def shear():
"""
Recreate some of the results of Bazant 2013
"""
F = lambda t: np.array([[1,t,0],[0,1.0,0],[0,0,1]])
tmax = 10.0
nsteps = 250
G = 100.0
K = 10.0
elastic = elasticity.IsotropicLinearElasticModel(G, "shear", K, "bulk")
model = models.SmallStrainElasticity(elastic)
res = drivers.def_grad_driver(model, F, tmax, nsteps)
theta = [Fi[0,1] / 2.0 for Fi in res['F']]
nstress = [Si[5] / G / np.sqrt(2) for Si in res['stress']]
plt.plot(theta, nstress, label = "Truesdell")
model = models.SmallStrainElasticity(elastic, truesdell = False)
res = drivers.def_grad_driver(model, F, tmax, nsteps)
theta = [Fi[0,1] / 2.0 for Fi in res['F']]
nstress = [Si[5] / G / np.sqrt(2) for Si in res['stress']]
plt.plot(theta, nstress, label = "Jaumann")
plt.xlabel(r"$\tan\left(\theta\right / 2)$")
plt.ylabel(r"$\tau_{12}/G$")
plt.legend(loc = 'best')
plt.show()
def rotation():
"""
Rotate a fixed stress tensor
"""
def F(t):
cut = 1.0
bF = lambda tt: np.array([[1+tt,0,0],[0,1.0-tt/4.0,0],[0,0,1-tt/4.0]])
R = lambda tt: np.array([
[np.cos(tt*(np.pi/2)), -np.sin(tt*(np.pi/2)),0],
[np.sin(tt*(np.pi/2)), np.cos(tt*(np.pi/2)),0],
[0, 0, 1]])
if t <= cut:
F = bF(t)
else:
F = np.dot(R(t-cut), bF(cut))
return F
tmax = 2.0
nsteps = 1000
E = 100.0
nu = 0.25
elastic = elasticity.IsotropicLinearElasticModel(E, "youngs", nu, "poissons")
model = models.SmallStrainElasticity(elastic)
res = drivers.def_grad_driver(model, F, tmax, 2*nsteps)
print(res['stress'][nsteps])
print(res['stress'][2*nsteps])
def setUp(self):
self.ro = 5
self.ri = 4.5
self.h = 2.5
self.nr = 10
self.nt = 20
self.nz = 5
self.E = 150000.0
self.nu = 0.35
self.tube = receiver.Tube(self.ro, self.ro - self.ri, self.h, self.nr,
self.nt, self.nz)
self.times = np.array([0, 1])
self.tube.set_times(self.times)
self.tube.set_pressure_bc(
receiver.PressureBC(self.times, self.times * 0))
self.emodel = elasticity.IsotropicLinearElasticModel(
self.E, "youngs", self.nu, "poissons")
self.mat = models.SmallStrainElasticity(self.emodel)
self.d = 0.25
self.force_exact = (np.pi * (self.ro**2.0 - self.ri**2.0) * self.E *
self.d / self.h)
self.stiffness_exact = (np.pi * (self.ro**2.0 - self.ri**2.0) *
self.E / self.h)
self.solver = structural.PythonTubeSolver(verbose=False)
def setUp(self):
self.G1 = 36000.0
self.G2 = 25000.0
self.K1 = 10000.0
self.K2 = 12000.0
self.elastic1 = elasticity.IsotropicLinearElasticModel(
self.G1, "shear", self.K1, "bulk")
self.elastic2 = elasticity.IsotropicLinearElasticModel(
self.G2, "shear", self.K2, "bulk")
self.emodel1 = models.SmallStrainElasticity(self.elastic1)
self.emodel2 = models.SmallStrainElasticity(self.elastic2)
self.tiny_strain = np.array([1e-6, 0, 0, 0, 0, 0])
self.T = 300.0
self.t = 1e-9
def setUp(self):
self.E = 100000.0
self.nu = 0.29
self.elastic = elasticity.IsotropicLinearElasticModel(
self.E, "youngs", self.nu, "poissons")
self.model = models.SmallStrainElasticity(self.elastic)
self.conditions = [{
'hist_n':
np.zeros((6, )),
'stress_n':
np.zeros((6, )),
'd_n':
np.zeros((6, )),
'd_np1':
np.array([0.1, 0.05, -0.025, 0.15, 0.2, -0.05]),
'w_n':
