Visualizing deformed geometry together with stresses in Paraview

I/O
1

How can one store the deformation field and the stresses in the same XDMF file such that one can deform the geometry by the deformation field and color the result by the stress field in ParaView?

Essentially, I want the same visualization that is done with pyvista in the linear elasticity tutorial but in ParaView.

I tried the following (adapted from the linear elasticity tutorial):

import pyvista
from dolfinx import mesh, fem, plot, io, default_scalar_type
from dolfinx.fem.petsc import LinearProblem
from mpi4py import MPI
import ufl
import numpy as np

L = 1
W = 0.2
mu = 1
rho = 1
delta = W / L
gamma = 0.4 * delta**2
beta = 1.25
lambda_ = beta
g = gamma

domain = mesh.create_box(
    MPI.COMM_WORLD,
    [np.array([0, 0, 0]), np.array([L, W, W])],
    [20, 6, 6],
    cell_type=mesh.CellType.hexahedron,
)
V = fem.functionspace(domain, ("Lagrange", 1, (domain.geometry.dim,)))


def clamped_boundary(x):
    return np.isclose(x[0], 0)


fdim = domain.topology.dim - 1
boundary_facets = mesh.locate_entities_boundary(domain, fdim, clamped_boundary)

u_D = np.array([0, 0, 0], dtype=default_scalar_type)
bc = fem.dirichletbc(u_D, fem.locate_dofs_topological(V, fdim, boundary_facets), V)
T = fem.Constant(domain, default_scalar_type((0, 0, 0)))
ds = ufl.Measure("ds", domain=domain)


def epsilon(u):
    return ufl.sym(ufl.grad(u))


def sigma(u):
    return lambda_ * ufl.nabla_div(u) * ufl.Identity(len(u)) + 2 * mu * epsilon(u)


u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
f = fem.Constant(domain, default_scalar_type((0, 0, -rho * g)))
a = ufl.inner(sigma(u), epsilon(v)) * ufl.dx
L = ufl.dot(f, v) * ufl.dx + ufl.dot(T, v) * ds


problem = LinearProblem(
    a, L, bcs=[bc], petsc_options={"ksp_type": "preonly", "pc_type": "lu"}
)
uh = problem.solve()

s = sigma(uh) - 1.0 / 3 * ufl.tr(sigma(uh)) * ufl.Identity(len(uh))
von_Mises = ufl.sqrt(3.0 / 2 * ufl.inner(s, s))

V_von_mises = fem.functionspace(domain, ("DG", 0))
stress_expr = fem.Expression(von_Mises, V_von_mises.element.interpolation_points())
stresses = fem.Function(V_von_mises)
stresses.interpolate(stress_expr)

with io.XDMFFile(domain.comm, "result.xdmf", "w") as xdmf:
    xdmf.write_mesh(domain)
    uh.name = "Deformation"
    xdmf.write_function(uh)
    stresses.name = "Von Mises"
    xdmf.write_function(stresses)

However, in Paraview, I can only color the deformed geometry by the deformation field, but not by the stresses. I suppose the problem is that there are multiple blocks in the XDMF that cannot interact in this way.

2

You can first extract each of the blocks, then use “Append Attributes” to combine them into one dataset:

image
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