> I have been reading through you paper a couple of times now but I od not see
> how it relates to anisotropic materials. I could be missing something or
> misunderstanding some parts. From what I can tell from the paper, the strong
> form of linear elasticity is:
>
> ∇· σ + b = 0 on Ω.
>
> where σ is the stress tensor which is modeled by σ = σ m + σ f. The isotropic
> linear constitutive law is given by: σm = C m : ε. Which is basically Hooke's
> law. Now, hooke's law does have an analogue for the polarization of a
> dielectric material when the material is exposed to an electric field. I am
> not very sure if this is the direction that I need to go in.
>
>
> I have been looking up anisotropic materials for linear elasticity. I might
> be
> missing something but I am having a hard time seeing how this relates to the
> electrostatic case? Maybe I need to spend a little bit more time on this
> topic. I do see that there is a similarity between div *[* *\epsilon* *e*] =
> \rho^{f} and ∇· σ + b = 0 where σ = *\epsilon* *e *and b = - \rho^{f}.
You have
sigma = C eps(u)
and
-div sigma = b
which together yields
-div (C eps(u)) = b
and is the equivalent of
-div (K grad u) = f
The elastic material is anisotropic if the stress-strain tensor C represents
an anisotropic material. In the elasticity case, it isn't just a dxd matrix,
but a dxdxdxd (rank-4) tensor. So it looks more complicated, but it isn't
really.
Best
W.
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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