i have a quite theoretical question regarding the arruda-boyce 8-chain model.
in their 1993 paper they give an expression for the free energy function and
then obtain the principal stresses of the cauchy stress by differentiation of the
energy function with respect to the principal stretches. so far is everything ok..
but the actual differentiation seems tricky to me, involving the inverse langevin
function and so on... can anyone give me a hint how to proceed here, perhaps
an reference.. since in the 1993 paper they just give the final result.
It actually turns out that the derivation might look ugly, but a few steps into it a lot of terms cancel each outher out. I think I added a more detailed derivation in my Ph.D. [URL= https://www.polymerfem.com/forums/showthread.php?t=9 ]thesis[/URL]. 😎
hi again jorgen!
thanks for the valuable hints, however i wounder if you could give me a hint
on how to calculate the term d \beta / d lambda* since this was not
written in your thesis.