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Table of Contents
"Fluid" materials
FluidHypoMaterial
Description
Material law describing a non viscous fluid.
Stresses are computed with
$$ \sigma_{ij} = s_{ij} + p\delta_{ij} $$
with $ s_{ij} = 0 $ in a non viscous fluid.
The equation which associates pressure and volume is
$$ dp = K \frac{dV}{V} $$
where $K$ is the bulk modulus.
Parameters
Name | Metafor Code | Dependency |
---|---|---|
Density | MASS_DENSITY | |
Bulk Modulus | BULK_MODULUS |
NortonHoffHypoMaterial
Description
Norton-Hoff law descriding a viscous fluid.
Stresses are computed with $$ \sigma_{ij} = s_{ij} + p \delta_{ij} $$
where $p$ is the hydrostatic pressure and $ s_{ij} $ the stress deviator tensor.
The stress deviator tensor ($ s_{ij} $) is determined upon the strain rate deviator tensor ($ D_{ij} $) through the following equation
$$ s_{ij} = 2 \mu D_{ij} \left( \sqrt{3} \ \sqrt{\frac{2}{3} D_{wz}.D_{wz}} \right)^{m-1}$$
Hydrostatic pressure is computed upon volume variation through the following eqation
$$ dp = K \frac{dV}{V} $$
where $K$ is the bulk modulus and $V$ the volume.
Parameters
Name | Metafor Code | Dependency |
---|---|---|
Viscosity parameter | NORTON_MU | TM |
Bulk modulus | BULK_MODULUS | TM |
Parameter m | NORTON_M | TM |
Density | MASS_DENSITY | TM |
Advice for modelling low viscosity fluid
NortonHoffPHypoMaterial
Description
This law is identical to NortonHoffHypoMaterial but it can account for the variation of the bulk modulus and the viscosity parameter with the hydrostatic pressure $p$.
Parameters
Name | Metafor Code | Dependency |
---|---|---|
Viscosity parameter | NORTON_MU | TM/IF_P |
Bulk modulus | BULK_MODULUS | TM/IF_P |
Parameter m | NORTON_M | TM |
Density | MASS_DENSITY | TM |
Accounting for bulk modulus variation with pressure
As mentionned above, the bulk modulus dependance with pressure must be linear.
$$ K(p) = K_0 + \frac{dK}{dp} p $$
Therefore two parameters must be provided by the user: the bulk modulus at atmospheric pressure and the derivative $\frac{dK}{dp}$
The function $K(p)$ is provided by the user through a PythonDirectorOneParameterFunction:
class MyBulkFunction(PythonDirectorOneParameterFunction): def __init__(self,_p): PythonDirectorOneParameterFunction.__init__(self) self.debugRefs() self.p = _p def __del__(self): print "MyBulkFunction : __del__ begin\n" print "callToDestructor of MyBulkFunction not allowed." print "Add MyBulkFunction.__disown__()" exit(1) def evaluate(self, pres): if pres>=0.0: # pression positive en traction ! return self.p['k0'] else : # pression négative en compression ! return self.p['k0']+self.p['dkdp']*pres def computeDerivation(self, pres): if pres>=0.0: return 0.0 else : return self.p['dkdp']
This class has to be defined above or below getMetafor().
The instance of MyBulkFunction is passed to the Norton Hoff material law thorugh the commands below
bulkLaw = MyBulkFunction(p) # <- p stands # for parameters dictionnary and not pressure materset = domain.getMaterialSet() materset.define(1,NortonHoffPHypoMaterial) materset(1).put(BULK_MODULUS , 1.0) materset(1).depend(BULK_MODULUS , bulkLaw, Field(IF_P)) materset(1).put(NORTON_MU , p['mu0'] ) materset(1).put(NORTON_M , 1.0 ) materset(1).put(MASS_DENSITY , p['rho'] )
TmNortonHoffHypoMaterial
Description
Norton-Hoff law including thermal aspects.
Parameters
Name | Metafor Code | Dependency |
---|---|---|
Density | MASS_DENSITY | |
Bulk modulus | BULK_MODULUS | |
Parameter m | NORTON_M | |
Viscosity parameter | NORTON_MU | |
Thermal expansion | THERM_EXPANSION | TO/TM |
Conductivity | CONDUCTIVITY | TO/TM |
Heat capacity | HEAT_CAPACITY | TO/TM |
Dissipated thermoelastic power fraction | DISSIP_TE | - |
Dissipated (visco)plastic power fraction (Taylor-Quinney factor) | DISSIP_TQ | - |