# Membrane theory in CMISS

I was wondering whether membrane theory was implemented properly in CMISS or not. This is because we have two options when defining your mechanisc equation to solve for: Plane stress and Membrane theory. When modelling skin for the multiaxial rig, people have chosen the Membrane theory option. But I just was not happy with just using it.

So, I looked up the book "Finite Elements of Nonlinear Continua" for an explanation of membrane theory. I then went through one newton iteration of example 512 from the CMISS example repository and made sure that the membrane theory option in CMISS was doing what the book said it should do.

After careful examination, I can say that CMISS does what the book says (compare ZERE50, ZGTG54, AG with pages from 302).

NOTE:

A second check has been made, as I have been experiencing some validation problems in my coupling scheme. I actually found that the residuals for membrane theory involve a multiplication by the initial undeformed thickness d. However, cmiss does not seem to do this. Therefore, for the same deformation (uniaxial displacement imposed on a 1 trilinear element 3d model of membrane and a 1 element 2d model of a membrane) the 2d model has reaction forces at nodes which are out by a factor of the thickness d.