Elasticity/Constitutive example 5

Example 5

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Given:

An isotropic material with Young's modulus   and Poisson's ration  .

Find:

The compliance matrix of the material in terms of the Young's modulus and Poisson's ratio.

Solution

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The strain is related to the stress via the compliance matrix by the equation

 

For an isotropic material

 

Therefore,

 

In engineering notation,

 

Converting into matrix notation,

 

We may also write the above equation as

 

where   is the shear modulus.