Isotropic and anisotropic subdomains in Linear Elasticity

General
1

Hi, im solving a underground mining problem, in this case, i have two materials (rocks types) in contact. In heterogeneus isotropic models, i can select diferents elasticity propierties like:

Er=30e3
Ev=25e3

class Young(UserExpression): # UserExpression instead of Expression
    def __init__(self, markers, **kwargs):
        super().__init__(**kwargs) # This part is new!
        self.markers = markers
    def eval_cell(self, values, x, cell):
        if self.markers[cell.index] == 1:
            values[0] = Er
      else:
            values[0] = Ev
E=Young(cd,degree=0)

And in homogeneus anisotropic models, i solve the problem whit a tensor like:

alfa=90
a=alfa*np.pi/180
G=5
nu=0.3
Ex=30
Ey=20
a11 = np.sin(a)**4/Ey + np.cos(a)**4/Ex + np.sin(2*a)**2*0.25*(1/G-2*nu/Ey)
a12 = np.sin(2*a)**2*0.25*(Ey**-1+Ex**-1-G**-1)-nu*Ey**-1*(np.cos(a)**4+np.sin(a)**4)
a16 = np.sin(2*a)*((np.sin(a)**2/Ey-np.cos(a)**2/Ex)+(0.5*G**-1-nu*Ex**-1)*np.cos(2*a))
a22 = np.cos(a)**4/Ey+np.sin(a)**4/Ex+np.sin(2*a)**2/4*(G**-1-2*nu/Ey)
a26 = np.sin(2*a)*((np.cos(a)**2/Ey-np.sin(a)**2/Ex)-(0.5/G-nu/Ey)*np.cos(2*a))
a66 = np.sin(2*a)**2*(1/Ey+1/Ex+2*nu/Ey)+np.cos(2*a)**2/G

S = as_matrix([[a11,a12,a16],[a12,a22,a26],[a16,a26,a66]])
C = inv(S)
x_max = 969.3292
def eps(v):
  return sym(grad(v))
def strain2voigt(e):
#"""e is a 2nd-order tensor, returns its Voigt vectorial representation"""
  return as_vector([e[0,0],e[1,1],2*e[0,1]])
def voigt2stress(s):
#"""
#s is a stress-like vector (no 2 factor on last component)
#returns its tensorial representation
#"""
  return as_tensor([[s[0], s[2]],
  [s[2], s[1]]])
def sigma(v):
  return voigt2stress(dot(C, strain2voigt(eps(v))))

But, now i need to implementate a model when one subdomain is an anisotropic rock and the other subdomain is an isotropic rock. I have not found the solution to this issue. I hope you can help me… Thanks