def test_3d(self):
prm = c.Parameters(c.Constraint.FULL)
mesh = df.UnitCubeMesh(5, 5, 5)
u_bc = 42.0
problem = c.MechanicsProblem(mesh, prm, law(prm))
bcs = []
bcs.append(df.DirichletBC(problem.Vd.sub(0), 0, boundary.plane_at(0)))
bcs.append(
df.DirichletBC(problem.Vd.sub(0), u_bc, boundary.plane_at(1)))
bcs.append(
df.DirichletBC(problem.Vd.sub(1), 0, boundary.plane_at(0, "y")))
bcs.append(
df.DirichletBC(problem.Vd.sub(2), 0, boundary.plane_at(0, "z")))
problem.set_bcs(bcs)
u = problem.solve()
xs = np.linspace(0, 1, 5)
for x in xs:
for y in xs:
for z in xs:
u_fem = u((x, y, z))
# print(u_fem)
u_correct = (x * u_bc, -y * u_bc * prm.nu,
-z * u_bc * prm.nu)
self.assertAlmostEqual(u_fem[0], u_correct[0])
self.assertAlmostEqual(u_fem[1], u_correct[1])
self.assertAlmostEqual(u_fem[2], u_correct[2])
def test_plane_at(self):
b = boundary.plane_at(0, "Y")
self.assertTrue(b.inside([0, 0], True))
self.assertTrue(b.inside([42, 0, 42], True))
self.assertFalse(b.inside([0, 1], True))
self.assertFalse(b.inside([0, 0], False))
with self.assertRaises(Exception):
b.inside([0], True)
def test_1d(self):
prm = c.Parameters(c.Constraint.UNIAXIAL_STRAIN)
mesh = df.UnitIntervalMesh(10)
u_bc = 42.0
problem = c.MechanicsProblem(mesh, prm, law(prm))
bcs = []
bcs.append(df.DirichletBC(problem.Vd, [0], boundary.plane_at(0)))
bcs.append(df.DirichletBC(problem.Vd, [u_bc], boundary.plane_at(1)))
problem.set_bcs(bcs)
u = problem.solve()
xs = np.linspace(0, 1, 5)
for x in xs:
u_fem = u((x))
u_correct = x * u_bc
self.assertAlmostEqual(u_fem, u_correct)
def test_plate(self):
L, radius = 4.0, 1.0
prm = c.Parameters(c.Constraint.PLANE_STRESS)
plate_with_hole = PlateWithHoleSolution(L=L, E=prm.E, nu=prm.nu, radius=radius)
mesh = plate_with_hole.build_mesh(resolution=50)
n = FacetNormal(mesh)
stress = StressSolution(plate_with_hole, degree=2)
traction = dot(stress, n)
problem = c.MechanicsProblem(mesh, prm, c.LinearElastic(prm.E, prm.nu, prm.constraint))
bc0 = DirichletBC(problem.Vd.sub(0), 0.0, boundary.plane_at(0, "x"))
bc1 = DirichletBC(problem.Vd.sub(1), 0.0, boundary.plane_at(0, "y"))
problem.set_bcs([bc0, bc1])
problem.add_force_term(dot(TestFunction(problem.Vd), traction)*ds)
u = problem.solve()
disp = DisplacementSolution(plate_with_hole, degree=2)
error = errornorm(disp, u)
self.assertLess(error, 1.e-6)
def test_uniaxial(self):
prm = c.Parameters(c.Constraint.UNIAXIAL_STRESS)
prm.deg_d = 1
prm.alpha = 0.999
prm.gf = 0.01
k0 = 2.0e-4
prm.ft = k0 * prm.E
law = law_from_prm(prm)
mesh = df.UnitIntervalMesh(1)
problem = c.MechanicsProblem(mesh, prm, law)
bc0 = df.DirichletBC(problem.Vd, [0], boundary.plane_at(0))
bc_expr = df.Expression(["u"], u=0, degree=0)
bc1 = df.DirichletBC(problem.Vd, bc_expr, boundary.plane_at(1))
problem.set_bcs([bc0, bc1])
ld = c.helper.LoadDisplacementCurve(bc1)
# ld.show()
solver = df.NewtonSolver()
solver.parameters["linear_solver"] = "mumps"
solver.parameters["maximum_iterations"] = 10
solver.parameters["error_on_nonconvergence"] = False
u_max = 100 * k0
for u in np.linspace(0, u_max, 101):
