Step 2: Shear Displacement

Features

• Tetrahedral cells

• pylith.meshio.MeshIOPetsc

• pylith.problems.TimeDependent

• pylith.materials.Elasticity

• pylith.materials.IsotropicLinearElasticity

• spatialdata.spatialdb.UniformDB

• pylith.meshio.OutputSolnBoundary

• pylith.meshio.DataWriterHDF5

• Static simulation

• LU preconditioner

• pylith.bc.DirichletTimeDependent

• spatialdata.spatialdb.SimpleDB

• spatialdata.spatialdb.ZeroDB

Simulation parameters

This example corresponds to shear deformation due to Dirichlet (displacement) boundary conditions. We apply Dirichlet (displacement) boundary conditions for the y displacement on the +x (boundary_xpos) and -x (boundary_xneg) boundaries and for the x displacement on the +y (boundary_ypos) and -y (boundary_yneg) boundaries. Fig. 39 shows the boundary conditions on the domain. The parameters specific to this example are in step02_sheardisp.cfg.

Fig. 41 Boundary conditions for shear deformation. We constrain the y displacement on the +x and -x boundaries and the x displacement on the +y and -y boundaries.

We create an array of 5 Dirichlet boundary conditions. On the -x, +x, -y, and +y boundaries we impose shear displacement.

Listing 49 Boundary conditions for Step 2. We only show the details for the -x boundary.

bc = [bc_xneg, bc_xpos, bc_yneg, bc_ypos, bc_zneg]
bc.bc_xneg = pylith.bc.DirichletTimeDependent
bc.bc_xpos = pylith.bc.DirichletTimeDependent
bc.bc_yneg = pylith.bc.DirichletTimeDependent
bc.bc_ypos = pylith.bc.DirichletTimeDependent
bc.bc_zneg = pylith.bc.DirichletTimeDependent

[pylithapp.problem.bc.bc_xneg]
label = boundary_xneg
label_value = 10
constrained_dof = [1]

db_auxiliary_field = spatialdata.spatialdb.SimpleDB
db_auxiliary_field.description = Dirichlet BC -x boundary
db_auxiliary_field.iohandler.filename = sheardisp_bc_xneg.spatialdb
db_auxiliary_field.query_type = linear

Running the simulation

Listing 50 Run Step 2 simulation

$ pylith step02_sheardisp.cfg

# The output should look something like the following.
 >> /software/unix/py39-venv/pylith-debug/lib/python3.9/site-packages/pylith/meshio/MeshIOObj.py:44:read
 -- meshiopetsc(info)
 -- Reading finite-element mesh
 >> /src/cig/pylith/libsrc/pylith/meshio/MeshIO.cc:94:void pylith::meshio::MeshIO::read(topology::Mesh *)
 -- meshiopetsc(info)
 -- Component 'reader': Domain bounding box:
    (-6000, 6000)
    (-6000, 6000)
    (-9000, 0)

# -- many lines omitted --

 >> /software/unix/py39-venv/pylith-debug/lib/python3.9/site-packages/pylith/problems/TimeDependent.py:139:run
 -- timedependent(info)
 -- Solving problem.
0 TS dt 0.01 time 0.
    0 SNES Function norm 1.811215061775e-02 
    Linear solve converged due to CONVERGED_ATOL iterations 1
    1 SNES Function norm 2.330640615892e-17 
  Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1
1 TS dt 0.01 time 0.01
 >> /software/unix/py39-venv/pylith-debug/lib/python3.9/site-packages/pylith/problems/Problem.py:201:finalize
 -- timedependent(info)
 -- Finalizing problem.

The output written to the terminal is nearly identical to what we saw for Step 1.

Visualizing the results

In Fig. 42 we use ParaView to visualize the x displacement field using the viz/plot_dispwarp.py Python script. First, we start ParaView from the examples/box-2d directory.

Listing 51 Open ParaView using the command line.

$ PATH_TO_PARAVIEW/paraview

# For macOS, it will be something like
$ /Applications/ParaView-5.10.1.app/Contents/MacOS/paraview

Next, we override the default name of the simulation file with the name of the current simulation.

Listing 52 Set the simulation in the ParaView Python Shell.

>>> SIM = "step02_sheardisp"

Finally, we run the viz/plot_dispwarp.py Python script as described in ParaView Python Scripts.

Fig. 42 Solution for Step 2. The colors of the shaded surface indicate the magnitude of the x displacement, and the deformation is exaggerated by a factor of 1000. The undeformed configuration is show by the gray wireframe.