I followed this excellent tutorial on the equations of linear elasticity and added the ability to import and mesh a .step file with 2nd order tetrahedrons. I can apply boundary conditions and solve for displacement successfully: [Screenshot 2025-02-16 at 9.31.49 PM] But when I compute the von mis…

The Von-Mises stresses are in the tutorial in a Dg-0 space as they contain the gradient of u through sigma in: s = sigma(uh) - 1. / 3 * ufl.tr(sigma(uh)) * ufl.Identity(len(uh)) von_Mises = ufl.sqrt(3. / 2 * ufl.inner(s, s)) As uh in the tutorial is a piecewise linear function, the gradient is a c…

[image] MattFerraro: What am I missing that makes the commercial results look so good and mine so poor? That this is precisely the strength of using a tool like FEniCS over commercial software. If the commercial software produces a smooth-looking von-Mises stress while using C^0 (e.g. piecewi…

Thank you for the help! Here is the code I’m running now, straight from the tutorial but modified so that u is a 2nd order Lagrange space: # Scaled variable import pyvista from dolfinx import mesh, fem, plot, io, default_scalar_type from dolfinx.fem.petsc import LinearProblem from mpi4py import MPI…

[image] MattFerraro: Traceback (most recent call last): File "/Users/matthewferraro/Documents/git/project/backend/linear_elasticity.py", line 91, in <module> warped.cell_data["VonMises"] = stresses.x.petsc_vec.array File "/Users/matthewferraro/miniconda3/envs/project/lib/python3.10/site-…

[image] MattFerraro: I modify epsilon (and/or sigma) to make it possible to have von mises live in a continuous function space? You can’t with a finite element method, without using finite elements with much higher regularity (H^2). This is not commonly done in FEM.

Thanks for the help! For posterity, all I had to do was make sure the von mises function space was ("Lagrange", 1) # Works and makes the solution piecewise linear and continuous V_von_mises = fem.functionspace(domain, ("Lagrange", 1)) stress_expr = fem.Expression( von_Mises, V…

[image] MattFerraro: This is exactly what I was looking for, and I think it is much better! This is not better from a mathematical point of view, as I tried to stress above. By moving something that is discontinuous into a continuous space, you are performing an operation that is not compati…

Gotcha, I did not understand that von mises stress really is discontinuous between cells. Given that is true, I see why enforcing continuity is in some sense “lying” about the data, which I do not want to do. So instead of: V_von_mises = fem.functionspace(domain, ("Lagrange", 1)) I switched to: V…

VTXWriter and VTKFile supports arbitrary order continuous and discontinuous Lagrange spaces, and should be used for outputting these variables. If you want to show the von Mises stresses on the deformed geometry, I would interpolate the displacement into the same DG-1 space, i.e. V_DG = dolfinx.fe…

I was able to get this working in the DG 1 space. I ended up writing my own viewer and I think it looks spectacular! [Screenshot 2025-02-28 at 9.41.37 PM] Thanks for your help!

Hi Matt, would you mind sharing your code for this? I’m working on an axisymmetric formulation for something similar at the moment and it would be very helpful for that!

How to make Von Mises Stress look better

General

Stein April 4, 2025, 7:21am 14

@kee You could consider pyvista4dolfinx. That should be a plug-and-play solution for you.

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How to make Von Mises Stress look better

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