- #1
honululu
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Homework Statement
Hello,
I am supposed to show that the quantity
TR=JTF-t
satisfies
TR=∂W/∂F
for some scalar function W(X, F, θ) in my continuum mechanics homework. The task is to identify this scalar function W(X, F, θ).
Homework Equations
This is part b) of a question. In part a), we get the following results which may or may not be relevant to the solution of the problem:
Constitutive equations are:
T=T(F,θ)
η=η(F,θ)
A=A(F,θ)
q=q(F,θ,gradθ)
where
η = -∂A/∂θ
TF-T = ρ*∂A/∂F
The Attempt at a Solution
By substitution of the results in 2., I got
TR=JTF-t
=J*ρ*∂A/∂F
=ρR(X)*∂A(F,θ)/∂F(X)
Is it as easy as saying that
W(X, F, θ) = ρR(X)*A(F,θ) ?
That's the solution I got but it seems too easy/I'm unsure... :D
I would greatly appreciate any advice.
Thank you so so much!
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