Although these discussions are generating interest, I think it's
important for those involved in the discussions to clearly separate
their beliefs or opinions from currently recognized theory. For
example, statements like "you cannot retrieve displacement from
strain." Not everybody on this list is fully knowledgeable about
mechanics, so statements like this can be misleading.
In linear elasticity theory, infinitesimal strain components (i.e.,
the strain tensor) can be integrated directly to retrieve all three
displacement vector components. These relationships are embodied in
the kinematic equations upon which linear elasticity theory is based.
So what was meant by that statement?
Also, statements like "displacement is obviously more fundamental
than strain" are pretty bold and require at least some iota of
explanation.
As scientists, it is our responsibility to never confuse knowledge
with truth, and many historical earth scientists had to live down the
title of heretic before garnering ultimate respect. But bold
statements require clear, bold, convincing proof. Lacking that, our
current state of knowledge is all we have to fall back upon.
Simon
>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
>
>---------------------------------------------------------------------------
> 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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Simon Kattenhorn
Assistant Professor
Dept. of Geological Sciences
University of Idaho
P.O. Box 443022
Moscow, ID 83844-3022
Ph: (208) 885-5063 (office)
Ph.: (208) 885-5152 (lab)
FAX: (208) 885-5724
http://www.uidaho.edu/~simkat
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