An elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor

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 seri...

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Veröffentlicht in:	Applied mathematics and mechanics 2021, Vol.42 (5), p.747-754
Hauptverfasser:	Wang, Tianbo, Yang, Dinglin, Li, Chen, Shi, Diwei
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Classical Mechanics Fixed points (mathematics) Fluid- and Aerodynamics Mathematical analysis Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Mathematics, Applied Mechanics Partial Differential Equations Physical Sciences Representations Science & Technology Series expansion Taylor series Technology Tensors Theorem proving Theorems
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Zusammenfassung:	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.
ISSN:	0253-4827 1573-2754
DOI:	10.1007/s10483-021-2718-9