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.