Beitrag zur tensoriellen Verallgemeinerung einachsiger Stoffgesetze. (Tensorial generalization of uni-axial constitutive laws). (German) Zbl 0617.73001
The paper deals with stress-strain relations expressed by an isotropic tensor function which is presented in the form of a so-called minimal polynomial based on the Cayley-Hamilton equation. This fact is used to generalize a one-dimensional stress-strain relation approximated by a quadratic expression into a three-dimensional form.
Reviewer: Th.Lehmann
MSC:
74A20 | Theory of constitutive functions in solid mechanics |
74E15 | Crystalline structure |
41A05 | Interpolation in approximation theory |
41A10 | Approximation by polynomials |
Keywords:
generalize uni-axial relations to multi-axial states of stress; Norton- Bailey creep law; Ramberg-Osgood stress-strain relation; tensorial constitutive equations; stress-strain relations; isotropic tensor function; minimal polynomial; Cayley-Hamilton equationCitations:
Zbl 0546.41004References:
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[2] | Elastizitäts- und Plastizitätslehre, Vieweg-Verlag, Braunschweig/Wiesbaden 1985. · Zbl 0551.73009 |
[3] | Tensorial Expansions in Non-Linear Mechanics, Academia Nakladatelstvi Ceskoslovenské, Akademie VED, Praha 1984. |
[4] | Leckie, Acta Metallurgica 25 pp 1059– (1977) |
[5] | ; , Description of stress-strain curves by three parameters, NACA Technical Note No. 902 (July 1943). |
[6] | ; , Kriechfestigkeit Metallischer Werkstoffe, Springer-Verlag, Berlin/Göttingen/Heidelberg 1962. · doi:10.1007/978-3-642-52432-5 |
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