Dear all,
I've got some sort of a mathematical problem
concerning the relationship of stretch and k (as in the Flinn
diagram).
The stretch is defined as l/L, where l is the
finite length and L the initial lenght. The volumetric stretch s_v is defined in
the same fashion and it follows that:
s_v = v/V =
s_1*s_2*s_3
(1)
where the subscripts 1,2 and 3 denote the principal
stretches.
k relates the ratio of the principal stretches and
is defined as
k = (a-1)/(b-1) where a = s_1/s_2 and b =
s_2/s_3. (2)
I'd like to plot data in a Mohr circle for strain,
Flinn diagram etc. given the following data:
(1) The initial dimensions of the body L_x, L_y and
L_z,
(2) s_3 (maximum shortening),
(3) Dilatancy (in %), and
(4) the value of k.
It follows, that we have two equations and two
unknowns (i.e. s_1 and s_2).
There is no dilational component of extension along
the principal shortening axis s_3.
s_1 and s_2 comprise an extensional and a
dilational component. We assume that the non-dilational components along X and Y
are in the same ratio as the dilational components.
Looks pretty straightforward, but I just didn't
manage to get a solution. All I got was an equation in the form of:
ax^3 + bx^2 + c = 0
I'd be really grateful for a solution to that
problem.
All the best,
Martin
--------------------------------------------
Martin P.J.
Schöpfer
Fault Analysis Group
Department of Geology
University College
Dublin
Belfield
Dublin
4
EIRE
--------------------------------------------
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7162138
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