I Derivation of Voigt's Shear Modulus

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Voigt's derivation of the average shear modulus for anisotropic materials is expressed as G=1/5 (A-B+3C), where A, B, and C are defined in terms of the elastic constants c11, c22, c33, c12, c13, c23, c44, c55, and c66. The original text, published in German nearly a century ago, lacks clear explanations of the derivation, with most subsequent papers merely citing the result. Suggestions have been made to use translation tools to access Voigt's original work for better understanding. The discussion highlights a gap in available literature regarding the detailed derivation of this important modulus. Accessing the original paper may provide the clarity that current sources do not offer.
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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.
 
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Have you tried to 'google translate' Voigt's 1889 German paper ?
 

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