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 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 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 complete(self): self.E = 92000.0 self.nu = 0.3 self.s0 = 180.0 self.Kp = 1000.0 self.H = 1000.0 self.elastic = elasticity.IsotropicLinearElasticModel(self.E, "youngs", self.nu, "poissons") surface = surfaces.IsoKinJ2() iso = hardening.LinearIsotropicHardeningRule(self.s0, self.Kp) kin = hardening.LinearKinematicHardeningRule(self.H) hrule = hardening.CombinedHardeningRule(iso, kin) flow = ri_flow.RateIndependentAssociativeFlow(surface, hrule) self.bmodel = models.SmallStrainRateIndependentPlasticity(self.elastic, flow) self.xi = 0.478 self.phi = 1.914 self.A = 10000000.0 self.model = damage.ModularCreepDamageModel_sd( self.elastic, self.A, self.xi, self.phi, self.effective_model(), self.bmodel) self.stress = np.array([100,-50.0,300.0,-99,50.0,125.0]) self.T = 100.0 self.s_np1 = self.stress self.s_n = np.array([-25,150,250,-25,-100,25]) self.d_np1 = 0.5 self.d_n = 0.4 self.e_np1 = np.array([0.1,-0.01,0.15,-0.05,-0.1,0.15]) self.e_n = np.array([-0.05,0.025,-0.1,0.2,0.11,0.13]) self.T_np1 = self.T self.T_n = 90.0 self.t_np1 = 1.0 self.t_n = 0.0 self.u_n = 0.0 self.p_n = 0.0 # This is a rather boring baseline history state to probe, but I can't # think of a better way to get a "generic" history from a generic model self.hist_n = np.array([self.d_n] + list(self.bmodel.init_store())) self.x_trial = np.array([50,-25,150,-150,190,100.0] + [0.41]) self.nsteps = 10 self.etarget = np.array([0.1,-0.025,0.02,0.015,-0.02,-0.05]) self.ttarget = 10.0
def setUp(self): self.model1 = parse.parse_xml("test/examples.xml", "test_perzyna") mu = 40000.0 K = 84000.0 elastic = elasticity.IsotropicLinearElasticModel( mu, "shear", K, "bulk") sy = 100.0 r = 100.0 d = 1000.0 KK = 1000.0 n = 5.0 eta = 500.0 surface = surfaces.IsoKinJ2() iso = hardening.VoceIsotropicHardeningRule(sy, r, d) kin = hardening.LinearKinematicHardeningRule(KK) hmodel = hardening.CombinedHardeningRule(iso, kin) gmodel = visco_flow.GPowerLaw(n, eta) vmodel = visco_flow.PerzynaFlowRule(surface, hmodel, gmodel) flow = general_flow.TVPFlowRule(elastic, vmodel) self.model2 = models.GeneralIntegrator(elastic, flow) self.T = 550.0 + 273.15 self.tmax = 10.0 self.nsteps = 100.0 self.emax = np.array([0.1, 0, 0, 0, 0, 0])
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 setUp(self): self.n = 12.0 self.K = 150.0 self.k = 6.0 self.C = 24800.0 self.g0 = 300.0 self.Q = 86 - self.k self.gs = 300.0 self.b = 10.0 self.beta = 0.0 self.surface = surfaces.IsoKinJ2() self.iso = hardening.VoceIsotropicHardeningRule(self.k, self.Q, self.b) cs = [self.C] gs = [hardening.SatGamma(self.gs, self.g0, self.beta)] As = [0.0] ns = [1.0] self.hardening = hardening.Chaboche(self.iso, cs, gs, As, ns) self.fluidity = visco_flow.ConstantFluidity(self.K) self.model = visco_flow.ChabocheFlowRule(self.surface, self.hardening, self.fluidity, self.n) self.hist0 = np.zeros((7, )) self.T = 300.0
