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2. Determine the body force field in conditions
of static equilibrium for the following stress
tensor:
£.x;y; z /
2
3
3x 2
C 5y 2 z 3 4x C 3xy 3x z
4x C 3xy
4
5
2x 3
D
4y 0
3
3x z
0
2 z 2
and comment the result;
3. Consider the following transformation of the
stress tensor:
£ ij ! £ ij C a• ij
Fig. 7.17 A simple rheological profile, illustrating the
variations of yield stress with depth ( solid line )
where a is a constant. What is the effect on the
principal axes?
4. What is the relation between the principal
axes of the stress tensor and those of the
deviator?
5. Find a constitutive equation for the standard
solid rheology and determine the creep and
relaxation curves.
This non-Newtonian flow behaviour is very com-
mon in silicate polycrystals at high temperature
and low stresses ( T > T s /2 and £ S between 10
and 100 MPa). The lower part of a rheological
profile for the lithosphere shows the rock strength
in a context of ductile deformation. It is largely
insensitive to hydrostatic pressure variations but
decreases exponentially with depth due to ther-
mal softening.
At any given depth, the strength is defined
as the lowest between brittle and ductile yield
stresses. Therefore, inverting ( 7.78 )for£ S and
assuming a temperature versus depth relation
(see Chap. 12 ) allows to build a lithospheric
strength profile like that illustrated in the
example of Fig. 7.17 . More complex profiles
can be built for different tectonic environ-
ments assuming specific crustal compositions,
lithospheric
References
Argus DF, Peltier WR (2010) Constraining models of
postglacial rebound using space geodesy: a detailed
assessment of model ICE-5G (VM2) and its relatives.
Geophys J Int 181(2):697-723
Brace WF, Kohlstedt DL (1980) Limits on lithospheric
stress imposed by laboratory experiments. J Geophys
Res 85(B11):6248-6252
Byerlee JD (1968) Brittle-ductile transition in rocks. J
Geophys Res 73(14):4741-4750
Findley WN, Lai JS, Onaran K (1989) Creep and relax-
ation of nonlinear viscoelastic materials. Dover Books,
London, p 371
Goldstein
layering,
and
temperature
field
(e.g., Ranalli and Murphy 1987 ).
H
(1980)
Classical
mechanics,
2nd
edn.
Addison-Wesley, Reading, p 672
Ranalli G (1995) Rheology of the earth, 2nd edn. Chap-
man & Hall, London, p 413
Ranalli
Problems
G,
Murphy
DC
(1987)
Rheological
stratifi-
cation
of
the
lithosphere.
Tectonophysics
132(4):
281-295
Schubert G, Turcotte D, Olson P (2001) Mantle convec-
tion in the earth and planets. Cambridge University
Press, Cambridge, p 940
Turcotte DL, Schubert G (2002) Geodynamics, 2nd edn.
Cambridge University Press, Cambridge, p 848
Wang K, Hu Y, He J (2012) Deformation cycles of
subduction earthquakes in a viscoelastic earth. Nature
484(7394):327-332
1. Find the principal axes for the 2-D stress
20 p 125
MPa and de-
p 125 40
tensor: £ D
termine: (1) the components of traction on
a vertical fault oriented E-W; (2) the plane
of maximum shear stress and the shear and
normal stresses along this plane;
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