Reverse Classical Laminate Theory

[Ld3Ake]

Hi, has anyone tried performing classical laminate theory in reverse, i.e. getting lamina stiffness and strength values from experimental laminate data? I have been attempting to do so but I can’t seem to get my formulation to work correctly. I’m 99% sure it is correct because I can go from Q Matrix ---> A Matrix, but not the reverse calculation.

Surprisingly there doesn’t appear to be any commercial software that calculates this, and I have only found two academic papers which mention the reverse process. I’ve attached a PDF showing my workings as that will be a lot clearer than writing it out here.

Thanks for any help

 

[SWComposites]

You are trying to solve for 4 unknowns. You will need data for at least 4 different laminates in order to back out the values. I don't have time to bother working thru all of the algebra, but it should be do able. But the values for E2, G12 and nu12 for many laminates only have a small effect on Ex so experimental error may be too large to accurately back those values out. Best to assume reasonable values for E2, G12, nu12 and back out E1 values (this assumes you are dealing with uni tape).

 

[Ld3Ake]

I am actually testing woven fabrics but I am trying to back out an equivalent unidirectional laminate so I can use the properties for FEA. In the end I managed to get my program to work but I had to make some tweaks to it after working out what was the problem. Basically for a balanced laminate the A11 and A22 equations are the same, e.g. for a 0/90/90/0 laminate:

A11 = [2*Q11 + 2*Q22] * t
A22 = [2*Q11 + 2*Q22] * t

(Note that Q11 and Q22 are of course reversed for 0 and 90 plies but as they are the same value the summation is still the same result)

This means that it is impossible to find a unique solution of Q11 and Q22. The only way you can do this is if you eliminate one of the unknowns and choose a value for it – so I got rid othe Q22 equation as I can calculate E2 from micromechanics. It’s quite annoying and feels wrong to have to use a theoretical calculation to derive experimental results. I am not a mathematician so I can’t explain why these equations won’t reverse to a unique solution.