DIRECTIONS OF EXTREME STIFFNESS AND STRENGTH IN LINEAR ELASTIC ANISOTROPIC SOLIDS

Authors

  • Paweł SZEPTYŃSKI AGH University of Science and Technology

DOI:

https://doi.org/10.7494/mech.2012.31.3.124

Keywords:

linear elasticity, anisotropy, stiffness moduli, strength, optimization, material design

Abstract

An investigation for directions of extreme - maximum or minimum - values of the longitudinal and transverse stiffness moduli as well as of the limit uniaxial and limit shear stresses in anisotropic linear elastic solids is performed in the pa­per. The cases of cubic symmetry (regular crystal system) and of volumetrically isotropic cylindrical symmetry (hexago­nal crystal system with additional constraints) are considered. The systems of non-linear equations for the components of the versors of investigated directions are derived with use of the spectral decomposition of the elasticity (stiffness and compliance) tensors.

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References

Berryman J.G. 2005, Bounds and self-consistent estimates for elastic constants of random polycrystals with hexagonal, trigonal, and tetragonal symmetries. J. Mech. Phys. Solids, 53, pp. 2141-2173.

Burzyński W. 1928, Studium nad hipotezami wytężenia, Akademia Nauk Technicznych, Lwów 1928; see also: 2009, Selected passages from Włodzimierz Burzyński 's doctoral dissertation ''Study on material effort hypotheses", Engng. Trans., 57, 3-4, pp. 185-215.

Cowin S.C., Mehrabadi M.M. 1987: On the identification of material symmetry for anisotropic elastic materials. Q. J. Mech. Appl. Math., 40, 4, pp. 451-476.

Kowalczyk-Gajewska K., Ostrowska-Maciejewska J. 2009: Review on spectral decomposition of Hooke's tensor for all symmetry groups of linear elastic material. Engns. Trans., 57, 3-4, pp. 145-183.

Mehrabadi M.M., Cowin S.C. 1990: Eigentensors of anisotropic elastic materials. Quart. J. Mech. Appl. Math., 43, 1, pp. 15-41.

Mises R. von 1928: Mechanik der plastischen Formanderung von Kristallen. Z. Angew. Math. u. Mech., pp. 8, 161-185.

Ostrowska-Maciejewska J., Rychlewski J. 2001: Generalized proper states for anisotropic elastic materials. Arch. Mech., 53, 4-5, pp. 501-518.

Rychlewski J. 1984: On Hooke 's law. J. Appl. Math. Mech., 48, pp. 303-314.

Yoo M.H., Fu C.L. 1998, Physical constants, deformation twinning, and microcracking of titanium aluminides, Metal. Mater. Trans. A, 29A, pp. 49-63.

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Issue

Vol. 31 No. 3 (2012)

Section

Articles

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