Isotropic Kelvin Material
As proposed by Kelvin [15] material strain
can be decomposed into
an elastic part
and visco-plastic part
:
 |
(129) |
with the elastic strain given as
 |
(130) |
where
is the deviatoric stress (Notice that
).
If the material is composed by materials
the visco-plastic strain can be decomposed as
 |
(131) |
where
is the strain in material
given as
 |
(132) |
where
is the viscosity of material
. We assume the following
betwee the the strain in material
with  |
(133) |
for a given power law coefficients
and transition stresses
, see [15].
Notice that
gives a constant viscosity.
After inserting equation 6.43 into equation 6.42 one gets:
with  |
(134) |
and finally with 6.40
 |
(135) |
The total stress
needs to fullfill the yield condition
 |
(136) |
with the Drucker-Prager cohesion factor
, Drucker-Prager friction
and total pressure
.
The deviatoric stress needs to fullfill the equilibrion equation
 |
(137) |
where
is a given external fource. We assume an incompressible media:
 |
(138) |
Natural boundary conditions are taken in the form
 |
(139) |
which can be overwritten by a constraint
 |
(140) |
where the index
may depend on the location
on the bondary.
Subsections
esys@esscc.uq.edu.au