Elasticity calculations involving rigid bodies

[MaxiLechner]

I've been trying to make the elasticity calculations work with rigid bodies. One problem that I've run into is that the calculations show the wrong scaling behavior and I'm not quite sure why that is the case. I've attached a notebook that demonstrates the behavior.

In short when shearing the system by the strain tensor $\hat \epsilon = \gamma \epsilon$ the function $(U - U_0) / V_0 - \sigma_0 \epsilon$ should scale as $\gamma^2$ but it scales as $\gamma^1$.

One possible culprit that I could imagine is that I'm not quite sure if the perturbation argument of the displacement function does the right job. It seems to me that it ignores the rigid body constraint which might explain the wrong scaling behavior.

If you happen to have a suggestion please let me know.