I have an orthotropic material with a (6x1) stress vector known in the global coordinate system and yield surfaces known in a local coordinate system. So far I have only needed to convert from local to the global system and this has been done in the standard way of C = G.T*D*G where C is the stiffness matrix in the global coordinates, G is a 6x6 transformation matrix and D is the stiffness matrix in the local coordinate system. Now I need to convert my stresses living in the global system into stresses in the local system. The way I attempted to do this is using Sl = G.I*Sg, where Sl is the stress vector in the local coordinates and Sg is the stress vector in the globals, and G.I is the inverse of G. However I find that in some cases G is singular, ie not invertible.
Can anyone suggest a way around this problem, preferably by not inverting G?