from ufl import Coefficient, as_vector
from fenics import *

C01 = 12100.0
C10 = 7.99
k1  = 242300.0
k2  = 57.62

V = VectorElement("Lagrange", tetrahedron, 2)

f0 = Coefficient(V)
X = Coefficient(V)
F = grad(X)
C = F.T*F
I1 = tr(C)
I4 = inner(f0, C*f0)


P = 2.0*C01*C10*exp(C01*(I1-3))*F + 2.0*k1*(I4-1)*exp(k2*(I4-1.0)*(I4-1.0))*F*outer(f0,f0)


u = TrialFunction(V)
v = TestFunction(V)

# F = inner(first_PK_stress(disp), grad(v))*dx + inner(u, v)*dx
F = inner(F, grad(v))*dx(degree=5) + inner(u, v)*dx

a = lhs(F)
L = rhs(F)