This document discusses stress and strain ellipsoids in structural geology. It defines stress as a force applied over an area that causes rock deformation. Stress can be tensional, compressional, or shear. Strain is the response of rock to stress and describes the change in shape of an object under stress. Stress and strain are represented geometrically using ellipsoids. The relationship between stress and strain ellipsoids is that the greatest and least axes are opposite. The orientation of stress and strain ellipsoids provides information about the deformative forces acting on rocks.

1. DOS in Earth Science, University of Mysore
Center for Advanced Studies in Precambrian Geology

2. Introduction
Stress
Strain
Deformation
cept of stress and strain ellipsoids
Stress ellipsoid
Strain ellipsoid
tion between stress and strain ellipsoid
Stress and strain ellipsoids

3. The aim of structural geologists is to analyse the
deformation of rock masses.
the deformation of the rock caused by the stress
developed in the rocks due to the external force resulted from
tectonic plate movements , subduction, and volcanic activity
To understand the deformation in rocks we should
analyse the stress and strain of that rocks.
Stress and strain of the rock geometrically represented
by constructing the stress and strain ellipsoids.

4. Stress on a rock body is defined as a force applied over an
area to cause the deformation.
Stress:
Tensional
compression
Shear

5. Stress on a rock body is defined as a force applied over an
area to cause the deformation.
Stress:
Tensional
compression
Shear

6. Stress on a rock body is defined as a force applied over an
area to cause the deformation.
Stress:
Tensional
compression
Shear

7. Stress on a rock body is defined as a force applied over an
area to cause the deformation.
Stress:
Tensional
compression
Shear
Stress acting on a plane
Normal stress
Shear stress
Shear stress

8. Strain:
Strain may be defined as response of rock to the stress,
which can be depends on temperature pressure and
mineralogical composition of rock.

9. Deformation:
Changes in the size, shape, position of the body with
respect to the original position of the body is known as
deformation.
DuctileBrittle

10. of stress and strain el
As the measurement of deformation certain initial body form
is required to be known.
Geologist deals with the rocks and minerals, so the amount of
change in the original shape of the mineral is measure of
deformation.
But since the minerals are of mixed shape the concept of stress
and strain ellipsoids put forth.

11. σ1
σ2
tress ellipsoid:
Stress ellipsoid or ellipse describes the state of stress at a point
in a rock.
Greatest
stress
Minimum
stress

12. tress ellipsoid:
Stress ellipsoid or ellipse describes the state of stress at a point
in a rock.
Greatest
stress(σ1)
Minimum
stress(σ3)
σ1
σ2
σ3

13. train ellipsoid:
It is the convenient way of visualising deformation is to
imagine the change in shape of imaginary sphere or circle.
A A'
B
B'

14. train ellipsoid:
It is the convenient way of visualising deformation is to
imagine the change in shape of imaginary sphere or circle.
S1
S2
S3

15. Compression Tension Shear

16. n ellipsoid - flinns diag
The Flinn diagram is a graphical representation used to plot
finite strain ellipsoids. The Flinn diagram describes two main
types of strain ellipsoids, cigar and pancake.
S1
S2
S3
a = S1/S2 b = S2/S3
K = a-1/b-1

18. etween stress and strain
The relation is exactly opposite between these ellipsoids in
respect to the position of greatest and least principle axis.
σ2
σ3
σ1
Stress ellipsoid
S2
S3
S1
Strain ellipsoid

19. Stress and strain
ellipsoids– Rupture
The position of the
fracture planes and their
orientation in field, are very
important, because only from
such data the direction of actual
deformative forces , the
orientation of stress and strain
ellipsoids can be derived.

20. σ1
σ2
σ3
S3
S2
Tensional fractures

21. Compression
fractures
Intermediate strain axis
S2
S1

22. S1
S2
S3
Normal fault
Stress and strain
ellipsoids -faults

23. Thrust fault
S2

24. S1
S2
Strike-slip fault

25. Conclusions:
Stress and strain ellipsoids can not be constructed in the case of
uniform stress conditions
Strain ellipsoid represents the effect of deformative forces applied
on the body of rock
With the help of deformation in rocks we can construct the strain
ellipsoid, from strain ellipsoid and with other evidences orientation
of stress ellipsoid can be draw.

26. References :
N.W.Gokhale(1996), theory of structural geology ,1st edition
CBS publishers and distributors, PP:136 -146
Marland P. Billings(1984), structural geology, 3rd edition
Prentice-hall of india private Ltd, PP:159-167, 231-233.
Haaken Fossen(2010), structural geology, 1st edition
Published by Cambridge university press, PP:30-32,72,23
Ben A. Van Der Pluijm(2004), Earth structure, 2nd edition
Published by W. W. Norton & Company, Inc. PP:65,46

27.  http://www.geosci.usyd.edu.au/users/prey/Teaching/Geol-
3101/Strain/STRAINe.htm
 http://homepage.ufp.pt/biblioteca/WebBasPrinTecton
ics/BasPrincTectonics/Page2.htm
 http://www.geosci.usyd.edu.au/users/prey/Teaching/
Geol-3101/Strain02/index.html
 http://www.geosci.usyd.edu.au/users/prey/Teaching/Geol-
3101/EReport03/GroupA/Report2/Kathy_E_Report.html