def setUp(self):
self.model1 = parse.parse_xml("test/examples.xml", "test_nonassri")
mu = 40000.0
K = 84000.0
ys = 100.0
r = 100.0
d = 1000.0
cs = [5.0, 10.0]
gs = [1000.0, 1000.0]
As = [0.0, 0.0]
ns = [1.0, 1.0]
elastic = elasticity.IsotropicLinearElasticModel(
mu, "shear", K, "bulk")
surface = surfaces.IsoKinJ2()
iso = hardening.VoceIsotropicHardeningRule(ys, r, d)
gammas = [hardening.ConstantGamma(g) for g in gs]
hmodel = hardening.Chaboche(iso, cs, gammas, As, ns)
flow = ri_flow.RateIndependentNonAssociativeHardening(surface, hmodel)
self.model2 = models.SmallStrainRateIndependentPlasticity(
elastic, flow)
self.T = 300.0
self.tmax = 10.0
self.nsteps = 100
self.emax = np.array([0.05, 0, 0, 0, 0, 0])
def setUp(self):
E = 200000.0
nu = 0.27
mu = E / (2 * (1.0 + nu))
K = E / (3 * (1 - 2 * nu))
s0 = 300.0
Kp = 0.0
c = [30000.0]
r = [60.0]
A = [0.0]
n = [1.0]
elastic = elasticity.IsotropicLinearElasticModel(
mu, "shear", K, "bulk")
surface = surfaces.IsoKinJ2()
iso = hardening.LinearIsotropicHardeningRule(s0, Kp)
gmodels = [hardening.ConstantGamma(g) for g in r]
hrule = hardening.Chaboche(iso, c, gmodels, A, n)
flow = ri_flow.RateIndependentNonAssociativeHardening(surface, hrule)
self.model = models.SmallStrainRateIndependentPlasticity(
elastic, flow, verbose=False, check_kt=False)
self.umodel = uniaxial.UniaxialModel(self.model)
self.de = 0.001
self.dt = 1.0
self.dT = 0.0
self.T0 = 0.0
self.nsteps = 100
def verify_warp3d():
E = 30000.0
nu = 0.3
sy = 100.0
Q = 50.0
b = 100.0
C = 1000.0
g = 10.0
mu = E / (2 * (1.0 + nu))
K = E / (3 * (1 - 2 * nu))
elastic = elasticity.IsotropicLinearElasticModel(mu, "shear", K, "bulk")
surface = surfaces.IsoKinJ2()
iso = hardening.VoceIsotropicHardeningRule(sy, Q, b)
hrule = hardening.Chaboche(iso, [C], [hardening.ConstantGamma(g)], [0.0],
[1.0])
flow = ri_flow.RateIndependentNonAssociativeHardening(surface, hrule)
model = models.SmallStrainRateIndependentPlasticity(elastic,
flow,
verbose=False)
res = drivers.strain_cyclic(model, 0.0075, -1.0, 1.0e-4, 50)
strain = res['strain']
stress = res['stress']
data_warp = np.load('data_fa_warp.npy')
plt.plot(strain, stress, 'k-')
plt.plot(data_warp[0], data_warp[1], 'r-')
plt.show()
def verify_Cg():
E = 30000.0
nu = 0.3
sy = 100.0
Q = 0.0
b = 0.0
C = 1000.0
g = 10.0
mu = E / (2 * (1.0 + nu))
K = E / (3 * (1 - 2 * nu))
elastic = elasticity.IsotropicLinearElasticModel(mu, "shear", K, "bulk")
surface = surfaces.IsoKinJ2()
iso = hardening.VoceIsotropicHardeningRule(sy, Q, b)
hrule = hardening.Chaboche(iso, [C], [hardening.ConstantGamma(g)], [0.0],
[1.0])
flow = ri_flow.RateIndependentNonAssociativeHardening(surface, hrule)
model = models.SmallStrainRateIndependentPlasticity(elastic,
flow,
verbose=False)
res = drivers.strain_cyclic(model, 0.4, -1.0, 1.0e-4, 1)
strain = res['strain']
stress = res['stress']
mv = np.max(np.abs(stress))
hu = mv - sy
print("C/y: %f / %f" % ((C / g), hu))
def verify_Q():
E = 30000.0
nu = 0.3
sy = 100.0
Q = 50.0
b = 100.0
C = 0.0
g = 0.0
mu = E / (2 * (1.0 + nu))
K = E / (3 * (1 - 2 * nu))
elastic = elasticity.IsotropicLinearElasticModel(mu, "shear", K, "bulk")
surface = surfaces.IsoKinJ2()
iso = hardening.VoceIsotropicHardeningRule(sy, Q, b)
gmodels = [hardening.ConstantGamma(g)]
hrule = hardening.Chaboche(iso, [C], gmodels, [0.0], [1.0])
