Zheng, Q.-S. On the representations for isotropic vector-valued, symmetric tensor- valued and skew-symmetric tensor-valued functions. (English) Zbl 0781.15011 Int. J. Eng. Sci. 31, No. 7, 1013-1024 (1993). In this paper, all tensors are of second order in a 3-dimensional vector space. A function \(\varphi(A_ i,W_ p,v_ m)\) is said to be isotropic if it is invariant under orthogonal transformation, where \(A_ i\), \(W_ p\) and \(V_ m\) are given symmetric tensors, skew-symmetric tensors and vectors respectively. The functions can be scalar-valued, symmetric or skew-symmetric tensor-valued.The author gives a new derivation procedure for determining the representations of the isotropic functions, i.e., determining the sets of generators for these isotropic (vector-valued, symmetric or skew- symmetric tensor-valued) functions. Reviewer: Chen Zhijie (Shanghai) Cited in 25 Documents MSC: 15A72 Vector and tensor algebra, theory of invariants Keywords:representations; vector-valued functions; tensor-valued functions; scalar-valued functions; isotropic functions PDFBibTeX XMLCite \textit{Q. S. Zheng}, Int. J. Eng. Sci. 31, No. 7, 1013--1024 (1993; Zbl 0781.15011) Full Text: DOI References: [1] Wang, C.-C., Archs ration. Mech. Analysis, 33, 268 (1969) [2] Wang, C.-C., Archs ration. Mech. Analysis, 36, 198 (1970) [3] Wang, C.-C., Archs ration. Mech. Analysis, 43, 392 (1971) [4] Smith, G. F., Archs ration. Mech. Analysis, 36, 161 (1970) [5] Smith, G. F., Int. J. Engng Sci., 9, 899 (1971) [6] Wang, C.-C., Archs ration. Mech. Analysis, 33, 249 (1969) [7] Wang, C.-C., Archs ration. Mech. Analysis, 36, 166 (1970) [8] Boehler, J. P., ZAMM, 57, 323 (1977) [9] Pennisi, S.; Trovato, M., Int. J. Engng Sci., 25, 1059 (1987) [10] Rivlin, R. S.; Ericksen, J. L., J. ration. Mech. Analysis, 4, 323 (1955) [11] Korsgaard, J., Int. J. Engng Sci., 28, 653 (1990) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.