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): n = 20.0 eta = 108.0 sY = 89.0 Q = 165.0 b = 12.0 self.m = 3 C1 = 80.0e3 C2 = 14.02e3 C3 = 3.333e3 y1 = 0.9e3 y2 = 1.5e3 y3 = 1.0 surface = surfaces.IsoKinJ2() iso = hardening.VoceIsotropicHardeningRule(sY, Q, b) cs = [C1, C2, C3] gs = [y1, y2, y3] gmodels = [hardening.ConstantGamma(g) for g in gs] A = [0.0, 0.0, 0.0] ae = [1.0, 1.0, 1.0] hmodel = hardening.Chaboche(iso, cs, gmodels, A, ae) fluidity = visco_flow.ConstantFluidity(eta) self.hist0 = np.zeros((19, )) self.T = 300.0 self.model = visco_flow.ChabocheFlowRule(surface, hmodel, fluidity, n)
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 setUp(self): self.E = 92000.0 self.nu = 0.3 self.s0 = 180.0 self.Kp = 1000.0 self.H = 1000.0 self.elastic = elasticity.IsotropicLinearElasticModel(self.E, "youngs", self.nu, "poissons") surface = surfaces.IsoKinJ2() iso = hardening.LinearIsotropicHardeningRule(self.s0, self.Kp) kin = hardening.LinearKinematicHardeningRule(self.H) hrule = hardening.CombinedHardeningRule(iso, kin) flow = ri_flow.RateIndependentAssociativeFlow(surface, hrule) self.bmodel = models.SmallStrainRateIndependentPlasticity(self.elastic, flow) self.fn = interpolate.PolynomialInterpolate([-6.653e-9,2.952e-4,-6.197e-1]) self.C = 32.06 self.lmr = larsonmiller.LarsonMillerRelation(self.fn, self.C) self.effective = damage.VonMisesEffectiveStress() self.model = damage.LarsonMillerCreepDamageModel_sd( self.elastic, self.lmr, self.effective, self.bmodel) self.stress = np.array([100,-50.0,300.0,-99,50.0,125.0]) self.T = 100.0 self.s_np1 = self.stress self.s_n = np.array([-25,150,250,-25,-100,25]) self.d_np1 = 0.5 self.d_n = 0.4 self.e_np1 = np.array([0.1,-0.01,0.15,-0.05,-0.1,0.15]) self.e_n = np.array([-0.05,0.025,-0.1,0.2,0.11,0.13]) self.T_np1 = self.T self.T_n = 90.0 self.t_np1 = 1.0 self.t_n = 0.0 self.dt = self.t_np1 - self.t_n self.u_n = 0.0 self.p_n = 0.0 # This is a rather boring baseline history state to probe, but I can't # think of a better way to get a "generic" history from a generic model self.hist_n = np.array([self.d_n] + list(self.bmodel.init_store())) self.x_trial = np.array([50,-25,150,-150,190,100.0] + [0.41]) self.nsteps = 10 self.etarget = np.array([0.1,-0.025,0.02,0.015,-0.02,-0.05]) self.ttarget = 10.0
def setUp(self): self.model1 = parse.parse_xml("test/examples.xml", "test_j2comb") mu = 40000.0 K = 84000.0 ys = 100.0 r = 100.0 d = 1000.0 KH = 1000.0 elastic = elasticity.IsotropicLinearElasticModel( mu, "shear", K, "bulk") surface = surfaces.IsoKinJ2() iso = hardening.VoceIsotropicHardeningRule(ys, r, d) kin = hardening.LinearKinematicHardeningRule(KH) hrule = hardening.CombinedHardeningRule(iso, kin) flow = ri_flow.RateIndependentAssociativeFlow(surface, hrule) self.model2 = models.SmallStrainRateIndependentPlasticity( elastic, flow) self.T = 300.0 self.tmax = 10.0 self.nsteps = 100.0 self.emax = np.array([0.1, 0, 0, 0, 0, 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.H = 1000.0 self.elastic = elasticity.IsotropicLinearElasticModel( self.mu, "shear", self.K, "bulk") surface = surfaces.IsoKinJ2() iso = hardening.LinearIsotropicHardeningRule(self.s0, self.Kp) kin = hardening.LinearKinematicHardeningRule(self.H) hrule = hardening.CombinedHardeningRule(iso, kin) flow = ri_flow.RateIndependentAssociativeFlow(surface, hrule) 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 = 10
def setUp(self): n = 20.0 eta = 108.0 sY = 89.0 Q = 165.0 b = 12.0 self.m = 3 C1 = 80.0e3 C2 = 14.02e3 C3 = 3.333e3 y1 = 0.9e3 y2 = 1.5e3 y3 = 1.0 surface = surfaces.IsoKinJ2() iso = hardening.VoceIsotropicHardeningRule(sY, Q, b) cs = [C1, C2, C3] gs = [y1, y2, y3] As = [0.0, 0.0, 0.0] ns = [1.0, 1.0, 1.0] gmodels = [hardening.ConstantGamma(g) for g in gs] hmodel = hardening.Chaboche(iso, cs, gmodels, As, ns) fluidity = visco_flow.ConstantFluidity(eta) self.hist0 = np.zeros((19, )) self.T = 300.0 vmodel = visco_flow.ChabocheFlowRule(surface, hmodel, fluidity, n) E = 92000.0 nu = 0.3 mu = E / (2 * (1 + nu)) K = E / (3 * (1 - 2 * nu)) self.elastic = elasticity.IsotropicLinearElasticModel( mu, "shear", K, "bulk") flow = general_flow.TVPFlowRule(self.elastic, vmodel) self.model = models.GeneralIntegrator(self.elastic, flow, max_divide=3, force_divide=True) self.efinal = np.array([0.05, 0, 0, 0.02, 0, -0.01]) self.tfinal = 10.0 self.T = 300.0 self.nsteps = 100
def unload_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 = 2e-5 a = 2.2 model = damage.NEMLPowerLawDamagedModel_sd(elastic, A, a, bmodel) driver = drivers.Driver_sd(model) nsteps = 25 sdir = np.array([1, 0, 0, 0, 0, 0]) erate = 1.0e-5 e_inc = 0.1 / nsteps for i in range(nsteps): einc, ainc = driver.erate_einc_step(sdir, erate, e_inc, 0.0) estrain = model.elastic_strains(driver.stress_int[-1], driver.T_int[-1], driver.stored[-1]) print("Calculated elastic strain: %f" % estrain[0]) nsteps = 20 dt = 0.1 rstress = driver.stress_int[-1] rstrain = driver.strain_int[-1][0] for m in np.linspace(0, 1.0, nsteps, endpoint=False)[::-1]: driver.stress_step(rstress * m, driver.t_int[-1] + dt, driver.T_int[-1]) fstrain = driver.strain_int[-1][0] print("Actual elastic strain: %f" % (rstrain - fstrain)) print("Calculated final elastic strain: %f" % model.elastic_strains( driver.stress_int[-1], driver.T_int[-1], driver.stored[-1])[0]) plt.plot(driver.strain[:, 0], driver.stress[:, 0]) plt.show()
