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I am a newbie in fenics and finite element methods.

I try to implement a method to estimate the elasticity parameters (young modulus and poisson ratio) of a deformable object. What I want to do is this:

  • An object fixed from the bottom(as a start a cube)
  • To apply an external force on a particular place on the top of the object and using a method like gradient descent etc. estimate the elasticity parameters by comparing the real displacement and estimated displacement.

I am looking over Hyperelasticity demo in fenics (http://fenicsproject.org/documentation/dolfin/1.0.1/python/demo/pde/hyperelasticity/python/documentation.html) but I couldn't figure out how to apply to on a particular node on the mesh and then deform the object based on that force. I think in that demo a force is applied in the -y direction on the whole mesh. There is body force vector:
B = Constant((0.0, -0.5, 0.0))

Should I change this to a vector in the same size with the mesh and put a force value to on the element of the vector which corresponds to the nodal element on the mesh.

Sorry if I don not make much sense. This concepts are new for me so I am having troubles in stating what is in my head.

user1288289
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1 Answers1

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If it's an isotropic, homogeneous elastic material I'd say you don't need a cube. A 2D problem will do just fine.

I don't understand what you mean by "estimate elasticity parameters". You're going to have to input those values into the model in order to calculate a displacement. Are you suggesting that you have experimental data to compare to your calculated results. Is that correct?

I wouldn't apply a body force. If your body is a rectangle oriented along the x-axis with length L-x in the x-direction and L-y in the y-direction, I'd apply a traction (distributed uniform force) along the vertical face at x = L-x.

You can easily calculate the Young's modulus for a simple 1D body in tension: 

stress = modulus * strain

For 1D extension where strains are small:

sigma-xx = E * eps-xx

You know that 

sigma-xx = f-x/area-x = F/A

and 

eps-xx = u-x/L-x = u/L

Substituting:

F = (AE/L) * u

You can rearrange to get a simple equation for E:

E = FL/Au

where F = applied load, L = length of the body, A = cross-sectional area, u = displacement

If you know the relationship between shear stress and shear strain you can get a similar relationship for Poisson's ratio.

duffymo
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