Simon Kattenhorn schrieb:
Simon,
> 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?
There is no such thing as linear elasticity. Linear elasticity is like saying,
"at the scale of my office the earth is flat". The first objection to Hooke's
linear law came soon after it was proposed, from G.W. Leibniz, based on
experimental evidence. Hooke's experiments considers only the tiny initial part
of a function; from Hooke's date it cannot be decided if the function to which
they belong, are a part of y = ax, y = ln x, or y = sin x. That can only be
decided by looking at the conceptual context. We can conclude that y = sin x is
not an option because the idea that the work done decreases from some point on,
is nonsense. But how do you make the decision between the other two options?
> Also, statements like "displacement is obviously more fundamental
> than strain" are pretty bold and require at least some iota of
> explanation.
Leo did that.
> 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.
Would you accept experimental evidence? Is the known disparity between
infinitesimal and finite deformation theory enough? In another posting I
described the difference in the energetics of elastic/plastic-simple/pure shear
deformation.
The problem is that on the one hand, everybody knows that 1000 experiments
cannot prove a theory, but 1 well-placed experiment can prove a theory wrong. On
the other hand, this principle does not apply to continuum mechanics because
this theory is known to be correct. Experimental evidence to the contrary is
only evidence in the direction that our understanding of the theory is still
insufficient. - In the last sentence I am paraphrasing a number of opinions from
the literature. My efforts in this discussion are aimed at softening the ground
for all of you to consider the possibility that we do need a new theory - and
the courage to do it.
The approach which I offer, does not know the difference between infinitesimal
and finite deformation.
Falk Koenemann
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| Dr. Falk H. Koenemann Aachen, Germany |
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| stress elasticity deformation of solids plasticity strain |
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