Stress / strain deformation

Hi,

I've been reading up on orthotropic stress-strain and trying to wrap my head around some of the maths involved!

I've cobbled together something which starts to look somewhat similar to what I've seen in some papers / Wikipedia / etc. but I'm curious to know how it could be applied to finding deformations of objects, a la FEA style, and how to properly construct the input stress matrices and interpret the output strain matrices. The fun application of this might be to script some custom Kangaroo2 goals to approximate the deformation of more complex objects / meshes under various loads, etc. 

So, specific questions:

- How do you construct a stress matrix? I'm assuming that the normal stresses can be gotten from the components of some force vector (as I've done in the attached definition), but what about the shear stresses?

- How do you interpret the strain matrix? By the looks of it, using the diagonal values as scaling factors (after adding 1.0) seems to do what the books say it should do, i.e. elongate along the main force axis, while contracting along the other two (again, as in the attached def). But again, what about the shear strain?

- Finally, how would you begin to apply this to more complex bodies? I.e. meshes, voxels, or tetra grids?

Screenshot and definition attached.

P.S. I'm basing the compliance matrix on what I read in J. M. Dinwoodie, 2000, 'Timber: Its nature and behaviour', Chapter 6.2.4 Orthotropic elasticity and timber.