bc_expr.u = u
converged = solver.solve(problem, problem.u.vector())
assert converged
problem.update()
ld(u, df.assemble(problem.R))
GF = np.trapz(ld.load, ld.disp)
self.assertAlmostEqual(GF,
0.5 * k0**2 * prm.E + prm.gf,
delta=prm.gf / 100)
def test_plane_strain(self):
prm = c.Parameters(c.Constraint.PLANE_STRAIN)
mesh = df.UnitSquareMesh(10, 10)
u_bc = 42.0
problem = c.MechanicsProblem(mesh, prm, law(prm))
bcs = []
bcs.append(df.DirichletBC(problem.Vd.sub(0), 0, boundary.plane_at(0)))
bcs.append(
df.DirichletBC(problem.Vd.sub(0), u_bc, boundary.plane_at(1)))
bcs.append(
df.DirichletBC(problem.Vd.sub(1), 0, boundary.plane_at(0, "y")))
problem.set_bcs(bcs)
u = problem.solve()
xs = np.linspace(0, 1, 5)
for x in xs:
for y in xs:
u_fem = u((x, y))
u_correct = (x * u_bc, -y * u_bc * (prm.nu) / (1 - prm.nu))
self.assertAlmostEqual(u_fem[0], u_correct[0])
self.assertAlmostEqual(u_fem[1], u_correct[1])
def test_bending(self):
# return
LX = 6.0
LY = 0.5
LZ = 0.5
mesh_resolution = 6.0
def loading(t):
level = 4 * LZ
N = 1.5
return level * np.sin(N * t * 2 * np.pi)
# show_loading(loading) # if you really insist on it :P
prm = c.Parameters(c.Constraint.PLANE_STRESS)
prm.E = 1000.0
prm.Et = prm.E / 100.0
prm.sig0 = 12.0
prm.H = 15.0 * prm.E * prm.Et / (prm.E - prm.Et)
prm.nu = 0.3
prm.deg_d = 3
prm.deg_q = 4
law = None # for now, plays no role.
mesh = df.RectangleMesh(
df.Point(0, 0),
df.Point(LX, LY),
int(LX * mesh_resolution),
int(LY * mesh_resolution),
)
yf = Yield_VM(prm.sig0, prm.constraint, H=prm.H)
ri = c.RateIndependentHistory()
# mat = PlasticConsitutivePerfect(prm.E, prm.nu, prm.constraint, yf=yf)
mat = PlasticConsitutiveRateIndependentHistory(prm.E,
prm.nu,
prm.constraint,
yf=yf,
ri=ri)
plasticity = Plasticity(mat)
problem = c.MechanicsProblem(mesh, prm, law=law, iploop=plasticity)
left = boundary.plane_at(0.0)
right_top = boundary.point_at((LX, LY))
bc_expr = df.Expression("u", degree=0, u=0)
bcs = []
bcs.append(
df.DirichletBC(problem.Vd.sub(1),
bc_expr,
right_top,
method="pointwise"))
bcs.append(df.DirichletBC(problem.Vd, (0, 0), left))
problem.set_bcs(bcs)
linear_solver = df.LUSolver("mumps")
solver = df.NewtonSolver(df.MPI.comm_world, linear_solver,
df.PETScFactory.instance())
solver.parameters["linear_solver"] = "mumps"
solver.parameters["maximum_iterations"] = 10
solver.parameters["error_on_nonconvergence"] = False
def solve(t, dt):
print(t, dt)
bc_expr.u = loading(t)
return solver.solve(problem, problem.u.vector())
ld = c.helper.LoadDisplacementCurve(bcs[0])
ld.show()
if not ld.is_root:
set_log_level(LogLevel.ERROR)
fff = df.XDMFFile("output.xdmf")
fff.parameters["functions_share_mesh"] = True
fff.parameters["flush_output"] = True
def pp(t):
problem.update()
# this fixes XDMF time stamps
import locale
locale.setlocale(locale.LC_NUMERIC, "en_US.UTF-8")
fff.write(problem.u, t)
ld(t, df.assemble(problem.R))
TimeStepper(solve, pp, problem.u).dt_max(0.02).adaptive(1.0, dt=0.01)
def test_tensile_meso():
mesh = df.Mesh()
mvc = df.MeshValueCollection("size_t", mesh, 1)
LX, LY = 80.0, 80.0 # magic!
