Stress and Strain - Quantitative Plate Tectonics - page 237

Fig. 7.14 Analog model
for the burgers rheology

from environmental parameters such as temper-
ature, pressure, and the frequency of the propa-
gating wave. Therefore, the study of anelasticity
gives valuable information about the physical
conditions and the rheological parameters of the
Earth's mantle.
We conclude this review of rheological models
with a short mention to the plastic rheology of
solids. Plasticity occurs when a body does not
deform until the stress has attained a critical
value £ c , which is referred to as the yield stress .
Starting from this point, a plastic body deforms
continuously under constant stress, thereby, we
can say that it cannot support a stress greater
than the critical value £ c . At the yield stress,
deformation is permanent and irreversible and
proceeds at constant rate. Therefore, ideally the
amount of deformation is unlimited as long as
the yield stress is maintained, and the strain rate
is independent of stress. Plastic strain is a form
of shear strain, thereby, it can only be associated
with shear stress.
An analog model for the plastic rheology is
given by a mass at rest on a flat and rough surface
( Saint - Venant body )(Fig. 7.15 ). Static friction
prevents displacement of the mass if the applied
stress £ is less than the frictional resistance. As
soon as £ overcomes the frictional resistance,
the mass starts moving. A key feature of plastic
deformation is that it implies strain localization ,
as strain may take place only locally, in regions
where the critical value of stress is reached.
Therefore, it is possible to use the plastic rheol-
ogy to build analog models describing the brittle
and ductile behaviours of the upper crust and the

Fig. 7.15 Response of a plastic body to a stress step. An
analog model for this system is a mass at rest on a rough
surface. There is continuous deformation at constant rate
for £ D

£ c

Fig. 7.16 Analog model for the visco-plastic rheology. © p
is the amount of plastic strain

upper part of subducting slabs, where deforma-
tion occurs either by seismic slip (associated with
faulting) or strain localization without loss of
continuity. In the simplest model, we combine the
plastic behaviour with an instantaneous elastic
response by the introduction of a spring element,
as shown in Fig. 7.16 . Such a rheological model
is called the Prandtl body , and the correspond-
ing mechanical behavior is referred to as the