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.
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.