cowin} and {\it G. Yang} [J. Elasticity 46, No. 2, 151--180 (1997; Zbl 0902.73006)] for the case of the elasticity tensor of generalized Hooke's law.

MSC 2000:: *74B05 Classical linear elasticity
15A48 Positive matrices and their generalizations
15A72 Vector and tensor algebra

Keywords: geometric mean; Kullback-Leibler mean

Citations: Zbl 0902.73006

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