mesh_file = Path(__file__).parent / "mesh.xdmf"
with df.XDMFFile(str(mesh_file)) as f:
f.read(mesh)
f.read(mvc, "gmsh:physical")
subdomains = df.MeshFunction("size_t", mesh, mvc)
if not TEST:
import matplotlib.pyplot as plt
df.plot(subdomains)
plt.show()
mat_l = 2.0
Q = c.Q
s = GDMSpaces(mesh, c.Constraint.PLANE_STRAIN, subdomains)
s.create()
R = df.inner(s.eps(s.d_), s.q[Q.SIGMA]) * s.dxm(1)
dR = df.inner(s.eps(s.dd), s.q[Q.DSIGMA_DEPS] * s.eps(s.d_)) * s.dxm(1)
R += s.e_ * (s.e - s.q[Q.EEQ]) * s.dxm(1)
R += df.dot(df.grad(s.e_), mat_l**2 * df.grad(s.e)) * s.dxm(1)
dR += s.de * df.dot(s.q[Q.DSIGMA_DE], s.eps(s.d_)) * s.dxm(1)
dR += df.inner(s.eps(s.dd), -s.q[Q.DEEQ] * s.e_) * s.dxm(1)
dR += s.de * s.e_ * s.dxm(1)
dR += df.dot(df.grad(s.de), mat_l**2 * df.grad(s.e_)) * s.dxm(1)
R += df.inner(s.eps(s.d_), s.q[Q.SIGMA]) * s.dxm(2)
dR += df.inner(s.eps(s.dd), s.q[Q.DSIGMA_DEPS] * s.eps(s.d_)) * s.dxm(2)
dR += s.de * s.e_ * s.dxm(2)
R += df.inner(s.eps(s.d_), s.q[Q.SIGMA]) * s.dxm(3)
dR += df.inner(s.eps(s.dd), s.q[Q.DSIGMA_DEPS] * s.eps(s.d_)) * s.dxm(3)
dR += s.de * s.e_ * s.dxm(3)
VQF, VQV, VQT = c.helper.spaces(s.mesh, s.deg_q, c.q_dim(s.constraint))
calculate_eps = c.helper.LocalProjector(s.eps(s.d), VQV, s.dxm)
calculate_e = c.helper.LocalProjector(s.e, VQF, s.dxm(1))
F = 0.75 # interface reduction
t = 0.5 # interface thickness
lawAggreg = c.LinearElastic(2 * 26738, 0.18, s.constraint)
lawInterf = c.LocalDamage(
26738,
0.18,
s.constraint,
c.DamageLawExponential(k0=F * 3.4 / 26738.0,
alpha=0.99,
beta=3.4 / 26738.0 / (0.12 * F / t)),
c.ModMisesEeq(k=10, nu=0.18, constraint=s.constraint),
)
lawMatrix = c.GradientDamage(
26738.0,
0.18,
s.constraint,
c.DamageLawExponential(k0=3.4 / 26738.0,
alpha=0.99,
beta=3.4 / 26738.0 / 0.0216),
c.ModMisesEeq(k=10, nu=0.18, constraint=s.constraint),
)
loop = c.IpLoop()
loop.add_law(lawMatrix, np.where(s.ip_flags == 1)[0])
loop.add_law(lawAggreg, np.where(s.ip_flags == 2)[0])
loop.add_law(lawInterf, np.where(s.ip_flags == 3)[0])
loop.resize(s.n)
bot = boundary.plane_at(0, "y")
top = boundary.plane_at(LY, "y")
bc_expr = df.Expression("u", degree=0, u=0)
bcs = []
