Here's a book with mineralogical
examples: McLellan, A.G., 1980. The
classical thermodynamics of deformable
materials. London: Cambridge Univ.
Press. It requires only linear algebra &
calculus, I believe; but it used to be
expensive.
I'm only observing this thread, with
interest, because I have no knowledge of
continuum mechanics. I didn't know this
was a thermodynamic topic, for an
agreement upon 'work' would seem to
precede thermodynamic theory.
Thanks to Robert Twiss for the excellent
reference.
Saying that, I should say why I am
slightly uncomfortable with his elegant
argument. This is for two reasons, which
others will understand better.
First, it drew upon a chapter on
thermodynamics. With heat added (and
using the second law, not just the
first), definitions of stress & strain
begin to increase in variety. I'm not
sure what stress tensor is a function of
'free energy' and Green's deformation
tensor, and what variables are held
constant. One can be sure though, that
work will be path-dependent in a
thermodynamic treatment: and so it was
(in general). This conclusion, which I
accept upon authority, appeared a
foregone conclusion when this chapter
was selected. No tensor algebra was
really needed -- except in restricting
'Green's deformation tensor' to
preserving volume.
With interest,
Bruce Bathurst
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