Plane strain and axisymmetric computations in small strain von Mises

demos/small_strain_vonMises_plasticity.py

@@ -3,8 +3,6 @@ import mfront_wrapper as mf
 import numpy as np
 import ufl
 
-hypothesis = "axisymmetric" # axisymmetric
-
 Re, Ri = 1.3, 1.   # external/internal radius
 # elastic parameters
 E = 70e3
@@ -20,59 +18,63 @@ mesh = Mesh("../meshes/thick_cylinder.xml")
 facets = MeshFunction("size_t", mesh, "../meshes/thick_cylinder_facet_region.xml")
 ds = Measure('ds', subdomain_data=facets)
 
-if hypothesis == "plane_strain":
-    q_lim = float(2/sqrt(3)*ln(Re/Ri)*sig0)
-    measure = 1
-elif hypothesis == "axisymmetric":
-    x = SpatialCoordinate(mesh)
-    q_lim = float(2*ln(Re/Ri)*sig0)
-    measure = 2*pi*abs(x[0])
 
 V = VectorFunctionSpace(mesh, "CG", 2)
-u  = Function(V, name="Displacement")
 bc = [DirichletBC(V.sub(1), 0, facets, 1), DirichletBC(V.sub(0), 0, facets, 3)]
 n = FacetNormal(mesh)
-loading = Expression("-q*t", q=q_lim, t=0, degree=2)
 
-mat_prop = {"YoungModulus": E,
-           "PoissonRatio": nu,
-           "HardeningSlope": H,
-           "YieldStrength": sig0}
-material = mf.MFrontNonlinearMaterial('../materials/src/libBehaviour.so',
-                                      'IsotropicLinearHardeningPlasticity',
-                                      hypothesis=hypothesis,
-                                      material_properties=mat_prop)
-problem = mf.MFrontNonlinearProblem(u, material, quadrature_degree=4)
-problem.set_loading(loading*dot(n, u)*measure*ds(4))
-problem.bc = bc
+for hypothesis in ["plane_strain", "axisymmetric"]:
+    u  = Function(V, name="Displacement")
+    if hypothesis == "plane_strain":
+        print("Expansion of a thick cylinder in plane strain")
+        q_lim = float(2/sqrt(3)*ln(Re/Ri)*sig0)
+        measure = 1
+    elif hypothesis == "axisymmetric":
+        x = SpatialCoordinate(mesh)
+        q_lim = float(2*ln(Re/Ri)*sig0)
+        measure = 2*pi*abs(x[0])
+    print("---------------------------------------------")
+    loading = Expression("-q*t", q=q_lim, t=0, degree=2)
+
+    mat_prop = {"YoungModulus": E,
+               "PoissonRatio": nu,
+               "HardeningSlope": H,
+               "YieldStrength": sig0}
+    material = mf.MFrontNonlinearMaterial('../materials/src/libBehaviour.so',
+                                          'IsotropicLinearHardeningPlasticity',
+                                          hypothesis=hypothesis,
+                                          material_properties=mat_prop)
+    problem = mf.MFrontNonlinearProblem(u, material, quadrature_degree=4)
+    problem.set_loading(loading*dot(n, u)*measure*ds(4))
+    problem.bc = bc
 
-p = problem.get_state_variable(name="EquivalentPlasticStrain")
-assert (ufl.shape(p) == ())
-epsel = problem.get_state_variable(name="ElasticStrain")
-assert (ufl.shape(epsel)==(4, ))
+    p = problem.get_state_variable(name="EquivalentPlasticStrain")
+    assert (ufl.shape(p) == ())
+    epsel = problem.get_state_variable(name="ElasticStrain")
+    assert (ufl.shape(epsel)==(4, ))
 
-file_results = XDMFFile("results/plasticity_results.xdmf")
-file_results.parameters["flush_output"] = True
-file_results.parameters["functions_share_mesh"] = True
-P0 = FunctionSpace(mesh, "DG", 0)
-p_avg = Function(P0, name="Plastic_strain")
+    file_results = XDMFFile("results/plasticity_{}_results.xdmf".format(hypothesis))
+    file_results.parameters["flush_output"] = True
+    file_results.parameters["functions_share_mesh"] = True
+    P0 = FunctionSpace(mesh, "DG", 0)
+    p_avg = Function(P0, name="Plastic_strain")
 
-Nincr = 40
-load_steps = np.linspace(0, 1.1, Nincr+1)[1:]**0.5
-results = np.zeros((Nincr+1, 2))
-for (i, t) in enumerate(load_steps):
-    loading.t = t
-    problem.solve(u.vector())
+    Nincr = 40
+    load_steps = np.linspace(0, 1.1, Nincr+1)[1:]**0.5
+    results = np.zeros((Nincr+1, 2))
+    for (i, t) in enumerate(load_steps):
+        loading.t = t
+        problem.solve(u.vector())
 
-    file_results.write(u, t)
+        file_results.write(u, t)
 
-    p_avg.assign(project(epsel[0], P0))
-    file_results.write(p_avg, t)
-    results[i+1, :] = (u(Ri, 0)[0], t)
+        p_avg.assign(project(epsel[0], P0))
+        file_results.write(p_avg, t)
+        results[i+1, :] = (u(Ri, 0)[0], t)
 
 
-import matplotlib.pyplot as plt
-plt.plot(results[:, 0], results[:, 1], "-o")
-plt.xlabel("Displacement of inner boundary")
-plt.ylabel(r"Applied pressure $q/q_{lim}$")
-plt.show()
+    import matplotlib.pyplot as plt
+    plt.plot(results[:, 0], results[:, 1], "-o")
+    plt.xlabel("Displacement of inner boundary")
+    plt.ylabel(r"Applied pressure $q/q_{lim}$")
+    plt.show()