This is the initial problem:

```
def TopBoundary(x, on_boundary):
return on_boundary and near(x[1],10) and x[0]<7.5 and x[0]>2.5
def BottomBoundary(x, on_boundary):
return on_boundary and near(x[1], 0)
class Subdomain1(SubDomain):
r = 2
center = (6, 6)
def inside(self, x, on_boundary):
return (x[0] - self.center[0]) ** 2 + (x[1] - self.center[1]) ** 2 <= self.r ** 2
class Subdomain2(SubDomain):
r = 1
center = (3, 2)
def inside(self, x, on_boundary):
return (x[0] - self.center[0]) ** 2 + (x[1] - self.center[1]) ** 2 <= self.r ** 2
class Subdomain3(SubDomain):
r = 0.5
center = (8, 3)
def inside(self, x, on_boundary):
return (x[0] - self.center[0]) ** 2 + (x[1] - self.center[1]) ** 2 <= self.r ** 2
domain = Rectangle(Point(0, 0), Point(10, 10))
subdomain = Subdomain1()
subdomain2 = Subdomain2()
subdomain3 = Subdomain3()
mesh = generate_mesh(domain, 64)
subdomains = MeshFunction("size_t", mesh, mesh.topology().dim())
subdomains.set_all(1)
subdomain.mark(subdomains, 0)
subdomain2.mark(subdomains, 0)
subdomain3.mark(subdomains, 0)
V0 = FunctionSpace(mesh, "DG", 0)
k = Function(V0)
square_G = 1e4
circle_G = 1e3
G_vals = [circle_G, square_G]
# Create the function space for the material function
# material_space = FunctionSpace(mesh, "DG", 0)
# material = Function(material_space) # Material function
for cell in (cells(mesh)):
subdomain_no = subdomains[cell.index()]
k.vector()[cell.index()] = G_vals[subdomain_no]
nu = 0.3
mu = k
lmbda = 2*k*nu/(1-2*nu)
def eps(v):
return sym(grad(v))
def sigma(v):
return lmbda*tr(sym(grad(v)))*Identity(2) + 2.0*mu*sym(grad(v))
V = VectorFunctionSpace(mesh, 'CG', 1)
# Define subdomain markers and integration measure
boundaries = MeshFunction("size_t", mesh, mesh.topology().dim() - 1)
AutoSubDomain(TopBoundary).mark(boundaries, 1)
ds = Measure('ds', domain=mesh, subdomain_data=boundaries, subdomain_id=True)
# Define boundary condition
bc2 = DirichletBC(V, Constant((0, 0)), BottomBoundary)
du = TrialFunction(V)
u_ = TestFunction(V)
a = inner(sigma(du), sym(grad(u_)))*dx
l = dot(Constant((0, -500)), u_)*ds(1)
# Solve the problem with the boundary condition
u = Function(V, name="Displacement")
solve(a==l, u, bc2)
```

I now want to apply the strain field from that Function to a new mesh:

```
rand_mesh = generate_mesh(domain, 64)
rand_V0 = FunctionSpace(rand_mesh, "DG", 0)
rand_k = Function(rand_V0)
new_square_G = 1e5 # Young's modulus
new_circle_G = 1e2
new_G_vals = [new_circle_G, new_square_G]
# code for random initialization
for cell in (cells(rand_mesh)):
subdomain_no = random.randint(0, 1)
rand_k.vector()[cell.index()] = new_G_vals[subdomain_no]
rand_V = VectorFunctionSpace(rand_mesh, 'CG', 1)
rand_boundaries = MeshFunction("size_t", rand_mesh, rand_mesh.topology().dim() - 1)
AutoSubDomain(TopBoundary).mark(rand_boundaries, 1)
rand_ds = Measure('ds', domain=rand_mesh, subdomain_data=rand_boundaries, subdomain_id=True)
# Define boundary condition
rand_bc2 = DirichletBC(rand_V, Constant((0, 0)), BottomBoundary)
du = TrialFunction(rand_V)
u_ = project(eps(u), rand_V)
a = inner(sigma(du), u_)*dx
l = dot(Constant((0, -500)), u_)*rand_ds(1)
```