flow = ri_flow.RateIndependentNonAssociativeHardening(surface, hrule)
model = models.SmallStrainRateIndependentPlasticity(elastic,
flow,
verbose=False)
res = drivers.uniaxial_test(model, 1.0e-2, emax=0.2)
stress = res['stress']
print("Q: %f / %f" % (Q, stress[-1] - sy))
def setUp(self):
self.s0 = 200.0
self.K = 15000.0
self.n = 4
self.cs = range(1,self.n+1)
self.rs = range(1, self.n+1)
self.iso = hardening.LinearIsotropicHardeningRule(self.s0, self.K)
self.gmodels = [hardening.ConstantGamma(g) for g in self.rs]
As = [0.0] * self.n
ns = [1.0] * self.n
self.hardening = hardening.Chaboche(self.iso, self.cs, self.gmodels, As,
ns)
self.surface = surfaces.IsoKinJ2()
self.model = ri_flow.RateIndependentNonAssociativeHardening(self.surface, self.hardening)
self.hist0 = np.zeros((1+6*self.n,))
self.T = 300.0
def setUp(self):
self.hist0 = np.zeros((13, ))
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.s0 = 180.0
self.Kp = 1000.0
self.n = 2
self.cs = [10.0, 2.0]
self.rs = [5.0, 1.0]
self.gmodels = [hardening.ConstantGamma(g) for g in self.rs]
self.As = [0.0] * self.n
self.ns = [1.0] * self.n
self.elastic = elasticity.IsotropicLinearElasticModel(
self.mu, "shear", self.K, "bulk")
surface = surfaces.IsoKinJ2()
iso = hardening.LinearIsotropicHardeningRule(self.s0, self.Kp)
hmodel = hardening.Chaboche(iso, self.cs, self.gmodels, self.As,
self.ns)
flow = ri_flow.RateIndependentNonAssociativeHardening(surface, hmodel)
self.model = models.SmallStrainRateIndependentPlasticity(
self.elastic, flow, check_kt=False)
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 = 30
s0 = 300.0
Kp = 0.0
c = [30000.0]
r = [60.0]
elastic = elasticity.IsotropicLinearElasticModel(mu, "shear", K, "bulk")
surface = surfaces.IsoKinJ2()
iso = hardening.LinearIsotropicHardeningRule(s0, Kp)
gmodels = [hardening.ConstantGamma(g) for g in r]
As = [0.0]
ns = [1.0]
hrule = hardening.Chaboche(iso, c, gmodels, As, ns)
flow = ri_flow.RateIndependentNonAssociativeHardening(surface, hrule)
model = models.SmallStrainRateIndependentPlasticity(elastic,
flow,
verbose=False,
check_kt=False)
# Uniaxial stress/strain curves at decades of strain rates
erates = np.logspace(-6, 2, 9)
for rate in erates:
res = drivers.uniaxial_test(model, rate)
plt.plot(res['strain'], res['stress'])
plt.xlabel("Strain (-/-)")
plt.ylabel("Stress (MPa)")
plt.show()
def setUp(self):
# Fully-defined perfectly plastic model
Epoly = [-78.2759, 236951.0]
nu = 0.3
A = -9.6187
B = -1.4819
C = -5.0486
g0 = 0.3708
b = 0.248 * 1.0e-6
kboltz = 1.38064e-23 * 1000.0
eps0 = 1.0e10
# Temperature range over which to consider (K)
Tmin = 550.0
Tmax = 950.0
Trange = np.linspace(Tmin, Tmax)
# Elastic
E_m = interpolate.PolynomialInterpolate(Epoly)
nu_m = interpolate.ConstantInterpolate(nu)
elastic_m = elasticity.IsotropicLinearElasticModel(
E_m, "youngs", nu_m, "poissons")
self.elastic = elastic_m
# Rate sensitivity interpolates values
mu_values = np.array([elastic_m.G(T) for T in Trange])
n_values = -mu_values * b**3.0 / (kboltz * Trange * A)
eta_values = np.exp(B) * eps0**(kboltz * Trange * A /
(mu_values * b**3.0)) * mu_values
# Rate independent interpolate values
flow_stress = mu_values * np.exp(C)
# Common objects
surface = surfaces.IsoKinJ2()
hmodulus = interpolate.PolynomialInterpolate([-10.0, 12000.0])
# Setup visco model
n_interp = interpolate.PiecewiseLinearInterpolate(
