I have an issue where the following Nonlinear Elasticity code will not compile the form on the last line when the commented out code for "Q" is uncommented.
import dolfin as dl
dl.parameters["form_compiler"]["representation"] = "uflacs"
dl.parameters["form_compiler"]["quadrature_degree"] = 6
mesh = dl.UnitCubeMesh(1,1,1)
vectorP2Element = dl.VectorElement("P", mesh.ufl_cell(), 2)
scalarP1Element = dl.FiniteElement("P", mesh.ufl_cell(), 1) ]
TaylorHoodV = dl.FunctionSpace(mesh, dl.MixedElement([vectorP2Element,scalarP1Element]))
parameterV = dl.VectorFunctionSpace(mesh,"R",0,7)
y = dl.Function(TaylorHoodV)
ytest = dl.TestFunction(TaylorHoodV)
ytrial = dl.TrialFunction(TaylorHoodV)
u,p = dl.split(y)
a = dl.Function(parameterV)
atest = dl.TestFunction(parameterV)
atrial = dl.TrialFunction(parameterV)
#Model Parameters
m0 = 543.09
m1 = 4.73
m2 = 4.57
m3 = 5.27
m4 = 4.49
m5 = 4.49
m6 = 12.02
m = (m0,m1,m2,m3,m4,m5,m6)
parameters = dl.interpolate(dl.Constant(m),parameterV)
#Model
d = len(u)
I = dl.Identity(d) # Identity tensor
F = I + dl.grad(u) # Deformation gradient
C = F.T*F # Right Cauchy-Green tensor
J = dl.det(F) # Jacobian of deformation gradient
Cbar = C*(J**(-2.0/3.0)) # Deviatoric Right Cauchy-Green tensor
E = dl.Constant(0.5)*(Cbar-I) # Deviatoric Green strain
c0,c1,c2,c3,c4,c5,c6 = dl.split(parameters)
Q = c1*(E[0,0]**2)+c2*(E[1,1]**2)+c3*(E[2,2]**2) + c4*(dl.Constant(4.0)*(E[1,2]**2)) #+c5*(dl.Constant(4.0)*(E[0,1]**2))#)#+c6*(dl.Constant(4.0)*(E[0,2]**2))
Energy = dl.Constant(0.5)*c0*(dl.exp(Q)-dl.Constant(1.0))
IncompressibilityConstraint = (J-dl.Constant(1.0))
Lagrangian = p*IncompressibilityConstraint*dl.dx + Energy*dl.dx
yhat = dl.interpolate(dl.Constant((1,1,1,1)),TaylorHoodV)
residual_form = dl.derivative(Lagrangian,y,yhat)
residual_form_a = dl.derivative(residual_form, a,atest)
residual_form_y = dl.derivative(residual_form, y,ytest)
residual_form_ya = dl.assemble(dl.derivative(residual_form_y, a,atrial))
residual_form_ay = dl.assemble(dl.derivative(residual_form_a, y,ytrial))
residual_form_aa = dl.assemble(dl.derivative(residual_form_a, a,atrial))
residual_form_yy = dl.assemble(dl.derivative(residual_form_y, y,ytrial)) #error here
#Error: Unable to perform just-in-time compilation of form.
# Traceback (most recent call last):
# File "/workspace/fenics/2016.2_intel_mkl/bld/profile/cghe6hodndkt/lib/python2.7/site-packages/dolfin/compilemodules/jit.py", line 128, in jit
# result = ffc.jit(ufl_object, parameters=p)
# File "/workspace/fenics/2016.2_intel_mkl/bld/profile/cghe6hodndkt/lib/python2.7/site-packages/ffc/jitcompiler.py", line 198, in jit
# module = jit_build(ufl_object, module_name, parameters)
# File "/workspace/fenics/2016.2_intel_mkl/bld/profile/cghe6hodndkt/lib/python2.7/site-packages/ffc/jitcompiler.py", line 120, in jit_build
# generate=jit_generate)
# File "/workspace/fenics/2016.2_intel_mkl/bld/profile/cghe6hodndkt/lib/python2.7/site-packages/dijitso/jit.py", line 160, in jit
# header, source, dependencies = generate(jitable, name, signature, params["generator"])
# File "/workspace/fenics/2016.2_intel_mkl/bld/profile/cghe6hodndkt/lib/python2.7/site-packages/ffc/jitcompiler.py", line 66, in jit_generate
# prefix=module_name, parameters=parameters, jit=True)
# File "/workspace/fenics/2016.2_intel_mkl/bld/profile/cghe6hodndkt/lib/python2.7/site-packages/ffc/compiler.py", line 141, in compile_form
# prefix, parameters, jit)
# File "/workspace/fenics/2016.2_intel_mkl/bld/profile/cghe6hodndkt/lib/python2.7/site-packages/ffc/compiler.py", line 198, in compile_ufl_objects
# code = generate_code(oir, parameters)
# File "/workspace/fenics/2016.2_intel_mkl/bld/profile/cghe6hodndkt/lib/python2.7/site-packages/ffc/codegeneration.py", line 86, in generate_code
# for ir in ir_integrals]
# File "/workspace/fenics/2016.2_intel_mkl/bld/profile/cghe6hodndkt/lib/python2.7/site-packages/ffc/codegeneration.py", line 324, in _generate_integral_code
# code = r.generate_integral_code(ir, ir["prefix"], parameters)
# File "/workspace/fenics/2016.2_intel_mkl/bld/profile/cghe6hodndkt/lib/python2.7/site-packages/ffc/uflacs/uflacsgenerator.py", line 39, in generate_integral_code
# uflacs_code = generate_tabulate_tensor_code(ir, prefix, parameters)
# File "/workspace/fenics/2016.2_intel_mkl/bld/profile/cghe6hodndkt/lib/python2.7/site-packages/ffc/uflacs/uflacsgenerator.py", line 63, in generate_tabulate_tensor_code
# parts = ig.generate()
# File "/workspace/fenics/2016.2_intel_mkl/bld/profile/cghe6hodndkt/lib/python2.7/site-packages/ffc/uflacs/generation/integralgenerator.py", line 103, in generate
# body += self.generate_unstructured_partition(num_points, "piecewise")
# File "/workspace/fenics/2016.2_intel_mkl/bld/profile/cghe6hodndkt/lib/python2.7/site-packages/ffc/uflacs/generation/integralgenerator.py", line 409, in generate_unstructured_partition
# num_points)
# File "/workspace/fenics/2016.2_intel_mkl/bld/profile/cghe6hodndkt/lib/python2.7/site-packages/ffc/uflacs/generation/integralgenerator.py", line 351, in generate_partition
# vops = [vaccesses[op] for op in v.ufl_operands]
# KeyError: Sum(Product(Sum(Sum(Product(Sum(IntValue(1), Sum(Sum(Product(Indexed(ReferenceGrad(ReferenceValue(Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), -1), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange
Is there an easier way to write Q in terms of a quadratic form for E using a 4th order tensor for c that someone could help me with, if this issue can't be easily resolved? I believe this is an issue with FEniCS, not my code..
