Given the radial displacement in the form of a linear elasticity equation's solution, how do I calculate the stress tensor considering the solid is hookian?
Thanks for the reply....Nope...I was doing a problem and got stuck in the middle...How do I find F?....I found strain using the symmetric matrix relation but F?...
This is the relation but isnt this too simplistic? Wikipedia gives me a formula which involves sigma on the RHS for finding sigma. Something similar to the foll equation:
You can find F using the definition of a Neo-Hookean material. Differentiate the strain energy density function with respect to the deformation gradient and you should get the first Piola-Kirchhoff stress tensor as a function of strain.
Hmm .. this looks like
Hmm .. this looks like simple substitution.
\Sigma = F(strain)
You know strain (because it's a given quantity), you know F (because you know the material to be Neo-Hookean).
Is this a homework question?
In reply to Hmm .. this looks like by Amit.Ranade
Thanks for the
Thanks for the reply....Nope...I was doing a problem and got stuck in the middle...How do I find F?....I found strain using the symmetric matrix relation but F?...
This is the relation but isnt this too simplistic? Wikipedia gives me a formula which involves sigma on the RHS for finding sigma. Something similar to the foll equation:
In reply to Thanks for the by amberprince
I forgot to add that the
I forgot to add that the second equation is just and example where the sigma is present on either side.
In reply to Thanks for the by amberprince
You can find F using the
You can find F using the definition of a Neo-Hookean material. Differentiate the strain energy density function with respect to the deformation gradient and you should get the first Piola-Kirchhoff stress tensor as a function of strain.