def setUp(self): self.A = np.array([[4.1,2.8,-1.2],[3.1,7.1,0.2],[4,2,3]]) self.A = 0.5*(self.A - self.A.T) self.TA = tensors.Skew(self.A) self.B = np.array([[10.2,-9.3,2.5],[0.1,3.1,2.8],[0.1,3.2,-6.1]]) self.B = 0.5*(self.B - self.B.T) self.TB = tensors.Skew(self.B) self.a = np.array([2.2,-1.2,2.5]) self.va = tensors.Vector(self.a) self.s = 2.1
def setUp(self): self.SS = np.array([ [ 5.99159801, -2.24342348, 0.26667281, -0.95466199, 3.98931478, -0.10846981], [ 1.86468226, -4.32391908, -7.82738638, -7.45008989, 5.89874777, 0.45820648], [-5.92565398, 2.4862829 , -6.02112389, 6.75455965, 4.65183463, 9.96900579], [ 0.60378883, -3.72189328, -7.63388446, -5.76559403, -0.3119789 , -1.1527258 ], [ 4.56813135, -6.06783828, -6.18341368, 8.06169686, -9.56928844, 9.08114655], [-8.25516614, 6.30663846, 7.2084381 , -7.38280703, -5.96279902, 8.9935982 ]]) self.SS_full = common.ms2ts(self.SS) self.TSS = tensors.SymSymR4(self.SS) self.W = np.array([[-9.36416517, 2.95527444, 8.70983194], [-1.54693052, 8.7905658 , -5.10895168], [-8.52740468, -0.7741642 , 2.89544992]]) self.W = 0.5 * (self.W - self.W.T) self.TW = tensors.Skew(self.W) self.S = np.array([[4.1,2.8,-1.2],[3.1,7.1,0.2],[4,2,3]]) self.S = 0.5*(self.S + self.S.T) self.TS = tensors.Symmetric(self.S) self.WS = np.array([ [-8.3567359 , -5.39728818, -8.00844442, -8.33365112, -0.97903364, -8.23943149], [-6.97125417, 4.34802055, 7.06281056, -1.57511617, 7.83359933, -9.37625432], [-6.0799489 , -6.0309543 , 3.68575895, 8.84296976, 6.55799427, -9.22029379]]) self.WS_full = common.wws2ts(self.WS) self.TWS = tensors.SkewSymR4(self.WS)
def test_spin_rate(self): Cfull = ms2ts( self.emodel.C_tensor(self.T, self.Q).data.reshape((6, 6))) Sfull = ms2ts( self.emodel.S_tensor(self.T, self.Q).data.reshape((6, 6))) d = usym(self.d.data) w = uskew(self.w.data) Ofull = uskew(self.fspin.data) dp = usym( self.imodel.d_p(self.S, self.Q, self.H, self.L, self.T, self.fixed).data) wp = uskew( self.imodel.w_p(self.S, self.Q, self.H, self.L, self.T, self.fixed).data) O = wp + Ofull stress = usym(self.S.data) e = np.einsum('ijkl,kl', Sfull, stress) spin1 = tensors.Skew(w - wp - np.dot(e, dp) + np.dot(dp, e)) spin2 = self.model.spin(self.S, self.d, self.w, self.Q, self.H, self.L, self.T, self.fixed) self.assertTrue(spin1, spin2)
def setUp(self): self.strength = 35.0 self.H = history.History() self.H.add_scalar("strength") self.H.set_scalar("strength", self.strength) self.H.add_scalar("whatever") self.H.set_scalar("whatever", 0.5) self.tau0 = 10.0 self.tau_sat = 50.0 self.b = 2.5 self.strengthmodel = slipharden.VoceSlipHardening( self.tau_sat, self.b, self.tau0) self.g0 = 1.0 self.n = 3.0 self.slipmodel = sliprules.PowerLawSlipRule(self.strengthmodel, self.g0, self.n) self.imodel = inelasticity.AsaroInelasticity(self.slipmodel) self.L = crystallography.CubicLattice(1.0) self.L.add_slip_system([1, 1, 0], [1, 1, 1]) self.Q = rotations.Orientation(35.0, 17.0, 14.0, angle_type="degrees") self.S = tensors.Symmetric( np.array([[100.0, -25.0, 10.0], [-25.0, -17.0, 15.0], [10.0, 15.0, 35.0]])) self.T = 300.0 self.mu = 29000.0 self.E = 120000.0 self.nu = 0.3 self.emodel = elasticity.CubicLinearElasticModel( self.E, self.nu, self.mu, "moduli") self.dn = np.array([[4.1, 2.8, -1.2], [3.1, 7.1, 0.2], [4, 2, 3]]) self.dn = 0.5 * (self.dn + self.dn.T) self.d = tensors.Symmetric(self.dn) self.wn = np.array([[-9.36416517, 2.95527444, 8.70983194], [-1.54693052, 8.7905658, -5.10895168], [-8.52740468, -0.7741642, 2.89544992]]) self.wn = 0.5 * (self.wn - self.wn.T) self.w = tensors.Skew(self.wn) self.dmodel = crystaldamage.NilDamageModel() self.model = kinematics.DamagedStandardKinematicModel( self.emodel, self.imodel, self.dmodel) self.fspin = self.model.spin(self.S, self.d, self.w, self.Q, self.H, self.L, self.T, history.History()) self.fixed = self.model.decouple(self.S, self.d, self.w, self.Q, self.H, self.L, self.T, history.History())
def setUp(self): self.scalar = 2.5 self.vector = tensors.Vector(np.array([1.0, 2.0, 3.0])) self.ranktwo = tensors.RankTwo( np.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0], [7.0, 8.0, 9.0]])) self.symmetric = tensors.Symmetric(np.eye(3)) q = np.array([[1.0, 2.0, 3.0], [3.0, 4.0, 5.0], [6.0, 7.0, 8.0]]) q = 0.5 * (q - q.T) self.skew = tensors.Skew(q) self.orientation = rotations.Orientation(30.0, 60.0, 80.0, angle_type="degrees") self.hist1 = history.History() self.hist2 = history.History(store=False) self.add_all(self.hist1) self.add_all(self.hist2) self.storage = np.zeros((self.hist2.size, )) self.hist2.set_data(self.storage) self.set_all(self.hist1) self.set_all(self.hist2)
def test_W(self): for i in range(self.lattice.ngroup): for j in range(self.lattice.nslip(i)): self.assertEqual( tensors.Skew( np.dot(self.QM,np.dot(np.outer(self.lattice.slip_directions[i][j].data, self.lattice.slip_planes[i][j].data), self.QM.T))), self.lattice.N(i,j,self.Q))
def setUp(self): self.S = np.array([[4.1,2.8,-1.2],[3.1,7.1,0.2],[4,2,3]]) self.S = 0.5*(self.S + self.S.T) self.TS = tensors.Symmetric(self.S) self.G = np.array([[10.2,-9.3,2.5],[0.1,3.1,2.8],[0.1,3.2,-6.1]]) self.TG = tensors.RankTwo(self.G) self.W = np.array([[-5.0,7.1,1.0],[-0.2,0.25,1.2],[-0.4,0.4,-2]]) self.W = 0.5*(self.W - self.W.T) self.TW = tensors.Skew(self.W)
def setUp(self): self.q = rotations.Orientation(30.0, 60.0, 80.0, angle_type = "degrees") self.Q = self.q.to_matrix() self.v = np.array([1.2,-2.0,3.0]) self.Tv = tensors.Vector(self.v) self.A = np.array([[4.1,2.8,-1.2],[3.1,7.1,0.2],[4,2,3]]) self.TA = tensors.RankTwo(self.A) self.S = np.array([[4.1,2.8,-1.2],[3.1,7.1,0.2],[4,2,3]]) self.S = 0.5*(self.S + self.S.T) self.TS = tensors.Symmetric(self.S) self.W = np.array([[4.1,2.8,-1.2],[3.1,7.1,0.2],[4,2,3]]) self.W = 0.5*(self.W - self.W.T) self.TW = tensors.Skew(self.W) self.R1 = np.array([[[[ 7.09627147, 9.22330744, -1.36602973], [-7.86118175, -1.6342633 , -5.75516189], [ 2.61734248, 6.40678382, 3.37981603]], [[ 5.65100254, -7.88797059, 7.31396665], [-6.35471595, 5.67698069, -8.18795178], [ 9.10447016, 8.91183436, -6.65254333]], [[ 3.20429862, 2.99308849, 4.0035241 ], [-4.02440197, -4.39975872, -4.33542791], [ 9.36746226, -2.91156335, 4.51572032]]], [[[-9.23675199, 8.63546962, 6.83448027], [ 4.35044123, 2.24508666, 9.80054664], [ 0.30835223, -4.05208575, 5.68966326]], [[ 6.40300092, -8.25998136, 5.63566553], [-5.02801101, 5.64005224, -7.39586166], [ 5.90893633, 