# Issue with the incompressible elasticity example of JuAFEM package

Hi,

I plan to use the JuAFEM package as a basis for my phd work dealing with brittle damage modeling.
First of all, I would like to thank the authors(@kristoffer.carlsson et @fredrikekre) for this beautifully written package. I explored its interface by running some of the examples provided in the documentation. It turns out that I get weird results for simple cases.
I modified the example of the 2D incompressible elastic material to obtain a square domain with normal compressive boundary conditions on the upper and lower boundaries, without constraining displacements anywhere on the domain. The only changes made to the example are therefore :

This function is used instead of `create_cook_grid` :

``````function create_square_grid(nx, ny)
grid = generate_grid(Triangle, (nx, ny), Vec(0.0,0.0), Vec(50.0,50.0));
return grid
end;
``````

I removed the Dirichlet boundary conditions in `create_bc(dh)`, and the traction boundary conditions contributions to the force vector are replaced with:

``````@inbounds for face in 1:nfaces(cell)
if onboundary(cell, face) && (cellid(cell), face) ā getfaceset(grid, "top")
reinit!(facevalues_u, cell, face)
dĪ = getdetJdV(facevalues_u, q_point)
for i in 1:n_basefuncs_u
Ī“u = shape_value(facevalues_u, q_point, i)
fe[i] += (Ī“u ā t) * dĪ
end
end
elseif onboundary(cell, face) && (cellid(cell), face) ā getfaceset(grid, "bottom")
reinit!(facevalues_u, cell, face)
dĪ = getdetJdV(facevalues_u, q_point)
for i in 1:n_basefuncs_u
Ī“u = shape_value(facevalues_u, q_point, i)
fe[i] += (Ī“u ā -t) * dĪ
end
end

end
end
``````

with `t = Vec{2}((0.0,-1e8))`, `Emod = 70e9` and `Ī½ = 0.4999999`

With the quadratic/linear interpolation functions and a 50*50 elements domain, Iām getting a displacement field that doesnāt show the expected behavior.

Do you have any ideas as to why this is happening?
The same type of erroneous displacement field appears when I force only the vertical displacement of the upper and lower ends of the domain. The solution is only acceptable when the horizontal displacement of these same edges is set to zero.

I take this opportunity to ask you if you plan to develop a way to import meshes generated elsewhere?

Thank you!

1 Like

Donāt you still need to at least prescribe enough Dirichlet boundary conditions to remove rigid body motion so the system will not be singular? This is generally the case for standard formulations of stationary continuum mechanical problems.

For your example you should divide the domain along the symmetry line and put symmetric Dirichlet boundary conditions on it.

Yeah, there is code spread around in various repos that does this for Abaqus and Gmsh files but we havenāt put any āofficialā way of doing it into the JuaFEM repo yet.

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I import inp files to JuAFEM in TopOpt using a regex-based parser TopOpt.jl/src/TopOptProblems/IO/INP/Parser at master Ā· JuliaTopOpt/TopOpt.jl Ā· GitHub. But not all the features of inp are supported. You might want to read and extend it.

Oh, makes sense indeed! Itās the first time I explore this kind of problem. I worked on a finite difference geodynamical model of the lithosphere before, but I never had to ask myself this question.

Considering only the left part of my previous domain, and implementing Dirichlet boundary condition `ux = 0` along the right boundary, as well as `ux = uy = 0` on the bottom right corner node, with still the symmetric compressive Neumann boundary condition on the top and bottom boundaries, it now works like a charm, thanks!

Great to know that mesh import is available as well!

Thanks, iāll take a look at it!

1 Like