Custom Newton Solver problem with Dirichlet conditions

8

Hi, I am also trying to achieve the same thing with boundary conditions as -

# Boundary conditions
class top(SubDomain):
    def inside(self, x, on_boundary):
        return on_boundary and near(x[1], 1., 1e-8)
class bot(SubDomain):
    def inside(self, x, on_boundary):
        return on_boundary and near(x[1], 0., 1e-8)

boundaries = MeshFunction("size_t", mesh, mesh.geometry().dim() - 1)

top().mark(boundaries, 1)
bot().mark(boundaries, 2)

bc_top = DirichletBC(V.sub(1), Constant(1.), boundaries, 1)
bc_bottom = DirichletBC(V, Constant((0., 0.)), boundaries, 2)

bc_u = [bc_bottom, bc_top]

And I modified the elasto-plastic code with 2 conditions stated by @bleyerj as -

Nitermax, tol = 200, 1e-6 # parameters of the Newton-Raphson procedure
Nincr = 20
load_steps = [1., 2., 3.]
results = np.zeros((Nincr+1, 2))

for (i,t) in enumerate(load_steps):
    A, Res = assemble_system(a, L, bc_u)     
    err0 = Res.norm("l2")
    err1 = err0
    print(err1/ err0)
    print("Increment:", str(i + 1))
    
    ## 1st iteration with nonzero DirichletBC conditions
    Du.interpolate(Constant((0, 0.1)))
    niter = 0
    while err1/err0 > tol and niter < Nitermax:
        solve(A, du.vector(), Res, "umfpack")
        Du.assign(Du+du)
        deps = eps(Du)
        sig_, n_elas_, beta_, dp_ = proj_sig(deps, sig_old, p)
        local_project(sig_, W, sig)
        local_project(n_elas_, W, n_elas)
        local_project(beta_, W0, beta)
        A, Res = assemble_system(a, L, bc_u)
        err1 = Res.norm("l2")  
        print(err1/err0)
        
        ## 2nd iteration onwards => zero DirichletBC conditions
        for bc in bc_u:
            bc.homogenize()
            
        niter += 1
    u.assign(u+Du)
    p.assign(p+local_project(dp_, W0))
    sig_old.assign(sig)    
    p_avg.assign(project(p, P0))
    results[i+1, :] = (u(0.5, 1.)[1], t)

But still the newton solver doesn’t converge and give nan values from 3rd iteration. Any guidance would be highly appreciable.
Thanks.
PS: Kindly have a look at my post Iterative solver diverging to get a better understanding of what I’m trying to do.

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