def simple_ex():
E = 92000.0
nu = 0.3
s0 = 180.0
Kp = 1000.0
H = 1000.0
elastic = elasticity.IsotropicLinearElasticModel(E, "youngs", nu,
"poissons")
surface = surfaces.IsoKinJ2()
iso = hardening.LinearIsotropicHardeningRule(s0, Kp)
kin = hardening.LinearKinematicHardeningRule(H)
hrule = hardening.CombinedHardeningRule(iso, kin)
flow = ri_flow.RateIndependentAssociativeFlow(surface, hrule)
bmodel = models.SmallStrainRateIndependentPlasticity(elastic, flow)
A = 0.0e-6
a = 2.2
model_off = damage.NEMLPowerLawDamagedModel_sd(elastic, A, a, bmodel)
A = 2e-5
model_on = damage.NEMLPowerLawDamagedModel_sd(elastic, A, a, bmodel)
res_off = drivers.uniaxial_test(model_off, 1.0e-2, emax=0.13)
res_on = drivers.uniaxial_test(model_on, 1.0e-2, emax=0.13)
plt.plot(res_off['strain'], res_off['stress'], 'k-')
plt.plot(res_on['strain'], res_on['stress'], 'r-')
plt.show()
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 check_regression(model):
nmodel = parse.parse_xml(xml, model)
res = drivers.uniaxial_test(nmodel, strain_rate)
reference = pickle.load(open(os.path.join('test/regression',
model+'.pickle'), 'rb'))
assert(np.allclose(res['strain'], reference['strain']))
assert(np.allclose(res['stress'], reference['stress']))
assert(np.allclose(res['energy_density'], reference['energy_density']))
assert(np.allclose(res['plastic_work'], reference['plastic_work']))
def run_model(model_name, xml_file, repeat):
model = parse.parse_xml(xml_file, model_name)
fstr = " Running %s..." % model_name
print(fstr, end='')
start = time.time()
for i in range(repeat):
res = drivers.uniaxial_test(model, strain_rate)
end = time.time()
avg = (end - start) / repeat
pad = " " * (align - len(fstr))
print(pad + "%f s (avg)" % avg)
return res
frule2 = walker.WalkerKremplSwitchRule(emodel, vmodel, 0.0, eps_ref)
model2 = models.GeneralIntegrator(emodel, frule2)
frule3 = walker.WalkerKremplSwitchRule(emodel, vmodel, 0.99, eps_ref)
model3 = models.GeneralIntegrator(emodel, frule3)
rates = [1.0e-6, 1.0e-4, 1.0e-2, 1.0]
surface = surfaces.IsoJ2()
iso = hardening.LinearIsotropicHardeningRule(s0, K)
flow = ri_flow.RateIndependentAssociativeFlow(surface, iso)
model4 = models.SmallStrainRateIndependentPlasticity(emodel, flow)
for r in rates:
res1 = drivers.uniaxial_test(model1, r)
l, = plt.plot(res1['strain'], res1['stress'])
res2 = drivers.uniaxial_test(model2, r)
plt.plot(res2['strain'],
res2['stress'],
color=l.get_color(),
ls='--',
lw=2)
res3 = drivers.uniaxial_test(model3, r)
plt.plot(res3['strain'],
res3['stress'],
color=l.get_color(),
ls=':',
lw=3)
res4 = drivers.uniaxial_test(model4, r)
plt.plot(res4['strain'], res4['stress'], color='k', ls='-')
