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词条 Zener ratio
释义

  1. Cubic materials

  2. Universal Elastic Anisotropy Index

  3. See also

  4. References

The Zener ratio is a dimensionless number that is used to quantify the anisotropy for cubic crystals. It is sometimes referred as anisotropy ratio and is named after Clarence Zener.[1] Conceptually, it quantifies how far a material is from being isotropic (where the value of 1 means an isotropic material).

Its mathematical definition is[1][2]

where refers to Elastic constants in Voigt notation.

Cubic materials

Cubic materials are special orthotropic materials that are invariant with respect to 90° rotations with respect to the principal axes, i.e., the material is the same along its principal axes. Due to these additional symmetries the stiffness tensor can be written with just three different material properties like

The inverse of this matrix is commonly written as[3]

where is the Young's modulus, is the shear modulus, and is the Poisson's ratio. Therefore, we can think the ratio as the relation between the shear modulus for the cubic material and its (isotropic) equivalent:

Universal Elastic Anisotropy Index

The Zener ratio is only applicable to cubic crystals. To overcome this limitation, a 'Universal Elastic Anisotropy Index (AU)' [4] was formulated from variational principles of elasticity and tensor algebra. The AU is now widely used to quantify the anisotropy of elastic crystals of all classes.

See also

  • Anisotropy
  • Orthotropic material
  • Linear elasticity
  • Hooke's law

References

1. ^{{cite journal|author=Z. Li and C. Bradt|title=The single-crystal elastic constants of cubic (3C) SiC to 1000°C|journal=Journal of Materials Science|date=July 1987|volume=22|issue=7|pages=2557–2559|doi=10.1007/BF01082145}}
2. ^{{cite book| author=L. B. Freund; S. Suresh| title=Thin Film Materials Stress, Defect Formation and Surface Evolution| publisher=Cambridge University Press| year=2004}}
3. ^Boresi, A. P, Schmidt, R. J. and Sidebottom, O. M., 1993, Advanced Mechanics of Materials, Wiley.
4. ^{{cite journal|last=Ranganathan|first=S.I.|last2=Ostoja-Starzewski|first2=M.|date=2008|title=Universal Elastic Anisotropy Index|url=|journal=Physical Review Letters|volume=101|pages=055504–1–4}}

3 : Crystallography|Orientation (geometry)|Elasticity (physics)

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