Greg Egan
Jul6-07, 05:01 AM
In article <f6hdlb$8fg$1@theodyn.ncf.ca>, af250@FreeNet.Carleton.CA (John
Park) wrote:
> Greg Egan (gregegan@netspace.net.au) writes:
[snip]
> > The whole thing is based on a simple model of relativistic elasticity
> > which I call the "hyperelastic model", which assumes that the potential
> > energy per unit of unstretched length of the material obeys the formula:
> >
> > U = (k/2)(s-1)^2
> >
> > where s is the strain, or factor by which the material has been
> > stretched. This leads to the tension in the material being:
> >
> > -P = k(s-1)
> >
> So in the unstretched state, when the strain is zero, the tension is k?
Sorry, I've used the wrong terminology here in calling s "the strain".
Rather, s is the ratio of the current length of an element of the
material to its original, relaxed length. So in the unstretched state
s=1, and the tension is zero. The strain is s-1.
I should point out something else: this model is absurd for situations
of high compression, because a finite pressure of k allows the material
to be compressed to zero size (when s=0, P=k). But we're not using it
for situations of compression, and all the weird things happen in the
presence of tension (tension, however, that still falls well short of
violating the weak energy condition...)
Park) wrote:
> Greg Egan (gregegan@netspace.net.au) writes:
[snip]
> > The whole thing is based on a simple model of relativistic elasticity
> > which I call the "hyperelastic model", which assumes that the potential
> > energy per unit of unstretched length of the material obeys the formula:
> >
> > U = (k/2)(s-1)^2
> >
> > where s is the strain, or factor by which the material has been
> > stretched. This leads to the tension in the material being:
> >
> > -P = k(s-1)
> >
> So in the unstretched state, when the strain is zero, the tension is k?
Sorry, I've used the wrong terminology here in calling s "the strain".
Rather, s is the ratio of the current length of an element of the
material to its original, relaxed length. So in the unstretched state
s=1, and the tension is zero. The strain is s-1.
I should point out something else: this model is absurd for situations
of high compression, because a finite pressure of k allows the material
to be compressed to zero size (when s=0, P=k). But we're not using it
for situations of compression, and all the weird things happen in the
presence of tension (tension, however, that still falls well short of
violating the weak energy condition...)