Bingham fluid  BinghamFluid
Constitutive model of Bingham fluid. This is a constitutive model of
nonNewtonian type. The model parameters are summarized
in Tab. 63.
In the Bingham model the flow is characterized by following
constitutive equation



(276) 



(277) 
where
is the shear stress applied to material,
is the shear stress measure,
is
the shear rate,
is the yield stress, and is the plastic
viscosity.
The parameters for the model can be in general determined using two
possibilities: (i) stress controlled rheometer, when the stress is applied
to material and shear rate is measured, and (ii) shear rate controlled
rheometer, where concrete is sheared and stress is measured. However,
most of the widely used tests are unsatisfactory in the sense, that
they measure only one parameter. These onefactor tests include slump
test, penetrating rod test, and VeBe test. Recently, some tests
providing two parameters on output have been designed (BTRHEOM, IBB,
and BML rheometers). Also a refined version of the
standard slump test has been developed for estimating yield stress and
plastic viscosity. The test is based on measuring the time necessary
for the upper surface of the concrete cone in the slump to fall a
distance 100 mm. Semiempirical models are then proposed for estimating
yield stress and viscosity based on measured results. The advantage
is, that this test does not require any special equipment, provided that
the one for the standard version is available.
In order to avoid numerical difficulties caused by the existence of
the sharp angle in material model
response at
, the numerical implementation uses
following smoothed relation for viscosity
where is so called stress growth parameter. The higher value of
parameter , the closer approximation of the original
constitutive equation (276) is obtained.
Table 63:
Bingham Fluid material  summary.
Description 
Bingham fluid material 
Record Format 
BinghamFluid num(in) #
d(rn) # mu0(rn) # tau0(rn) # 
Parameters 
 num material model number 

 d material density 

 mu0 viscosity 

 tau0 Yield stress 
Supported modes 
2d, 3d flow 

Borek Patzak
20180102