Introduction to Elasticity/Constitutive example 5

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Example 5[edit | edit source]

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[edit | edit source]

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.