list(Trange), list(n_values))
eta_interp = interpolate.PiecewiseLinearInterpolate(
list(Trange), list(eta_values))
eta_m = visco_flow.ConstantFluidity(eta_interp)
iso_rd = hardening.LinearIsotropicHardeningRule(
interpolate.ConstantInterpolate(0.0), hmodulus)
hard_rd = hardening.Chaboche(
iso_rd, [interpolate.ConstantInterpolate(0.0)],
[hardening.ConstantGamma(interpolate.ConstantInterpolate(0.0))],
[interpolate.ConstantInterpolate(0.0)],
[interpolate.ConstantInterpolate(1.0)])
visco_rd = visco_flow.ChabocheFlowRule(surface, hard_rd, eta_m,
n_interp)
general_rd = general_flow.TVPFlowRule(elastic_m, visco_rd)
rate_dependent = models.GeneralIntegrator(elastic_m, general_rd)
# Setup rate independent
sy_interp = interpolate.PiecewiseLinearInterpolate(
list(Trange), list(flow_stress))
iso_ri = hardening.LinearIsotropicHardeningRule(sy_interp, hmodulus)
hard_ri = hardening.Chaboche(
iso_ri, [interpolate.ConstantInterpolate(0.0)],
[hardening.ConstantGamma(interpolate.ConstantInterpolate(0.0))],
[interpolate.ConstantInterpolate(0.0)],
[interpolate.ConstantInterpolate(1.0)])
flow_ri = ri_flow.RateIndependentNonAssociativeHardening(
surface, hard_ri)
rate_independent = models.SmallStrainRateIndependentPlasticity(
elastic_m, flow_ri)
# Combined model
self.model = models.KMRegimeModel(elastic_m,
[rate_independent, rate_dependent],
[g0], kboltz, b, eps0)
self.efinal = np.array([0.05, 0, 0, 0.02, 0, -0.01])
self.tfinal = 10.0
self.T = 700.0
self.nsteps = 100
hmodel_rd = hardening.Chaboche(iso_rd, [K * 3.0 / 2.0],
[hardening.ConstantGamma(0.0)], [0.0],
[1.0])
hmodel_ri = hardening.Chaboche(iso_ri, [K * 3.0 / 2.0],
[hardening.ConstantGamma(0.0)], [0.0],
[1.0])
surface_m = surfaces.IsoKinJ2()
visco_flow_m = visco_flow.ChabocheFlowRule(surface_m, hmodel_rd, eta_m,
n_interp)
rd_flow = general_flow.TVPFlowRule(elastic_m, visco_flow_m)
rd_model = models.GeneralIntegrator(elastic_m, rd_flow)
ri_flow_m = ri_flow.RateIndependentNonAssociativeHardening(
surface_m, hmodel_ri)
ri_model = models.SmallStrainRateIndependentPlasticity(
elastic_m, ri_flow_m)
model = models.KMRegimeModel(elastic_m, [ri_model, rd_model], [g0], kboltz,
b, eps0)
smax = 400.0
Rs = [-1.0, -0.75, -0.5, -0.25, 0.0]
srate = 1.0e-3
ncycles = 50
for R in Rs:
res = drivers.stress_cyclic(model,
smax,
R,
srate,
visco_rd = visco_flow.ChabocheFlowRule(surface, hard_rd, eta_m, n_interp)
general_rd = general_flow.TVPFlowRule(elastic_m, visco_rd)
rate_dependent = models.GeneralIntegrator(elastic_m, general_rd)
# Setup rate independent
sy_interp = interpolate.PiecewiseLinearInterpolate(list(Trange),
list(flow_stress))
iso_ri = hardening.LinearIsotropicHardeningRule(sy_interp, hmodulus)
hard_ri = hardening.Chaboche(
iso_ri, [interpolate.ConstantInterpolate(0.0)],
[hardening.ConstantGamma(interpolate.ConstantInterpolate(0.0))],
[interpolate.ConstantInterpolate(0.0)],
[interpolate.ConstantInterpolate(1.0)])
flow_ri = ri_flow.RateIndependentNonAssociativeHardening(surface, hard_ri)
rate_independent = models.SmallStrainRateIndependentPlasticity(
elastic_m, flow_ri)
# Combined model
combined = models.KMRegimeModel(elastic_m,
[rate_independent, rate_dependent], [g0],
kboltz, b, eps0)
# Do things
# Strain rate jump
Ts = np.linspace(Tmin, Tmax, 5)
erates = [
1.0e-6, 1.0e-5, 1.0e-4, 1.0e-3, 1.0e-2, 1.0e-1, 1.0e-2, 1.0e-3, 1.0e-4,
