Interpolating a residual stress field in a new mesh

General
1

Hi,

I am doing something similar to Interpolation problem from mesh to mesh. I am trying to model a composite problem where there is an inclusion embedded in the matrix. In the inclusion, there is a residual stress field P_r, which need to be calculated from another simlation. Here is what I am planning to do:

  1. Calculate a function P_r in the first simulation with mesh1;
  2. During the first step, the function should be defined in the deformed configuration, so I have a set of deformed coordinates (x, y) and the corresponding function value, I will name it with P_r^*(x, y);
  3. Create a new mesh base on the displacement information in step 1;
  4. Apply this function as a flux term (residual stress) to the new mesh mesh2
  5. Model the inclusion problem with residual stress in another hyperelastic simulation.

Since I want to do some parametric study, i.e. changing matrix’s modulus, volume fraction of the inclusion, is there an elegant way to interpolate P_r^*(x, y) to a function defined on mesh2?

Note: It’s not easy to fit to some explicit form for this residual stress field.

Thank you in advance for any help!

2

With reference to the post you mentioned, you will notice that there is a call to dolfinx.fem.create_nonmatching_meshes_interpolation_data(...). If you need to do the interpolation several times, you may want to factor that out from the outer call to dolfinx.fem.Function..interpolate. That is

# Create nonmatching_meshes_interpolation_data once and for all
data = dolfinx.fem.create_nonmatching_meshes_interpolation_data(...)

# Create u1 and u2 once and for all
u1 = dolfinx.fem.Function(a function spaces that lives on mesh 1)
u2 = dolfinx.fem.Function(a function spaces that lives on mesh 2)

# Repeat interpolation several times
for i in range(100):
   u2.interpolate(u1)
3

Hi Francesco!

Thank you for your reply. You are my hero!!