WhatDifference:same stress-strain curve for linear elastic material with nonlinear young's modulus and hyperelastic material

Hi everyone,

Now I am trying to implement Ogden model in Comsol Multiphysics, but I had some problem.

Then I realized that in Comsol, it's possible to implement a nonlinear young's modulus.

But I am a little confused.

If you have a nonlinear Young's modulus, in the stress-strain curve, E is the tangent of this curve.

For hyperelastic material, let's say Ogden material. It's usually a nonlinear stress-strain curve as well.

My problem is, even if you can get some function for E young's modulus for the linear elastic material, and this stress-strain curve can be fitted to Ogden stress-strain curve in order to get the same shape of curve.

To summarize, f we have a same stress-strain curve for linear elastic material(but nonlinear young's modulus, maybe under this condition, we shouldn't call it linear material now) and a Ogden hyperelastic material, can we say these two material are equivalent? To me, they shouldn't be equivalant, since the Nonlinear young's modulus is much easier than Hyper ogden, but if they are not equivalant, what's the difference. Since we usually care about only the stress and strain.

In comsol, we can see the equation actually, I copied both equations for these two materials attached in the file.

F11,F12 ... are the component of deformation gradient,

invF11 .... are the component of the inverse matrix of deformation gradient.

u, v, w are the displacement in the x , y and z direction

ux, uy, uz, means the du/dx, du/dy, du/dz.

 Any comment will be really appreciated.

Thanks a lot!

Xiaogai Li