implementing linear viscoelasticity in getfem

[Lesage,Anne Cecile J]

Dear all

 

I prepared those notes to adapt Pr Poulios’s script on Quasi nonlinear viscoelastic to linear viscoelastic

Please find some important part of the script

I do not know how to define Sv2 in my script it is the second part of the viscous stress

 

Thank you

BR

Anne-Cecile

 

Please find the script enclosed in the email

                    

 

mfub = gf.MeshFem(meshb, 3)

mfub.set_classical_fem(disp_fem_order)

mimu3b = gf.MeshIm(meshb, 5)   # integration displacement on tetrahedra brain

 

mfpb = gf.MeshFem(meshb, 1)

mfpb.set_classical_fem(press_fem_order)

mimp3b = gf.MeshIm(meshb, 5)   # integration pressure on tetrahedra brain

 

mimd3x3 = gf.MeshImData(mimp3b, -1., [3,3])                                      

 

md.add_fem_variable("ub", mfub)      # displacements field brain. poroelastic

md.add_fem_data("ub_prev", mfub)

md.add_fem_data("Svprev2", mfpb)

md.add_fem_variable("Sv2",mfpb)

 

md.add_initialized_data("G0", G0)

md.add_initialized_data("Ginf", Ginf)

md.add_initialized_data("nub", Nub)

md.add_initialized_data("beta", beta)

 

…

 

md.add_macro("H1","Grad_ub")

md.add_macro("H2","1.0/(1-2*nub)*Div(ub)")

md.add_macro("Hprev1","Grad_ub_prev")

md.add_macro("Hprev2","1.0/(1-2*nub)*Div(ub_prev)")

 

md.add_im_data("Svprev1", mimd3x3)   # Viscous  stress at previous timestep

md.add_macro("Sv1","Svprev1-beta*(G0-Ginf)*dt*0.5*(Hprev1+exp(-beta*dt)*H1)")

 

#md.add_im_data("Svprev2", mimp3b)   # Viscous  stress at previous timestep

md.add_macro("Sv2","Svprev2-beta*(G0-Ginf)*dt*0.5*(Hprev2+exp(-beta*dt)*H2)")

 

steps = ma.floor(tmax/dt)

steps = 4

 

# brain elastic

md.add_initialized_data('cmub', Mub)

md.add_initialized_data('clambdab', Lambdab)

 

assemelas = 3

 

if assemelas ==1:

   md.add_isotropic_linearized_elasticity_brick(mimu3b, 'ub', 'clambdab', 'cmub')

elif assemelas==2:

   md.add_linear_term(mimu3b, 'G0*Grad(ub):Grad(Test_ub)+G0/(1-2*nub)*Div(ub)*Div(Test_ub)')

elif assemelas==3:

   md.add_linear_term(mimu3b, 'G0*H1:Grad(Test_ub)+G0*H2*Div(Test_ub)')

  

viscous = 1

if viscous ==1:

   md.add_linear_term(mimu3b, 'Sv1:Grad(Test_ub)+Sv2*Div(Test_ub)')

 

 

if gravdir=='-X':

   print('Assembling buoyancy term along -ex\n');

   md.add_linear_term(mimu3b, 'Test_ub(1)*g*(rhot-rhoa*Heaviside(X(1)-csflevel)-rhow*Heaviside(-X(1)+csflevel))')

elif gravdir=='X':

   print('Assembling buoyancy term along ex\n');

   md.add_linear_term(mimu3b, 'Test_ub(1)*g*-1.0*(rhot-rhoa*Heaviside(-X(1)+csflevel)-rhow*Heaviside(X(1)-csflevel))')

elif gravdir=='-Z':

   print('Assembling buoyancy term along -ez\n');

   md.add_linear_term(mimu3b, 'Test_ub(3)*g*(rhot-rhoa*Heaviside(X(3)-csflevel)-rhow*Heaviside(-X(3)+csflevel))')

     

      

                                        

print('Solve problem with ', md.nbdof(), ' dofs')

time_elapsed(timer)

 

mass_mat = gf.asm_mass_matrix(mimp3b, mfpb)

 

######################################

# track landmarks

pos_tracked = gf.Slice("points", meshb, preopf)

 

 

 

for step in range(steps):

   nit, conv = md.solve('noisy', 'max_iter', 25, 'max_res', 1e-10, 'lsolver', 'mumps',

                                'lsearch', 'simplest', 'alpha max ratio', 100, 'alpha min', 0.2, 'alpha mult', 0.6,

                        'alpha threshold res', 1e9)

   time_elapsed(timer)    

   it = step+1

     

   mfoutb.export_to_vtu("LVE%sbrain_%i.vtu" % (patient,it),

                      mfub, md.variable("ub"), "Displacements")

   #np.savetxt("brain_displacements.txt",md.variable("ub"))

   #mfouth.export_to_vtu("PoroEResect25head_%i.vtu" % step,

   #                   mfuh, md.variable("uh"), "Displacements")

   md.set_variable("ub_prev", md.variable("ub"))

   md.set_variable("Svprev1", md.interpolation("Sv1", mimd3x3, -1))

   md.set_variable("Svprev2", md.variable("Sv2"))

  u_tracked = gf.compute_interpolate_on( mfub, md.variable("ub"), pos_tracked)

….

 

 

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NotesLinearViscoElasticGFem.pdf
Description: NotesLinearViscoElasticGFem.pdf