Derivation of Voigt's Shear Modulus

In summary, Voigt's shear modulus is a material property that describes the resistance of a material to shear stress. It is derived using the Voigt model, which assumes a material is composed of a spring and dashpot in parallel. This property is important for understanding the mechanical behavior of materials and is commonly used in engineering applications. It differs from other types of shear modulus and can be measured experimentally using various techniques.
  • #1
mgong21
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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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  • #2
Welcome to PF.
Have you tried to 'google translate' Voigt's 1889 German paper ?
 

1. What is Voigt's shear modulus?

Voigt's shear modulus is a material property that describes the resistance of a material to shear deformation. It is a measure of the stiffness of a material when it is subjected to shear stress.

2. How is Voigt's shear modulus derived?

Voigt's shear modulus is derived from the elastic moduli of a material, specifically the Young's modulus and the Poisson's ratio. It is calculated using a mathematical equation that takes into account the material's shear stress and shear strain.

3. What is the significance of Voigt's shear modulus?

Voigt's shear modulus is an important material property in the field of solid mechanics. It is used to predict the behavior of materials under shear stress, which is important in various engineering applications such as in the design of structures and machines.

4. How does Voigt's shear modulus differ from other shear moduli?

Voigt's shear modulus is one of several shear moduli used to describe the behavior of materials under shear stress. It differs from other shear moduli, such as the Reuss shear modulus and the Hill shear modulus, in the way it takes into account the material's elastic properties.

5. Can Voigt's shear modulus be experimentally determined?

Yes, Voigt's shear modulus can be determined experimentally by performing shear tests on a material and measuring its shear stress and shear strain. These values can then be used to calculate the shear modulus using the appropriate equation.

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