Document Zbl 0617.73001

Beitrag zur tensoriellen Verallgemeinerung einachsiger Stoffgesetze. (Tensorial generalization of uni-axial constitutive laws). (German) Zbl 0617.73001

Z. Angew. Math. Mech. 66, 577-581 (1986).

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

Cited in 2 Documents

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 equation

Citations:

Zbl 0546.41004

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References:

[1]	Interpolation Methods for Tensor Functions, in: et al. (Herausg.), Mathematical Modelling in Science and Technology, Pergamon Press, New York etc. 1984, S. 52–57, vorgetragen auf der ”Fourth International Conference on Mathematical Modelling” in Zürich, August 1983. · doi:10.1016/B978-0-08-030156-3.50015-1
[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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