es = [en]
ss = [sn]
n = 100
emax = 0.1
for enp1 in np.linspace(0, emax, n+1)[1:]:
Tnp1 = Tn + dT
tnp1 = tn + dt
snp1, hnp1, Anp1, unp1, pnp1 = umodel.update(enp1, en, Tnp1, Tn,
tnp1, tn, sn, hn, un, pn)
es.append(enp1)
ss.append(snp1)
sn = snp1
hn = np.copy(hnp1)
en = enp1
Tn = Tnp1
tn = tnp1
un = unp1
pn = pnp1
plt.plot(es, ss, 'k-')
res = drivers.uniaxial_test(model, emax / n / dt, T = Tn, emax = emax)
plt.plot(res['strain'], res['stress'], 'r-')
plt.show()
elastic = elasticity.IsotropicLinearElasticModel(E, "youngs", nu,
"poissons")
surface = surfaces.IsoJ2()
pmodel = models.SmallStrainPerfectPlasticity(elastic, surface, sY)
model = models.SmallStrainCreepPlasticity(elastic, pmodel, cmodel)
res = drivers.creep(model, 200.0, 1.0e2, 1000.0, verbose=True)
plt.plot(res['time'], res['strain'])
plt.show()
res = drivers.strain_cyclic(model,
0.01,
-1,
1.0e-4,
15,
verbose=True,
nsteps=25,
hold_time=[10.0, 0])
plt.plot(res['strain'], res['stress'])
plt.show()
res = drivers.uniaxial_test(model,
1.0e-6,
sdir=np.array([1, -1, 0.5, -0.5, 0.1, -0.25]),
verbose=True)
plt.plot(res['strain'], res['stress'])
plt.show()
if __name__ == "__main__":
E = 150000.0
nu = 0.3
sY = 150.0
h = 1.0e-2
l = 1.0
emodel = elasticity.IsotropicLinearElasticModel(E, "youngs", nu,
"poissons")
surface = surfaces.IsoJ2I1(h, l)
model = models.SmallStrainPerfectPlasticity(emodel, surface, sY)
res_tension = drivers.uniaxial_test(model, 1.0e-2)
res_compres = drivers.uniaxial_test(model,
1.0e-2,
sdir=np.array([-1, 0, 0, 0, 0, 0]))
plt.plot(res_tension['strain'], res_tension['stress'], 'k-')
plt.plot(res_compres['strain'], res_compres['stress'], 'r-')
plt.show()
E = 150000.0
nu = 0.3
sY = 150.0
h = 1.0e-2
l = 1.0
K = E / 50.0
slipmodel = sliprules.PowerLawSlipRule(strengthmodel, g0, n)
imodel = inelasticity.AsaroInelasticity(slipmodel)
emodel = elasticity.IsotropicLinearElasticModel(E, "youngs", nu, "poissons")
kmodel = kinematics.StandardKinematicModel(emodel, imodel)
lattice = crystallography.CubicLattice(1.0)
lattice.add_slip_system([1,1,0],[1,1,1])
model = singlecrystal.SingleCrystalModel(kmodel, lattice, verbose = False)
orientations = rotations.random_orientations(N)
dt = emax / erate / steps
pmodel = polycrystal.TaylorModel(model, orientations, nthreads = nthreads)
res = drivers.uniaxial_test(pmodel, erate, emax = emax, nsteps = steps)
strains.append(res['strain'])
stresses.append(res['stress'])
plt.figure()
for e,s,r in zip(strains, stresses, rhos):
plt.plot(e,s, label = r"$\rho=%3.1e\,\mathrm{m^{-2}}$" % r)
plt.xlabel("Strain (mm/mm)")
plt.ylabel("Stress (MPa)")
plt.legend(loc='best')
plt.tight_layout()
plt.show()
def uniaxial():