np.zeros((3, )),
'w_np1':
np.array([-0.15, 0.1, 0.05]),
'dt':
1.0,
'T':
300.0
}, {
'hist_n':
np.zeros((6, )),
'stress_n':
np.array([10.0, -5.0, 30.0, -5.0, 10.0, 15.0]),
'd_n':
np.zeros((6, )),
'd_np1':
np.array([0.05, 0.5, 0.25, 0.20, -0.2, 0.25]),
'w_n':
np.zeros((3, )),
'w_np1':
np.array([-0.15, 0.25, 0.05]),
'dt':
1.0,
'T':
300.0
}]
self.directions = [{
'd': np.array([0.1, -0.15, 0.2, -0.05, 0.15, 0.25]),
'w': np.array([0.25, -0.15, 0.1])
}]
self.nsteps = 10
self.dt = 1.0
self.T = 300.0
def setUp(self):
self.hist0 = np.array([])
self.E = 92000.0
self.nu = 0.3
self.mu = self.E / (2 * (1 + self.nu))
self.K = self.E / (3 * (1 - 2 * self.nu))
self.elastic = elasticity.IsotropicLinearElasticModel(
self.mu, "shear", self.K, "bulk")
self.model = models.SmallStrainElasticity(self.elastic)
self.efinal = np.array([0.1, -0.05, 0.02, -0.03, 0.1, -0.15])
self.tfinal = 10.0
self.T = 300.0
self.nsteps = 10
def gen_tube(k, tforce, tube_length, tube_ri, E, alpha, nr=5):
emodel = elasticity.IsotropicLinearElasticModel(E, "youngs", 0.25,
"poissons")
mmodel = models.SmallStrainElasticity(emodel, alpha=alpha)
solver = structural.PythonTubeSolver(atol=1.0e-4)
ro = np.sqrt(tube_length * k / (np.pi * E) + tube_ri**2.0)
A = np.pi * (ro**2.0 - tube_ri**2.0)
tube = receiver.Tube(ro, ro - tube_ri, tube_length, nr, 1, 1)
tube.set_times(np.array([0, 1.0]))
tube.make_1D(tube_length / 2.0, 0)
dT = tforce / (E * alpha * A)
temp = np.zeros((2, nr))
temp[1] = dT
tube.add_results("temperature", temp)
tube.set_pressure_bc(
receiver.PressureBC(np.array([0, 1]), np.array([0, 0])))
return spring.TubeSpring(tube, solver, mmodel)
def test_linear_elastic(self):
model = models.SmallStrainElasticity(self.elastic1)
self.are_equal(self.elastic1, model.elastic)
model.set_elastic_model(self.elastic2)
self.are_equal(self.elastic2, model.elastic)
s0 = 100.0
A = s0**(-n)
A = 1.0e-22
# Damage parameters
xi = 0.478
phi = 1.914
S = 1.0e19
# Loading
srate = 100.0
# Setup model
emodel = elasticity.IsotropicLinearElasticModel(E, "youngs", nu,
"poissons")
bmodel = models.SmallStrainElasticity(emodel)
scmodel = creep.PowerLawCreep(A, n)
cfmodel = creep.J2CreepModel(scmodel)
cmodel = models.SmallStrainCreepPlasticity(emodel, bmodel, cfmodel)
model = damage.ClassicalCreepDamageModel_sd(emodel, S, xi, phi, cmodel)
model2 = damage.ModularCreepDamageModel_sd(
emodel, S, xi, phi, damage.VonMisesEffectiveStress(), cmodel)
# Computed life
srange = np.linspace(s0 / 2, s0, 10)
tfs = S**(xi) / (1 + phi) * srange**(-xi)
slife = []
slife2 = []
for s, tf in zip(srange, tfs):
def elastic_model(E, a, nu=0.3):
elmodel = elasticity.IsotropicLinearElasticModel(E, "youngs", nu,
"poissons")
return models.SmallStrainElasticity(elmodel, alpha=a)
def make_mat(self):
emodel = elasticity.IsotropicLinearElasticModel(
self.E, "youngs", self.nu, "poissons")
return models.SmallStrainElasticity(emodel, alpha=self.alpha)
def gen_material(E, nu, alpha): elastic = elasticity.IsotropicLinearElasticModel(E, "youngs", nu, "poissons") return models.SmallStrainElasticity(elastic, alpha = alpha)