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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
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Comments
Yes, you can find equivalent expression
Hi xiaogai,
Yes, for sure you can find a mathematically equivalent formulation for any nonlinear material law just by assuming that the stiffness tensor (E is not enough in general) is a function of the deformation.
But such a "material law" will have no practical usage since it is mathematically more complex and reveals no insight on the physics behind it.
Models like Ogden or Mooney-Revlin are more popular even if they sometimes don't fit the experimental curves so well, since 1) they are relatively simple, 2) they have some physical interpretation.
Hope this helps.
Wei
Thanks!
Hi Wei,
Thanks a lot for your reply. This do help me understand this.
Xiaogai
ogden model in COMSOL
Hi Xiaogai,
Were you able to implement the ogden model or stress-strain function in COMSOL? I have a similar problem where I have a stress-strain curve for a hyper-elastic material and would like to implement it in COMSOL. Thank you for your time.
-Jason
Hi Jason, Sorry for the
Hi Jason,
Sorry for the late response. Yes, I managed with 2D implementation. For 3D there is a little problem!