def creep_ex(): E = 92000.0 nu = 0.3 s0 = 120.0 A = 1.0e-10 n = 3.0 Kp = E / 500 H = E / 500 smodel = creep.PowerLawCreep(A, n) cmodel = creep.J2CreepModel(smodel) 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) pmodel = models.SmallStrainRateIndependentPlasticity(elastic, flow) bmodel = models.SmallStrainCreepPlasticity(elastic, pmodel, cmodel) A_damg = 1.0e-2 a_damg = 1.0 model = damage.NEMLPowerLawDamagedModel_sd(elastic, A_damg, a_damg, bmodel, verbose=False) #res = drivers.uniaxial_test(model, 1.0e-2, emax = 0.25) #plt.plot(res['strain'], res['stress']) #plt.show() res = drivers.creep(model, 120.0, 1.0, 393.0, verbose=False) plt.plot(res['rtime'], res['rstrain']) plt.show() plt.loglog(res['rtime'], res['rrate']) plt.show()
def setUp(self): n = 20.0 eta = 108.0 sY = 89.0 Q = 165.0 b = 12.0 self.m = 3 C1 = 80.0e3 C2 = 14.02e3 C3 = 3.333e3 y1 = 0.9e3 y2 = 1.5e3 y3 = 1.0 surface = surfaces.IsoKinJ2() iso = hardening.VoceIsotropicHardeningRule(sY, Q, b) cs = [C1, C2, C3] gs = [y1, y2, y3] As = [0.0, 0.0, 0.0] ns = [1.0, 1.0, 1.0] gmodels = [hardening.ConstantGamma(g) for g in gs] hmodel = hardening.Chaboche(iso, cs, gmodels, As, ns) fluidity = visco_flow.ConstantFluidity(eta) self.vmodel = visco_flow.ChabocheFlowRule(surface, hmodel, fluidity, n) E = 92000.0 nu = 0.3 mu = E / (2 * (1 + nu)) K = E / (3 * (1 - 2 * nu)) self.emodel = elasticity.IsotropicLinearElasticModel( mu, "shear", K, "bulk") self.model = general_flow.TVPFlowRule(self.emodel, self.vmodel) self.T_n = 300.0 self.e_n = np.zeros((6, )) self.t_n = 0.0 self.h_n = np.zeros((1 + 6 * self.m, ))
def setUp(self): self.n = 20.0 self.eta = 108.0 self.sY = 89.0 self.prefactor = np.asarray([2.]) self.prefactor = 2. self.Q = 165.0 self.b = 12.0 self.m = 3 C1 = 80.0e3 C2 = 14.02e3 C3 = 3.333e3 y1 = 0.9e3 y2 = 1.5e3 y3 = 1.0 surface = surfaces.IsoKinJ2() self.iso = hardening.VoceIsotropicHardeningRule( self.sY, self.Q, self.b) self.cs = [C1, C2, C3] self.gs = [y1, y2, y3] self.As = [0.0, 0.0, 0.0] self.ns = [1.0, 1.0, 1.0] self.gmodels = [hardening.ConstantGamma(g) for g in self.gs] self.hmodel = hardening.Chaboche(self.iso, self.cs, self.gmodels, self.As, self.ns) self.fluidity = visco_flow.ConstantFluidity(self.eta) self.hist0 = np.zeros((19, )) self.T = 300.0 self.model = visco_flow.ChabocheFlowRule(surface, self.hmodel, self.fluidity, self.n, prefactor=self.prefactor)
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.model1 = parse.parse_xml(localize("examples.xml"), "test_rd_chaboche") mu = 60384.61 K = 130833.3 elastic = elasticity.IsotropicLinearElasticModel( mu, "shear", K, "bulk") r = -80.0 d = 3.0 Cs = [135.0e3, 61.0e3, 11.0e3] gs = [5.0e4, 1100.0, 1.0] As = [0.0, 0.0, 0.0] ns = [1.0, 1.0, 1.0] gmodels = [hardening.ConstantGamma(g) for g in gs] eta = 701.0 n = 10.5 surface = surfaces.IsoKinJ2() iso = hardening.VoceIsotropicHardeningRule(0.0, r, d) hmodel = hardening.Chaboche(iso, Cs, gmodels, As, ns) fluidity = visco_flow.ConstantFluidity(eta) vmodel = visco_flow.ChabocheFlowRule(surface, hmodel, fluidity, n) flow = general_flow.TVPFlowRule(elastic, vmodel) self.model2 = models.GeneralIntegrator(elastic, flow) self.T = 550.0 + 273.15 self.tmax = 10.0 self.nsteps = 100 self.emax = np.array([0.1, 0, 0, 0, 0, 0])
