Dugald Carmichael wrote:
> There seems to be no dispute that a physically correct theory must take
> account of the work done by shearing components of strain as well as normal
> components, whether or not the deformation is volume-neutral. Rob Twiss
> says the orthodox theory takes account of shearing work; Falk says it
> doesn't. Not being conversant with tensor algebra, I can't make out whether
> this disagreement involves physics or merely mathematical grammar/syntax.
One counter example would appear to
prove that the classical thermodynamics
of elastic materials is lacking. It
should predict that an isovolumetric,
forceful change of shape requires work.
(We all know that force is needed to
squeeze something.)
Dr Falk Koenemann has argued, correctly
I suspect, that classical thermodynamics
predicts such a change is requires no
work. Classical theory would suggest
that work, in a thermally insulated
system, is a function of volume change
alone. This note is to remind us that
this counter example exists only if a
forcefull, isovolumetric deformation
exists.
That this should exist is not intuitive
to me. If a cube of halite is placed
within a rigid, thermally insulating box
without a top, pressing down upon it
will change the shape & size of the
crystal. Thermodynamic theory demands
that, to attain equilibrium, an increase
in pressure be accompanied by a decrease
in volume. Why this should not be true
when the sides of the box are removed is
unclear to me.
Falk has successfully argued that
shearing stresses can be removed by
diagonalizing the stress tensor into the
equation of an ellipsoid. So classical
theory takes shearing stresses into
account. The theory would appear to
state that the work performed upon an
insulated system is a function simply of
its decrease in volume.
Respectfully,
Bruce Bathurst
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