How to set up a function space consisting of multiple domains from an imported gmsh mesh for an elasticity analysis

[prusso630]

I also tried from:

Subdomain for different materials based on physical volume

Hi, I hope there is an existing answer: I have a complicated geometry with multiple materials combined, and I wish to use constant values that are unique to each material (e.g. Kappa in https://fenicsproject.org/pub/tutorial/sphinx1/._ftut1005.html). These materials are defined as Physical Volume in the mesh, so I wish to extract this data and apply that information to define these constants (k=1 for Physical Volume 1, k=1.25 for Physical Volume 2, etc.) without definind the boundary with mat…

import gmsh
import numpy as np
import pyvista
from dolfinx.fem import (Constant, dirichletbc, Function, FunctionSpace, assemble_scalar,
                         form, locate_dofs_geometrical, locate_dofs_topological)
from dolfinx.fem.petsc import LinearProblem
from dolfinx.io import XDMFFile
from dolfinx.mesh import create_unit_square, locate_entities,  locate_entities_boundary
from dolfinx.plot import create_vtk_mesh
from dolfinx.mesh import *
from ufl import (SpatialCoordinate, TestFunction, TrialFunction,
                 dx, grad, inner)
from mpi4py import MPI
from petsc4py.PETSc import ScalarType
from dolfinx.io import gmshio


mesh, materials, facet_markers = gmshio.read_from_msh("mesh3D.msh", MPI.COMM_WORLD, gdim=3) 

class EMod(UserExpression):
    def __init__(self,materials,volume_list,rho_list,**kwargs):
        super().__init__(**kwargs)
        self.materials = materials
        self.volume_list = volume_list
        self.rho_list = rho_list
    def value_shape(self):
        return ()
    def eval_cell(self,values,x,cell):
        values[0] = 0
        for i in range(len(self.volume_list)):
            if self.materials[cell.index] == self.volume_list[i]:
                values[0] = self.rho_list[i]   

volume_list = [11,12]                          # list of physical volume ID's
rho_list    = [100,200] # list of pre-defined values
rho = EMod(materials,volume_list,rho_list,degree=1)


#E.x.array[mu_indices] = np.full_like(mu_indices, 200, dtype=ScalarType)
#E.x.array[lambda_indices] = np.full_like(lambda_indices, 500, dtype=ScalarType)
print('done')

The difficulty here is that UserExpression is not being found. I looked around about UserExpression and found it to be deprected. Is it possible to switch over directly to Expression as opposed to UserExpression which was from fenics?