bcs.append(df.DirichletBC(s.Vd.sub(1), bc_expr, top))
bcs.append(df.DirichletBC(s.Vd.sub(1), 0.0, bot))
bcs.append(
df.DirichletBC(s.Vd.sub(0),
0.0,
boundary.point_at((0, 0)),
method="pointwise"))
# return
assembler = df.SystemAssembler(dR, R, bcs)
class SolveMe(df.NonlinearProblem):
def F(self, b, x):
calculate_eps(s.q_in[Q.EPS])
calculate_e(s.q_in[Q.E])
loop.evaluate(s.q_in[Q.EPS].vector().get_local(),
s.q_in[Q.E].vector().get_local())
# ... and write the calculated values into their quadrature spaces.
c.helper.set_q(s.q[Q.SIGMA], loop.get(c.Q.SIGMA))
c.helper.set_q(s.q[Q.DSIGMA_DEPS], loop.get(c.Q.DSIGMA_DEPS))
c.helper.set_q(s.q[Q.DEEQ], loop.get(c.Q.DEEQ))
c.helper.set_q(s.q[Q.DSIGMA_DE], loop.get(c.Q.DSIGMA_DE))
c.helper.set_q(s.q[Q.EEQ], loop.get(c.Q.EEQ))
assembler.assemble(b, x)
def J(self, A, x):
assembler.assemble(A)
linear_solver = df.LUSolver("mumps")
solver = df.NewtonSolver(df.MPI.comm_world, linear_solver,
df.PETScFactory.instance())
solver.parameters["linear_solver"] = "mumps"
solver.parameters["maximum_iterations"] = 10
solver.parameters["error_on_nonconvergence"] = False
problem = SolveMe()
def solve(t, dt):
print(t, dt)
bc_expr.u = 0.1 * t
# try:
return solver.solve(problem, s.u.vector())
# except:
# return -1, False
ld = c.helper.LoadDisplacementCurve(bcs[0])
if not TEST:
ld.show()
if not ld.is_root:
df.set_log_level(df.LogLevel.ERROR)
fff = df.XDMFFile("output.xdmf")
fff.parameters["functions_share_mesh"] = True
fff.parameters["flush_output"] = True
plot_space = df.FunctionSpace(s.mesh, "DG", 0)
k = df.Function(plot_space, name="kappa")
def pp(t):
calculate_eps(s.q_in[Q.EPS])
calculate_e(s.q_in[Q.E])
loop.update(s.q_in[Q.EPS].vector().get_local(),
s.q_in[Q.E].vector().get_local())
# this fixes XDMF time stamps
import locale
locale.setlocale(locale.LC_NUMERIC, "en_US.UTF-8")
d, e = s.u.split(0)
d.rename("disp", "disp")
e.rename("e", "e")
all_kappa = lawInterf.kappa() + lawMatrix.kappa()
k.vector().set_local(all_kappa[::s.nq])
fff.write(d, t)
fff.write(e, t)
fff.write(k, t)
ld(t, df.assemble(R))
t_end = 1.
if TEST:
t_end = 0.02
TimeStepper(solve, pp, s.u).adaptive(t_end, dt=0.02)