underworld.function.rheology module

This module contains functions relating to rheological operations.

Module Summary

classes:

underworld.function.rheology.stress_limiting_viscosity

Returns a viscosity value which effectively limits the maximum fluid stress.

Module Details

classes:

class underworld.function.rheology.stress_limiting_viscosity(fn_stress, fn_stresslimit, fn_inputviscosity, *args, **kwargs)

Bases: underworld.function._function.Function

Returns a viscosity value which effectively limits the maximum fluid stress. Where the stress invariant (as calculated using the provided fn_stress) is greater than the stress limit (as provided by the fn_stresslimit), the returned viscosity will affect a fluid stress at the stress limit. Otherwise, fn_inputviscosity is passed through.

Parameters:

• fn_stress (underworld.function.Function) – Function which returns the current stress in the fluid. Function should return a symmetric tensor of floating point values.
• fn_stresslimit (underworld.function.Function) – Function which defines the stress limit. Function should return a scalar floating point value.
• fn_inputviscosity (underworld.function.Function) – Function which defines the non-yielded viscosity value. Function should return a scalar floating point value.

Example

Lets setup a simple shear type configuration but with a viscosity that increase vertically:

>>> import underworld as uw
>>> import underworld.function as fn
>>> mesh = uw.mesh.FeMesh_Cartesian(elementRes=(16,16), periodic=(True,False))
>>> velVar = uw.mesh.MeshVariable(mesh,2)
>>> pressVar = uw.mesh.MeshVariable(mesh.subMesh,1)

Simple shear boundary conditions:

>>> bot_nodes = mesh.specialSets["MinJ_VertexSet"]
>>> top_nodes = mesh.specialSets["MaxJ_VertexSet"]
>>> bc = uw.conditions.DirichletCondition(velVar, (top_nodes+bot_nodes,top_nodes+bot_nodes))
>>> velVar.data[bot_nodes.data] = (-0.5,0.)
>>> velVar.data[top_nodes.data] = ( 0.5,0.)

Vertically increasing exponential viscosity:

>>> fn_visc = 1.
>>> stokesSys = uw.systems.Stokes(velVar,pressVar,fn_visc,conditions=[bc,])

Solve:

>>> solver = uw.systems.Solver(stokesSys)
>>> solver.solve()

Use the min_max function to determine a maximum stress:

>>> fn_stress =  2.*fn_visc*uw.function.tensor.symmetric( velVar.fn_gradient )
>>> fn_minmax_inv = fn.view.min_max(fn.tensor.second_invariant(fn_stress))
>>> ignore = fn_minmax_inv.evaluate(mesh)
>>> import numpy as np
>>> np.allclose(fn_minmax_inv.max_global(), 1.0, rtol=1e-05)
True

Now lets set the limited viscosity. Note that the system is now non-linear.

>>> fn_visc_limited = fn.rheology.stress_limiting_viscosity(fn_stress,0.5,fn_visc)
>>> stokesSys.fn_viscosity = fn_visc_limited
>>> solver.solve(nonLinearIterate=True)

Now check the stress:

>>> fn_stress = 2.*fn_visc_limited*uw.function.tensor.symmetric( velVar.fn_gradient )
>>> fn_minmax_inv = fn.view.min_max(fn.tensor.second_invariant(fn_stress))
>>> ignore = fn_minmax_inv.evaluate(mesh)
>>> np.allclose(fn_minmax_inv.max_global(), 0.5, rtol=1e-05)
True