Extrema of Young’s modulus for elastic solids with tetragonal symmetry

Cazzani, Antonio; Rovati, Marco

doi:10.1016/j.ijsolstr.2005.02.018

Cited by 50 publications

(26 citation statements)

References 7 publications

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“…Numerical searching is practical and straightforward; thus Cazzani and Rovati provide a detailed analysis of the extrema of Young's modulus for cubic and transversely isotropic materials Keywords: Poisson's ratio, Young's modulus, shear modulus, anisotropic. [Cazzani and Rovati 2003] and for materials with tetragonal symmetry [Cazzani and Rovati 2005], with extensive illustrative examples. Boulanger and Hayes [1995] obtained analytic expressions related to extrema of Young's modulus.…”

Section: Introductionmentioning

confidence: 99%

Extreme values of Poisson’s ratio and other engineering moduli in anisotropic materials

Norris

2006

JOMMS

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Conditions for a maximum or minimum of Poisson's ratio of anisotropic elastic materials are derived. For a uniaxial stress in the 1-direction and Poisson's ratio ν defined by the contraction in the 2-direction, the following three quantities vanish at a stationary value: s 14 , [2νs 15 + s 25 ] and [(2ν − 1)s 16 + s 26 ], where s IJ are the components of the compliance tensor. Analogous conditions for stationary values of Young's modulus and the shear modulus are obtained, along with second derivatives of the three engineering moduli at the stationary values. The stationary conditions and the hessian matrices are presented in forms that are independent of the coordinates, which lead to simple search algorithms for extreme values. In each case the global extremes can be found by a simple search over the stretch direction n only. Simplifications for stretch directions in a plane of orthotropic symmetry are also presented, along with numerical examples for the extreme values of the three engineering constants in crystals of monoclinic symmetry.

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Section: Introductionmentioning

confidence: 99%

Extreme values of Poisson’s ratio and other engineering moduli in anisotropic materials

Norris

2006

JOMMS

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“…They are triclinic, monoclinic, orthotropic, tetragonal, trigonal, hexagonal, cubic and isotropic. The stationary values of Young's modulus E(n) for orthotropic, tetragonal, trigonal, hexagonal and cubic materials have been investigated in [8,9,13]. The stationary values of Young's modulus E(n) for monoclinic and triclinic materials presented here completes the investigation of the stationary values of Young's modulus E(n) for all anisotropic elastic materials.…”

Section: Discussionmentioning

confidence: 58%

“…Cazzani and Rovati [8,9] studied Young's modulus for cubic, hexagonal and tetragonal materials and gave explicitly the stationary values E(n) and n. They also present graphically the direction surfaces of E(n) for several real materials. In a sequel to this paper, Ting [13] investigated the stationary values of Young's modulus E(n) for orthotropic, trigonal, tetragonal, hexagonal and cubic materials.…”

Section: Introductionmentioning

confidence: 99%

The Stationary Values of Young's Modulus For Monoclinic and Triclinic Materials

Ting

2005

J. mech.

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The stationary values (maximum, minimum, saddle point) of Young modulus E(n) for a general anisotropic elastic materials is studied. The general results are then spcialized for monoclinic materials. Equations that provide the direction n for a stationary value are given. Some have an explicit solution. Other may require a numerical computation. The equations that required numerical solutions are two coupled polynomials of degree no more than four.

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“…Following Cazzani and Rovati [48,49], the reciprocal value of Young modulus for uniaxial tension in the direction of the unit vector n can be expressed as…”

Section: Elastic Anisotropymentioning

confidence: 99%

Interatomic bonds and the tensile anisotropy of trialuminides in the elastic limit: a density functional study for Al₃(Sc, Ti, V, Cr)

Jahnátek

Krajčı́

Hafner

2007

Philosophical Magazine

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Extrema of Young’s modulus for elastic solids with tetragonal symmetry

Cited by 50 publications

References 7 publications

Extreme values of Poisson’s ratio and other engineering moduli in anisotropic materials

Extreme values of Poisson’s ratio and other engineering moduli in anisotropic materials

The Stationary Values of Young's Modulus For Monoclinic and Triclinic Materials

Interatomic bonds and the tensile anisotropy of trialuminides in the elastic limit: a density functional study for Al₃(Sc, Ti, V, Cr)

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Extrema of Young’s modulus for elastic solids with tetragonal symmetry

Cited by 50 publications

References 7 publications

Extreme values of Poisson’s ratio and other engineering moduli in anisotropic materials

Extreme values of Poisson’s ratio and other engineering moduli in anisotropic materials

The Stationary Values of Young's Modulus For Monoclinic and Triclinic Materials

Interatomic bonds and the tensile anisotropy of trialuminides in the elastic limit: a density functional study for Al3(Sc, Ti, V, Cr)

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Interatomic bonds and the tensile anisotropy of trialuminides in the elastic limit: a density functional study for Al₃(Sc, Ti, V, Cr)