I am busy doing research on the properties of a certain Carbon Glass laminate.

I am tasked now with finding the interlaminar stresses in the sample. To do that, I have conducted a tensile test using a load cell and strain gauges.

The data that I have is as follows:

Strain Longitudinal - e1
Strain Transverse - e2
Force longitudinal - F
Cross sectional Area - A

Ok... my problem is how to go about this:

Consider this matrix:





-v12/E1 and -v21/E2 are interchangeable due to the relation:

v12/E1 = v21/E2

so I can then get the formulas:

e1 = s1/E1 - s2v12/E1
e2 = s2/E2 - s1v21/E2

(s1 = Sigma 1 and s2 = Sigma 2)

v12 is easy to find, -(e2/e1) = v12
s1 = F/A

Now the issue. If I calculate the elastic modulus (E1) from s1/e1, then I cannot substitute it into:
e1 = s1/E1 - s2v12/E1

reason being that e1 = s1/E1, so you will have a value that is equal to itself minus something, which is invalid. So the question is, if F is the force reading from the load cell and e1 and e2 are the readings from the strain gauges, would it be correct to say that:
E1 = s1/e1 ???

Or should I calculate E1 from the formula:
e1 = s1/E1 - s2v12/E1

as this is a bidirectional analysis and not unidirectional. It is also an orthotropic material, which means that E1 will not equal E2.

At present I have 3 equations and 4 unknowns.

e1 = s1/E1 - s2v12/E1
e2 = s2/E2 - s1v21/E2
v12/E1 = v21/E2

so either I need to find a fourth equation or if I calculate E1 directly from the test data, how will I substitute is correctly?

Am I making any sense at all?