def test_damage(self): s0 = 180.0 Kp = 1000.0 H = 1000.0 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( self.elastic1, flow) W0 = 10.0 k0 = 0.0001 a0 = 2.0 model1 = damage.NEMLExponentialWorkDamagedModel_sd( self.elastic1, W0, k0, a0, bmodel) W02 = 10.0 k02 = 0.001 a02 = 1.5 model2 = damage.NEMLExponentialWorkDamagedModel_sd( self.elastic1, W02, k02, a02, bmodel) model = damage.CombinedDamageModel_sd(self.elastic1, [model1, model2], bmodel) self.very_close(model, self.emodel1) model.set_elastic_model(self.elastic2) self.very_close(model, self.emodel2)
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
def koo(): # Data from Koo & Kwon (2011) E = 157.0e3 nu = 0.27 sY = 0.0 b = 3.0 Q = -80.0 C1 = 135.0e3 C2 = 123.0e3 C3 = 4.0e3 g1 = 100e3 g2 = 0.85e3 g3 = 1.0 eta = 701.0 n = 10.5 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, C2, C3] gs = [hardening.ConstantGamma(g1), hardening.ConstantGamma(g2), hardening.ConstantGamma(g3)] hmodel = hardening.Chaboche(iso, cs, gs, [0.0]*len(cs), [1.0]*len(cs)) fluidity = visco_flow.ConstantFluidity(eta) vmodel = visco_flow.ChabocheFlowRule( surface, hmodel, fluidity, n) flow = general_flow.TVPFlowRule(elastic, vmodel) model = models.GeneralIntegrator(elastic, flow) e500 = np.array([0.0058793164, 0.0052876081, 0.004710156, 0.0042916722, 0.0038731605, 0.0032237573, 0.0027900399, 0.0024864991, 0.0017489338, 0.000635346, -0.0006668255, -0.0017811254, -0.0034891722, -0.0044012326, -0.0059358454, -0.005661599, -0.0051996206, -0.0048027165, -0.0044347716, -0.0039945684, -0.0034388636, -0.0032440594, -0.0026585856, -0.002036857, -0.001161945, -0.0003736313, 0.0008344368, 0.0022454705, 0.0035554683, 0.0052854997]) s500 = np.array([349.6965238343, 255.0932943767, 171.2928564634, 102.3697757811, 34.7967386021, -70.6166129529, -103.0909625627, -128.7931029969, -172.1191145041, -237.1093535238, -285.2558144812, -315.8199441656, -342.4341275638, -350.0133084444, -361.0726693423, -319.1748939033, -252.9445696747, -190.7753717856, -128.6110609317, -59.6843149729, 25.4625011672, 57.8965327357, 103.8969743143, 147.2034376803, 200.6779888803, 240.6374439409, 288.0930002819, 323.4323743399, 343.229143486, 357.0215788789]) res = drivers.strain_cyclic(model, 0.006, -1.0, 1.0e-4, 130, verbose = False, nsteps = 50) plt.plot(res['strain'][-100:], res['stress'][-100:], 'k-') plt.plot(e500, s500, 'kx') plt.xlabel("Strain (-/-)") plt.ylabel("Stress (MPa)") plt.show() n500 = np.array([1.8000456006, 7.2646606231, 17.3775914892, 25.6289731945, 35.040864809, 43.9864865417, 54.6731673353, 69.3076477381, 83.9405590891, 98.1077889527, 112.0424068927, 126.7891398736]) ns500 = sn500 = np.array([437.8476941068, 428.2481618804, 413.6055992266, 403.8518586317, 394.8643791744, 388.2393032756, 382.3835530687, 376.4641827161, 372.5718311079, 370.2817510291, 368.4971998147, 367.5615301197]) plt.plot(res['cycles'], res['max'], 'k-') plt.plot(n500, ns500, 'kx') plt.xlabel("Cycle") plt.ylabel("Stress (MPa)") plt.show()
