Dear all,
I can subscribe to Slava's comments, but I also feel that Falk's theories
need to be taken seriously. One thing that I found out for myself early
1994 is that DISPLACEMENT IS OBVIOUSLY MORE FUNDAMENTAL THAN STRAIN
(although I agree with Stephen's comments on the semantic confusion)!
An easy argument for the above statement (which may be an open door to most
of you) is that the position gradient tensor has 3 invariants in 2D (6 in
3D), whereas the strain tensor (irrespective of whether you take Green's or
Cauchy's formulation) has only 2 invariants in 2D (3 in 3D).
This means that strain is a reduction (or, if you wish, an invariant) of
the displacement field. The strain tensor contains important information,
but not all information. You can calculate strain by multiplying the
position gradient tensor with its transposed matrix, but the opposite is
not possible: you cannot retrieve displacement from strain.
Intuitively, I would therefore think (but here I feel more uncertain) that
stress should be coupled to displacement rather than strain, and this could
lend some support Falk's ideas.
Regards,
Leo Kriegsman
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Leo M. Kriegsman
Professor of Geology and Mineralogy
Department of Geology fax: +358 2 333 6580
University of Turku tel: +358 2 333 5481
20014 Turku, FINLAND e-mail: [log in to unmask]
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