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plot(u)
plot(u)
interactive()
interactive()
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=== Mixed Formulation for Poisson Equation ===
This time we compare the code with the c++ version of DOLFIN.
{{Code|HyperElasticity Problem: the ufl file|<syntaxhighlight lang="octave" style="font-size:13px">
# Function spaces
element = VectorElement("Lagrange", tetrahedron, 1)
# Trial and test functions
du = TrialFunction(element) # Incremental displacement
v = TestFunction(element) # Test function
# Functions
u = Coefficient(element) # Displacement from previous iteration
B = Coefficient(element) # Body force per unit volume
T = Coefficient(element) # Traction force on the boundary
# Kinematics
I = Identity(element.cell().d) # Identity tensor
F = I + grad(u) # Deformation gradient
C = F.T*F # Right Cauchy-Green tensor
# Invariants of deformation tensors
Ic = tr(C)
J = det(F)
# Elasticity parameters
mu = Constant(tetrahedron)
lmbda = Constant(tetrahedron)
# Stored strain energy density (compressible neo-Hookean model)
psi = (mu/2)*(Ic - 3) - mu*ln(J) + (lmbda/2)*(ln(J))**2
# Total potential energy
Pi = psi*dx - inner(B, u)*dx - inner(T, u)*ds
# First variation of Pi (directional derivative about u in the direction of v)
F = derivative(Pi, u, v)
# Compute Jacobian of F
J = derivative(F, u, du)
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{{Code|Define Poisson problem|<syntaxhighlight lang="octave" style="font-size:13px">
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{{Code|Define Poisson problem|<syntaxhighlight lang="c++" style="font-size:13px">
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