Abstract
Based on the Cayley-Hamilton theorem and fixed-point method, we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional (3D) inner-product space, which avoids introducing the generating function and Taylor series expansion. The proof is also extended to any finite-dimensional inner-product space.
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Acknowldgements
We are grateful to Prof. Quanshui ZHENG for his guidance in preparation of the paper.
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Wang, T., Yang, D., Li, C. et al. An elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor. Appl. Math. Mech.-Engl. Ed. 42, 747–754 (2021). https://doi.org/10.1007/s10483-021-2718-9
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DOI: https://doi.org/10.1007/s10483-021-2718-9