# Data from "Numerical modeling of elasto-viscoplastic Chaboche constitutive..."
# by A. Ambroziak
E = 159000.0
nu = 0.3
k = 514.21
b = 60.0
R1 = -194.39
a = 170000.0
c = 500.0
n = 4.0
eta = 1023.5
# Translate
Q = R1
b = b
C1 = a
g1 = c
eta = eta
sY = k
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)
cs = [C1]
gs = [hardening.ConstantGamma(g1)]
hmodel = hardening.Chaboche(iso, cs, gs, [0.0], [1.0])
fluidity = visco_flow.ConstantFluidity(eta)
vmodel = visco_flow.ChabocheFlowRule(
surface, hmodel, fluidity, n)
flow = general_flow.TVPFlowRule(elastic, vmodel)
model = models.GeneralIntegrator(elastic, flow)
erates = [1.0e-7, 1.0e-2, 1.0e-1]
e_7 = np.array([1.03E-007, 0.000977076, 0.0019927018, 0.0029695719, 0.0038278073, 0.0048024128, 0.0058155682, 0.0068186871, 0.0078116926, 0.0088238185, 0.0098260368, 0.0108280492, 0.0118396862, 0.0128318167, 0.0138433765, 0.0148451316, 0.0158469381, 0.0168487447, 0.017840798, 0.0188523063, 0.019844411])
s_7 = np.array([1.9738128815, 164.2845378653, 316.6592895303, 475.0018013938, 559.9786920852, 631.0205153016, 688.1581520788, 733.3950096246, 763.7549280987, 781.2104336727, 791.7254264156, 794.3039929179, 792.9104861704, 789.5405931218, 785.170926534, 777.8289602355, 772.4711004972, 767.1132407589, 760.7671878699, 754.413414722, 750.0514683933])
e_2 = np.array([-1.94E-005, 0.000976973, 0.0019830515, 0.0029890784, 0.0037900553, 0.0048443338, 0.0058197114, 0.0068040701, 0.0078172512, 0.0088300977, 0.0098231803, 0.0108257074, 0.0118377047, 0.0128397943, 0.0138612103, 0.0148630941, 0.0158551988, 0.0168667329, 0.017878267, 0.0188703202, 0.0198623735])
s_2 = np.array([-0.0025734197, 160.316324745, 319.6393095, 476.9781876949, 604.6365302068, 747.075308553, 847.8787301718, 919.9087465388, 978.0384365961, 1023.2714340124, 1056.6075123267, 1079.0271444306, 1091.5223836042, 1097.0771099468, 1097.66384963, 1095.2821497319, 1090.9202034031, 1085.5584835353, 1080.1967636674, 1073.8507107785, 1067.5046578896])
e_1 = np.array([-1.93E-005, 0.0009672712, 0.0019928047, 0.0029793251, 0.0037900295, 0.0047863804, 0.0058017489, 0.0068163453, 0.0078302727, 0.0088243075, 0.0098374371, 0.0108404531, 0.0118432376, 0.0128554407, 0.0138577362, 0.014850124, 0.01587154, 0.0168734495, 0.0178753075, 0.0188770883, 0.0198789206])
s_1 = np.array([2.9735864206, 161.3122381546, 320.6275026506, 475.9899945444, 603.6444769267, 762.9713218113, 905.4255406755, 1018.1181611373, 1105.0173963169, 1175.0594459942, 1231.2050294914, 1272.4736739169, 1304.8138388216, 1325.2455042359, 1338.7366568191, 1345.2872965712, 1345.8740362543, 1344.4843896363, 1341.1106364582, 1334.7607234397, 1330.3949169815])
plt.plot(e_7, s_7, 'kx')
plt.plot(e_2, s_2, 'rx')
plt.plot(e_1, s_1, 'bx')
res = drivers.uniaxial_test(model, erates[0], emax = 0.02)
plt.plot(res['strain'], res['stress'], 'k-')
res = drivers.uniaxial_test(model, erates[1], emax = 0.02)
plt.plot(res['strain'], res['stress'], 'r-')
res = drivers.uniaxial_test(model, erates[2], emax = 0.02)
plt.plot(res['strain'], res['stress'], 'b-')
plt.xlim([0,0.02])
plt.ylim([0,1500])
plt.show()
ns = [1.0]
hmodel = hardening.Chaboche(iso, cs, gs, As, ns)
fluidity = visco_flow.ConstantFluidity(eta)
vmodel = visco_flow.ChabocheFlowRule(
surface, hmodel, fluidity, n)
flow = general_flow.TVPFlowRule(elastic, vmodel)
model = models.GeneralIntegrator(elastic, flow, verbose = 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, verbose = False)
plt.plot(res['strain'], res['stress'])
plt.xlabel("Strain (-/-)")
plt.ylabel("Stress (MPa)")
plt.show()
# A strain-controlled cyclic test
res = drivers.strain_cyclic(model, 0.001, -0.25, 1.0e-4, 50,
verbose = False)
plt.plot(res['strain'], res['stress'], 'k-')
plt.xlabel("Strain (-/-)")
plt.ylabel("Stress (MPa)")
plt.show()
plt.plot(res['cycles'], res['max'], 'k-')
