Stress analysis

The following example from the ogs benchmark collection is used for the stress analysis:

<https://www.opengeosys.org/docs/benchmarks/thermo-mechanics/creepafterexcavation/>

import ogstools as ot
from ogstools import examples

mesh = examples.load_mesh_mechanics_2D()
fig = ot.plot.contourf(mesh, ot.variables.displacement)

Tensor components

We can inspect the stress (or strain) tensor components by indexing.

fig = ot.plot.contourf(mesh, ot.variables.stress["xx"])
fig = ot.plot.contourf(mesh, ot.variables.stress["xy"])

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Principal stresses

Let’s plot the the principal stress components and also overlay the direction of the corresponding eigenvector in the plot. Note: the eigenvalues are sorted by increasing order, i.e. eigenvalue[0] is the most negative / largest compressive principal stress.

eigvecs = ot.variables.stress.eigenvectors
fig = ot.plot.contourf(mesh, variable=ot.variables.stress.eigenvalues[0])
ot.plot.quiver(mesh, ax=fig.axes[0], variable=eigvecs[0], glyph_type="line")

fig = ot.plot.contourf(mesh, variable=ot.variables.stress.eigenvalues[1])
ot.plot.quiver(mesh, ax=fig.axes[0], variable=eigvecs[1], glyph_type="line")

fig = ot.plot.contourf(mesh, variable=ot.variables.stress.eigenvalues[2])
ot.plot.quiver(mesh, ax=fig.axes[0], variable=eigvecs[2], glyph_type="line")

We can also plot the mean of the principal stress, i.e. the magnitude of the hydrostatic component of the stress tensor. see: ogstools.variables.tensor_math.mean()

fig = ot.plot.contourf(mesh, ot.variables.stress.tensor_mean)

Von Mises stress

see: ogstools.variables.tensor_math.von_mises()

fig = ot.plot.contourf(mesh, ot.variables.stress.von_Mises)

octahedral shear stress

see: ogstools.variables.tensor_math.octahedral_shear()

fig = ot.plot.contourf(mesh, ot.variables.stress.octahedral_shear)

Stresses in polar coordinates

You can inspect stresses in a polar coordinate system by deriving a new Variable from the stress Variable. Specify the polar center and, if needed, the rotation axis (default is z-axis: [0, 0, 1]).

polar_stress = ot.variables.stress.to_polar(center=(150, -650, 0))
fig = ot.plot.contourf(mesh, polar_stress["rr"])
fig = ot.plot.contourf(mesh, polar_stress["tt"])
fig = ot.plot.contourf(mesh, polar_stress["pp"])

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Here is a 3D example with a cylindrical hole at (0, 0, 0) in y direction:

mesh_3D = examples.load_mesh_mechanics_3D_sphere()
polar_stress_3D = ot.variables.stress.to_polar()
for comp in ["rr", "tt", "pp"]:
    pl = ot.plot.contourf(mesh_3D, polar_stress_3D[comp])
    pl.view_xz()
    pl.show()

Static Scene

Interactive Scene

Static Scene

Interactive Scene

Static Scene

Interactive Scene

Integrity criteria

Evaluating models regarding their integrity is often dependent on the fluid pressure. If not already present, we have to calculate it manually, e.g. as a hypothetical water column proportional to the depth.

mesh["pressure"] = -1000 * 9.81 * mesh.points[:, 1]
fig = ot.plot.contourf(mesh, ot.variables.pressure)

Dilantancy criterion

see: ogstools.variables.mesh_dependent.dilatancy_critescu()

fig = ot.plot.contourf(mesh, ot.variables.dilatancy_critescu_tot)
fig = ot.plot.contourf(mesh, ot.variables.dilatancy_critescu_eff)

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Fluid pressure criterion

see: ogstools.variables.mesh_dependent.fluid_pressure_criterion()

fig = ot.plot.contourf(mesh, ot.variables.fluid_pressure_crit)