I would like to fit a couple of constitutive equations for uniaxial strain and see which of the models performs best. I am trying to fit both the eight chain model and the mooney rivlin model.
Before I can do this, I have however a couple of questions that I am hoping you can answer. I apologize if they seem trivial or dumb
On page 91 of your Phd thesis equation 3.15 states the continuum mechanics expression for the Cauchy stress. Is it possible to elaborate the derivation between eq. 3.15 and 3.16? This would help a lot.
Regarding eq. 3.17 and 18 is it true that 3*lambda^2=I1? Which I found in another paper on polymerfem.com. Because if this is true I cant rewrite 3.17 to become 3.18 since Im stuck with lambda^2.
When differentiating eq.3.13 with respect to lambda the dependence of beta (inverse langevin) on lambda seem to be ignored.is this correct?
How is expression 3.23 for incompressible uniaxial deformation obtained from eq 3.19, and why is this eq (3.23) different from the one stated in Modeling of the dynamic mechanical response of elastomers. (No division through a langevin term in the latter)
How would one obtain the Cauchy stress from a strain energy density function like mooney rivlin? And how would uniaxial tension stress be described?
I hope I havent bothered you too much, but Im really stuck.