Re: would inelastic (infinitely rigid) materials bounce off eachother?

Greetings, Richard:

As you have written, an "elastic" object is indeed one that
stores energy by compression.  But there is a little more to
it than just that.  One other feature of an elastic object is
that we can usually expect it to return to its original shape,
as the compression is relaxed.

As you also surmised, nonelastic materials behave differently.
But the difference is not what you implied, with respect to a
perfectly rigid material.  Instead, an inelastic object will
deform and STAY deformed.  Energy is not stored, but instead
is converted to heat inside the object, as molecules and/or
atoms are forced to move to new locations, and they experience
something like friction while doing so.

Thus, when two inelastic objects collide, a rebound is not a
given thing.  They may simply deform and stick together.  On
the other hand, just as there is no absolutely perfect elastic
solid substance, there is also no absolutely perfect inelastic
solid substance.  An "inelastic" thing may also be partly
elastic to some small degree, allowing it to store some energy
via compression, and thereby letting us compute some magnitude
of rebound after a collision.

Well, that may Answer your Question with respect to inelastic
objects, according to the meaning of the term in Physics, but
you have also, in a way, asked about the behavior of perfectly
rigid objects.  Even though there is no such thing, we can
still arrive at an Answer for that, too.

Consider that when any object experiences an impact, there is
some magnitude of Force involved in that event.  Well, Force
equals Mass times Acceleration, or (F)=(m)(a), and so that
Force of impact can be expected to lead to some Acceleration
and motion of the Mass-possessing object.  This Law of Physics
does not change if the object happens to be infinitely rigid!

Let us return to an ordinary elastic object for a moment.  As
a Force of impact occurs, the portion of the object where the
impact happened will experience some compression, as you know.
But there is more!  That "essence of compressed material" is
not a stationary thing!  The Force of impact actually causes
a WAVE of compression to begin moving through the body of the
object.  This wave can be thought of as the mechanism by which
the Force is "felt" by every portion of the object.  The speed
of this wave will equal the speed of sound in the substance of
the object, and for most solid objects, this is easily more
than a couple of kilometers per second.  After less than a
thousandth of a second, for most ordinary objects, the entire
object begins moving as a whole thing, rebounding from the
Force of impact.

Finally, regarding the hypothetical infinitely rigid object, a
logical consequence is that the speed of sound in the object
will be equal to infinity.  There will be no compression wave,
but the whole object will be instantly affected by the applied
Force!  It will rebound in accordance with (F)=(m)(a) WITHOUT
storing any energy!