Hi folks, I have been out of town, so my reply to this one is a little late.
Rob Twiss wrote:
> 3) Coaxial and non-coaxial deformation are probably the best
> generalizations of what people often mean when they talk of pure and simple
> shear in a geological context. If finite and incremental strain axes
> remain parallel throughout a deformation, it is coaxial; if they do not
> remain parallel, it is non-coaxial. Thus pure shear is coaxial; simple
> shear is non-coaxial. But coaxial deformation is more general than pure
> shear, and non-coaxial deformation is more general than simple shear.
> Coaxial and non-coaxial are useful characterizations of geological
> deformations, because the reference frames are internally defined by the
> deformation itself.
I think the problem may in part be the terminology itself. "Strain" is many
things: in the strict mathematical sense it is the change of shape expressed by
the strain tensor; but generally, "strain" is used almost synonymously with
"deformation" by many. What has nearly completely been forgotten is the
displacement field. For pure shear it is orthogonal, otherwise it is not.
I feel that "strain" should be used only and exclusively in reference to the
strain tensor. Rob Twiss's explanations can be summarized as follows (volume
constancy implied):
"If the principal axes of the strain tensor coincide with the
eigendirections of the displacement field during progressive
deformation, we observe a pure shear deformation;
otherwise there is at least some simple shear."
Putting the emphasis on the displacement field would relieve us from the awkward
discrepancy between infinitesimal and finite "strain" which is entirely
unnecessary. In fact, the very existence of this discrepancy clearly indicates
that strain by itself is kinematically irrelevant, and if so, it is surely
physically irrelevant.
> 4) We must not assume that the ideas of principal strain and
> principal stress can be used interchangably. [...] Since the
> relation of strain to stress is subject to considerable debate, we should
> restrict our discussions to strain.
Well spoken; but we are irrestistibly drawn to the subject of stress anyway
because (a) in physics we are interested in the relation of cause and effect,
and (b) if deformation is an effect, there must be a cause, which in all
likelihood is stress, whatever stress is. Restricting the discussion to the
properties of the effect is unsatisfying. If the stress-strain relation is
anything but clear as Rob correctly points out, this may be due to insufficient
understanding of stress, rather than strain.
But given the grave flaws in the theory of stress, that is not very surprising.
_______________________________________________________________
Falk H. Koenemann Aachen, Germany [log in to unmask]
http://home.t-online.de/home/peregrine/hp-fkoe.htm
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
