A simple hyperelastic (1-DoF) calculatin sheet - non-linear method required

First either generate best-fit functions (stress = fn(strain)) to your curves, or use an interpolating table.

Then you can use force = area*fn(deltax/x) to find force from extension or a Given .. Find solve block to find extension from force. Along the lines of

deltax = initial guess

Given

force = area*fn(deltax/x)

deltax:=Find(deltax)

Alan

Your figure raises as many questions as it answers:

• What stress is plotted? The maximum principle stress? a "Von Mises" stress?
• Why three curves? (Guessing:

- The lowest curve is for a tension specimen type of loading where stress is considered uniform across the area when it isn't.

- The middle curve is a sheet with tension along opposing edges with width much less than thickness

- A sheet pulled in two orthogonal directions, which raises the questions: equally in both directions? And: Which stress ? (Again!)

At any rate, assuming that you can answer the questions like those above and that you know what your loading scenario is (to decide which curve to choose), your curves are single-valued; for any strain there is only one stress

9or only one strain for a given stress.) (I believe that if you find the answers to the questions above you'll find out that there is really only one curve and those three are based on different assumptions.) Whether the strain/stress relationship is linear or not, there's no need to iterate for a solution.