Thin cylinder under internal pressure - hyperelastic?

[adlh01]

I'm trying to verify that some hyperlastic models I got from uniaxial data work in ANSYS. To do so, I am using a one-element uniaxial simulation (which works perfectly), and then I also wanted to do a simulation of another type of problem that I could solve analytically, to compare the results with a simulation of the same problem.

I'm using, as a guideline, a thesis written a few years ago by a professor's colleague. In it, the equations given to relate the hyperelastic energy function W to the stress and pressure are:

\sigma = \lambda \frac{\partial W}{\partial \lambda}

p = \frac{\sigma h}{r}


These aren't really sourced on the text nor have I seen them elsewhere. I'm getting some discrepancies between results obtained through the equations and results obtained through the simulations, regardless of which W function I use. I'm wondering if anyone can confirm that these relationships are correct?

 

[afreiden]

what are p, h, and r in your second formula?
Looks kind've like the simple formula for hoop stress of a thin-walled cylinder.. but aren't we talking about a FEA model?


The common way to relate the cauchy stress and the principal stretch is in index notation:
\sigma_i=\frac{1}{\lambda_j \lambda_k}\frac{\partial W}{\partial \lambda_i}

It is derived in Appendix C.3 here: http://utsv.net/solid-mechanics/appendix

Is this the same as what you wrote? In general, definitely not. However, perhaps for an incompressible material? If that's the case, however, I'd expect to see some pressure term in that relation., kind've like equation 2 here: http://utsv.net/solid-mechanics/hyperelasticity/phenomenological-and-micromechanical-models


Hope that helps