Geology Reference
In-Depth Information
7
Stress and Strain
Abstract
In this chapter, the fundamentals of continuum mechanics are presented,
in particular the concepts of stress and strain, and the general equations
of motion for a continuum medium. Finally, it is introduced the discipline
of rheology and the basic rheological models, which are widely used in
geodynamics.
world, by direct
pressure
along its boundary sur-
face. All these forces and force fields may simply
produce a change in the state of motion of a body,
if it has sufficient
rigidity
. In this instance, the
distance between any two points in the region
R
filled by the body does not change with time
and the relation between forces and motion is
described by Euler's equations (e.g., Goldstein
1980
). However, when we consider a tectonic
plate this representation is not generally ade-
quate, because in most cases plates deform under
the action of external forces. As soon as a body
changes its shape, a new force field is generated
within the deformed region
R
0
, which tries to re-
store the original undeformed shape
R
or simply
opposes deformation. This is a short-range force
field between adjacent molecules or atoms of the
body that can be represented as a
distributed
interaction across contact surfaces. Therefore, it
is usually referred to as a
surface forces
field.
A classic example of this class of forces is the
resistance opposed by a spring to an external
force during its extension or compression. An-
other example is the pressure field within a com-
pressed fluid, or its resistance to deformations
7.1
The Stress Tensor
In the first part of this topic, we have described
the principles of plate kinematics, hence the ge-
ometry of plate motions, independently from the
active and passive forces that drive the conti-
nental drift and the formation of new oceanic
crust. Now we are going to consider the system
of torques exerted on the lithosphere, and the
relation between these torques and deformation
processes at different time scales, using the for-
In the next chapters, we shall prove that both plate
motions and deformation of the lithosphere are
intimately related to the dynamics of the Earth's
mantle. Our starting point will be a review of the
relationships between forces and deformation in
a continuum body.
of
body forces
, which are external action-at-a-
distance force fields, such as gravity or magnetic
fields, that operate on each volume element
dV
of
a body. In addition to these forces, a body may
be subject to other interactions with the external
