Derivation of Voigt's Shear Modulus

Click For Summary
SUMMARY

Voigt derived the average shear modulus of an anisotropic material using the formula G=1/5 (A-B+3C), where 3A=c11+c22+c33, 3B=c12+c13+c23, and 3C=c44+c55+c66. This derivation has not been thoroughly explained in contemporary literature, as most sources merely reference the result without detailing the underlying mathematics. The original derivation is found in Voigt's 1889 paper, which is in German and may require translation for non-German speakers.

PREREQUISITES
  • Understanding of anisotropic materials and their properties
  • Familiarity with tensor notation and compliance coefficients (c11, c12, etc.)
  • Basic knowledge of shear modulus and its significance in material science
  • Ability to translate or interpret historical scientific texts, particularly in German
NEXT STEPS
  • Research the derivation of Voigt's shear modulus in detail
  • Study the implications of anisotropic material behavior in engineering applications
  • Learn about the historical context of Voigt's work and its impact on modern material science
  • Explore translation tools or resources for understanding scientific literature in German
USEFUL FOR

Material scientists, mechanical engineers, and researchers interested in the properties of anisotropic materials and their mathematical derivations.

mgong21
Messages
1
Reaction score
0
TL;DR
How did Voigt derive the average shear modulus of an anisotropic material, G=1/5 (A-B+3C), where 3A=c11+c22+c33, 3B=c12+c13+c23, 3C=c44+c55+c66?
How did Voigt derive the average shear modulus of an anisotropic material, G=1/5 (A-B+3C), where 3A=c11+c22+c33, 3B=c12+c13+c23, 3C=c44+c55+c66?

The original text is published in German about 100 years ago. I looked for other papers explaining this, but none has explained the derivation. They simply quote the result.
 
Physics news on Phys.org
Welcome to PF.
Have you tried to 'google translate' Voigt's 1889 German paper ?