8-chain elasticity

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# 8-chain elasticity

Posts: 3
Topic starter
(@Chittyimivy)
New Member
Joined: 13 years ago

hi everybody!!

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.

best regards

magnus

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Posts: 3924
Moderator
(@jorgen)
Member
Joined: 2 years ago

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]. 😎

- Jorgen

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2 Replies
Posts: 3
Topic starter
(@Chittyimivy)
New Member
Joined: 13 years ago

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

best regards

magnus

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