Fem-fenics: Difference between revisions

Fem-fenics (edit)

Revision as of 13:05, 28 May 2014

1,289 bytes added , 28 May 2014

→‎Hyperelasticity: Add ufl snippet to the example m-file

Eg123

22

edits

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 {{Code|Define HyperElasticity problem with fem-fenics|<syntaxhighlight lang="octave" style="font-size:13px">
 pkg load fem-fenics msh
-problem = 'HyperElasticity';
-import_ufl_Problem (problem);
+ufl start HyperElasticity
+ufl # Function spaces
+ufl element = VectorElement("Lagrange", tetrahedron, 1)
+ufl
+ufl # Trial and test functions
+ufl du = TrialFunction(element)     # Incremental displacement
+ufl v  = TestFunction(element)      # Test function
+ufl
+ufl # Functions
+ufl u = Coefficient(element)        # Displacement from previous iteration
+ufl B = Coefficient(element)        # Body force per unit volume
+ufl T = Coefficient(element)        # Traction force on the boundary
+ufl
+ufl # Kinematics
+ufl I = Identity(element.cell().d)  # Identity tensor
+ufl F = I + grad(u)                 # Deformation gradient
+ufl C = F.T*F                       # Right Cauchy-Green tensor
+ufl
+ufl # Invariants of deformation tensors
+ufl Ic = tr(C)
+ufl J  = det(F)
+ufl
+ufl # Elasticity parameters
+ufl mu    = Constant(tetrahedron)
+ufl lmbda = Constant(tetrahedron)
+ufl
+ufl # Stored strain energy density (compressible neo-Hookean model)
+ufl psi = (mu/2)*(Ic - 3) - mu*ln(J) + (lmbda/2)*(ln(J))**2
+ufl
+ufl # Total potential energy
+ufl Pi = psi*dx - inner(B, u)*dx - inner(T, u)*ds
+ufl
+ufl # First variation of Pi (directional derivative about u in the direction of v)
+ufl F = derivative(Pi, u, v)
+ufl
+ufl # Compute Jacobian of F
+ufl J = derivative(F, u, du)
+delete HyperElasticity.ufl
+problem = 'HyperElasticity';
@@ Line 517: / Line 557: @@
 using namespace dolfin;
 // Sub domain for clamp at left end
@@ Line 626: / Line 706: @@
    // Solve nonlinear variational problem F(u; v) = 0
    solve(F == 0, u, bcs, J);