Roger Musson & Others,

I wrote to Falk Koenemann querying his question No. 3 (but
did not post it on the discussion list immediately because I
wanted to find out if there was any basis what I wrote;
perhaps others can expand on my thoughts):

Koenemann asked:
"3. Which physical argument justifies Lagrange's conjecture
that it is strain that is causally related to stress despite
the fact that all experimental and natural evidence points
towards a cause-effect relation of stress to displacement?
Strain is by definition a tensor; according to current
understanding stress is assumed to be a tensor; displacement
is a vector field."

I put it to him that (paraphrased):
Text books (e.g. Twiss & Moores; Ramsay & Huber vol 1) and
general theory formulate the STRAIN tensor on the basis of
components of stretch and rotation, efectively (as I
understand it) describing displacement of particles in terms
of these parameters. That is, is the strain tensor not
formulated on parameters that describe a vector field?
If yes, and if the cause-effect relation of stress is with
displacement, and if the strain tensor is defined in terms
of vector field components (i.e. displacement), then I don't
really see (in principle) the problem of relating stress to
strain.

Parts of Koenemann's reply to me were (pardon me Falk for
passing on these paragraphs):
"Strain in the sense of Lagrange's definition is merely
stretch, ie lengthening and shortening. That is, strain does
_not_ tell you anything about particle positions, it tells
you only and exclusively about change of shape."

[Which I now, today, actually disagree with, because I think
that change in shape = relative change in particle positions
= relative displacements.]

"The problem is very much a semantic one. "Strain" has many
meanings; it is the strain in the sense of the strain
tensor; it is often used as a generic term in lieu of
"deformation", such as in "highly strained rocks"; and
sometimes it is definitely used for things where it should
not be, such as in "shear strain" which explicitly refers to
a particular displacement type; the reverse implication is
that unqualified (ie. non-shear) strain is a pure shear
strain.
Thus the terms strain and displacement are thoroughly mixed
up.

"I came to the conclusion that, just by looking at
Lagrange's definition, strain is only and exclusively the
change of shape, no matter if there is a rotational
component or not. If you consider particular ways how this
strain comes about - pure shear or simple shear - it is not
strain, but displacement.

"The definition of the strain tensor is mathematically
solid, no doubt about that. But why did Lagrange correlate
stress with strain?

"If stress is not a tensor, the effect may not be a tensor
either. That is, strain undoubtedly exists, but strain (in
the sense of the strain tensor, ie. change of shape only and
exclusively) may not be the physically relevant term. I
argue in contrast to Lagrange that if stress is a vector
field, the effect must be a vector field as well, and then
we can readily make a correlation of stress and
displacement.

" . . . - strain instead of displacement - is not
experimentally apparent unless you consider simple shear
and/or materials with low symmetry (the feldspars). . ."

Well, that's where I got to. Anyone else like to take it up?

Stephen White