eta_m = visco_flow.ConstantFluidity(eta_interp) flow_interp = interpolate.PiecewiseLinearInterpolate( list(Ts_rate), flow_stress_values) iso_rd = hardening.LinearIsotropicHardeningRule(0.0, -K / 10) iso_ri = hardening.LinearIsotropicHardeningRule( flow_interp, interpolate.ConstantInterpolate(-K / 10)) 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
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()
def setUp(self): self.E = 92000.0 self.nu = 0.3 self.s0 = 180.0 self.Kp = 1000.0 self.H = 1000.0 self.elastic = elasticity.IsotropicLinearElasticModel(self.E, "youngs", self.nu, "poissons") surface = surfaces.IsoKinJ2() iso = hardening.LinearIsotropicHardeningRule(self.s0, self.Kp) kin = hardening.LinearKinematicHardeningRule(self.H) hrule = hardening.CombinedHardeningRule(iso, kin) flow = ri_flow.RateIndependentAssociativeFlow(surface, hrule) self.bmodel = models.SmallStrainRateIndependentPlasticity(self.elastic, flow) self.fn = interpolate.PolynomialInterpolate([0.1,5.0, 1e-8]) self.n = 2.1 self.model = damage.NEMLWorkDamagedModel_sd( self.elastic, self.fn, self.n, self.bmodel, verbose = False) self.stress = np.array([100,-50.0,300.0,-99,50.0,125.0]) * 0.75 self.T = 100.0 self.s_np1 = self.stress self.s_n = np.array([-25,150,250,-25,-100,25]) * 0.0 self.d_np1 = 0.2 self.d_n = 0.1 self.e_np1 = np.array([0.1,-0.01,0.15,-0.05,-0.1,0.15]) * 0.75 self.e_n = np.array([-0.05,0.025,-0.1,0.2,0.11,0.13]) * 0.0 self.T_np1 = self.T self.T_n = 90.0 self.t_np1 = 5000.0 self.t_n = 0.9 self.u_n = 0.0 self.p_n = 0.0 # This is a rather boring baseline history state to probe, but I can't # think of a better way to get a "generic" history from a generic model self.hist_n = np.array([self.d_n] + list(self.bmodel.init_store())) self.x_trial = np.array([50,-25,150,-150,190,100.0] + [0.41]) self.nsteps = 10 self.etarget = np.array([0.1,-0.025,0.02,0.015,-0.02,-0.05]) self.ttarget = 2.0 self.ee = np.dot(self.elastic.S(self.T_np1), self.s_np1*(1.0-self.d_np1) - self.s_n*(1.0-self.d_n)) self.de = self.e_np1 - self.e_n self.dp = self.de - self.ee self.dt = self.t_np1 - self.t_n self.Wdot = np.dot(self.s_np1*(1.0-self.d_np1), self.dp) / self.dt
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
n = 20.0 eta = 108.0 sY = 89.0 Q = 165.0 b = 12.0 C1 = 80.0e3 C2 = 14.02e3 C3 = 3.333e3 y1 = 0.9e3 y2 = 1.5e3 y3 = 1.0 surface = surfaces.IsoKinJ2() iso = hardening.VoceIsotropicHardeningRule(sY, Q, b) cs = [C1, C2, C3] gs = np.array([y1, y2, y3]) gmodels = [hardening.ConstantGamma(g) for g in gs] hmodel = hardening.Chaboche(iso, cs, gmodels, [0.0] * len(cs), [1.0] * len(cs)) fluidity = visco_flow.ConstantFluidity(eta) vmodel = visco_flow.ChabocheFlowRule(surface, hmodel, fluidity, n) E = 92000.0 nu = 0.3 mu = E / (2 * (1 + nu))