stress in a non linear elastic material
A strain gage is exactly what its name says it is: a gage that measures strain. Gage answers the question: "How much did the material beneath the gage expand or contract?"
Information about stress from a strain gage is derived indirectly from the material properties relating strain to stress. In linear materials, this answer comes from a nice easy linear equation, strain = stress * modulus.
For a non-linear material, the equation is more complex, as the modulus changes as strain changes. No linear equation. If you are ambitious and know the material well, you can use calculus to integrate. Only if you like pain, though.
Easy method: You can still use the material's stress vs. strain graph to get stress from strain. All you need to do is match the point on the curve with the given strain value to get the stress. No stress-strain graph? Make one, by experimentation or have a lab do it for you.