Explanation of stiffness/compliance matrices

[chiraganand]

Hi, can someone please explain how we get 9 independent constants for orthotropic materials in the stiffness/compliance matrix which is reduced from 21 constants of anisotropic materials. A detailed expanation is required and mathematics behind it

 

[Chestermiller]

Have you researched this on your own before asking us?

 

[chiraganand]

Have you researched this on your own before asking us?

Hi yes.. I have found information on why it is reduced because of the three planes of symmetry.. But I have failed to find a detailed explanation as to how these three planes of symmetry reduce the independent constants.. That's the explanation I am looking for.. Books say that yes for orthotropic materials there are three planes of symmetry and hence it gets reduced.. but i am looking for the maths behind that.. exactly how the planes of symmetry affect these constants