6.02074669, 1.37112738]], [[-2.68485216, -4.67660156, 3.52618441], [-2.52484812, -0.08561168, 3.39072868], [ 9.11295675, 2.63102786, -4.82285415]]], [[[ 8.31973154, 4.76081593, 4.38377207], [ 6.22896742, -3.83995097, 5.37501029], [-0.16770967, 7.9453854 , -4.95548491]], [[-5.67884611, -8.44970885, -7.42037867], [-5.19908193, -7.87006493, 1.65949787], [-3.25934672, 6.27340198, 5.98643056]], [[-4.20166968, -2.38276224, 3.04551936], [ 3.68445989, -5.84357996, 3.61183543], [ 1.54886677, 3.3659842 , 6.43067337]]]]) self.TR1 = tensors.RankFour(self.R1) self.SS1 = np.array([ [ 5.99159801, -2.24342348, 0.26667281, -0.95466199, 3.98931478, -0.10846981], [ 1.86468226, -4.32391908, -7.82738638, -7.45008989, 5.89874777, 0.45820648], [-5.92565398, 2.4862829 , -6.02112389, 6.75455965, 4.65183463, 9.96900579], [ 0.60378883, -3.72189328, -7.63388446, -5.76559403, -0.3119789 , -1.1527258 ], [ 4.56813135, -6.06783828, -6.18341368, 8.06169686, -9.56928844, 9.08114655], [-8.25516614, 6.30663846, 7.2084381 , -7.38280703, -5.96279902, 8.9935982 ]]) self.SSS1 = ms2ts(self.SS1) self.TSS1 = tensors.SymSymR4(self.SS1)
def test_w_p(self): w = tensors.Skew(np.zeros((3, 3))) for g in range(self.L.ngroup): for i in range(self.L.nslip(g)): w += self.slipmodel.slip(g, i, self.S, self.Q, self.H, self.L, self.T, self.fixed) * self.L.N( g, i, self.Q) self.assertEqual( w, self.model.w_p(self.S, self.Q, self.H, self.L, self.T, self.fixed))
def setUp(self): self.scalar = 2.5 self.vector = tensors.Vector(np.array([1.0, 2.0, 3.0])) self.ranktwo = tensors.RankTwo( np.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0], [7.0, 8.0, 9.0]])) self.symmetric = tensors.Symmetric(np.eye(3)) q = np.array([[1.0, 2.0, 3.0], [3.0, 4.0, 5.0], [6.0, 7.0, 8.0]]) q = 0.5 * (q - q.T) self.skew = tensors.Skew(q) self.hist = history.History() self.add_all(self.hist) self.set_all(self.hist)
def test_correctly_integrates(self): # So we are rotating about x where t is the rotation in radians R = lambda t: np.array([[1.0,0,0],[0,np.cos(t),-np.sin(t)],[0,np.sin(t), np.cos(t)]]) q0 = rotations.Orientation(R(0.0)) spin = tensors.Skew(np.array([ [0,0,0], [0,0,-1.0], [0,1.0,0]])) nsteps = 1000 # Well it's not the most accurate integration ang = np.pi/4.0 qf = rotations.Orientation(R(ang)) q = q0 for i in range(nsteps): q = rotations.wexp(spin * ang/nsteps) * q self.assertTrue(np.allclose(q.quat, qf.quat))
def setUp(self): self.tau0 = 10.0 self.tau_sat = 50.0 self.b = 2.5 self.strengthmodel = slipharden.VoceSlipHardening( self.tau_sat, self.b, self.tau0) self.g0 = 1.0 self.n = 3.0 self.slipmodel = sliprules.PowerLawSlipRule(self.strengthmodel, self.g0, self.n) self.imodel = inelasticity.AsaroInelasticity(self.slipmodel) self.L = crystallography.CubicLattice(1.0) self.L.add_slip_system([1, 1, 0], [1, 1, 1]) self.Q = rotations.Orientation(35.0, 17.0, 14.0, angle_type="degrees") self.mu = 29000.0 self.E = 120000.0 self.nu = 0.3 self.emodel = elasticity.CubicLinearElasticModel( self.E, self.nu, self.mu, "moduli") self.kmodel = kinematics.StandardKinematicModel( self.emodel, self.imodel) self.model = singlecrystal.SingleCrystalModel(self.kmodel, self.L, initial_rotation=self.Q) self.model_no_rot = singlecrystal.SingleCrystalModel( self.kmodel, self.L, initial_rotation=self.Q, update_rotation=False, verbose=False) self.T = 300.0 self.stress_n = np.array([120.0, -60.0, 170.0, 35.0, 80.0, -90.0]) self.stress_np1 = np.array([15.0, -40.0, 120.0, 70.0, -10.0, -50.0]) self.d = np.array([0.1, -0.2, 0.25, 0.11, -0.05, 0.075]) self.w = np.array([0.1, 0.2, -0.2]) self.strength_n = 25.0 self.strength_np1 = 30.0 self.S_np1 = tensors.Symmetric(common.usym(self.stress_np1)) self.S_n = tensors.Symmetric(common.usym(self.stress_n)) self.D = tensors.Symmetric(common.usym(self.d)) self.W = tensors.Skew(common.uskew(self.w)) self.strength_n = 25.0 self.strength_np1 = 30.0 self.H_n = history.History() self.H_n.add_scalar("strength") self.H_n.set_scalar("strength", self.strength_n) self.H_np1 = history.History() self.H_np1.add_scalar("strength") self.H_np1.set_scalar("strength", self.strength_np1) self.dt = 2.0 self.fixed = self.kmodel.decouple(self.S_n, self.D, self.W, self.Q, self.H_n, self.L, self.T, history.History()) self.ts = singlecrystal.SCTrialState(self.D, self.W, self.S_n, self.H_n, self.Q, self.L, self.T, self.dt, self.fixed) self.x = np.zeros((self.model.nparams, )) self.x[:6] = self.stress_np1 self.x[6] = self.strength_np1 self.Ddir = np.array([0.01, -0.005, -0.003, 0.01, 0.02, -0.003]) * 2 self.Wdir = np.array([0.02, -0.03, 0.01]) * 2 self.nsteps = 10
def setUp(self): self.q = rotations.Orientation(30.0, 60.0, 80.0, angle_type = "degrees") self.W = np.array([[4.1,2.8,-1.2],[3.1,7.1,0.2],[4,2,3]]) self.W = 0.5*(self.W - self.W.T) self.TW = tensors.Skew(self.W)
def test_apply_skew(self): self.assertEqual(self.q.apply(self.TW), tensors.Skew(np.dot(self.Q, np.dot(self.W, self.Q.T))))
def setUp(self): self.L = crystallography.CubicLattice(1.0) self.L.add_slip_system([1, 1, 0], [1, 1, 1]) self.nslip = self.L.ntotal self.strength = 35.0 self.c = 10.0 self.beta = 2.0 self.H = history.History() for i in range(12): self.H.add_scalar("strength" + str(i)) self.H.set_scalar("strength" + str(i), self.strength) for j in range(4): self.H.add_scalar("slip_damage_" + str(j)) self.H.set_scalar("slip_damage_" + str(j), self.c * 0.4) self.static = 20.0 self.s0 = [self.static] * self.nslip self.k = 1000.0 self.sat = 40.0 self.m = 1.5 self.strengthmodel = slipharden.VocePerSystemHardening( self.s0, [self.k] * self.nslip, [self.sat] * self.nslip, [self.m] * self.nslip) self.g0 = 1.0 self.n = 3.0 self.slipmodel = sliprules.PowerLawSlipRule(self.strengthmodel, self.g0, self.n) self.imodel = inelasticity.AsaroInelasticity(self.slipmodel) self.Q = rotations.Orientation(35.0, 17.0, 14.0, angle_type="degrees") self.S = tensors.Symmetric( np.array([[100.0, -25.0, 10.0], [-25.0, -17.0, 15.0], [10.0, 15.0, 35.0]])) self.T = 300.0 self.mu = 29000.0 self.E = 120000.0 self.nu = 0.3 self.emodel = elasticity.CubicLinearElasticModel( self.E, self.nu, self.mu, "moduli") self.dn = np.array([[4.1, 2.8, -1.2], [3.1, 7.1, 0.2], [4, 2, 3]]) self.dn = 0.5 * (self.dn + self.dn.T) self.d = tensors.Symmetric(self.dn) self.wn = np.array([[-9.36416517, 2.95527444, 8.70983194], [-1.54693052, 8.7905658, -5.10895168], [-8.52740468, -0.7741642, 2.89544992]]) self.wn = 0.5 * (self.wn - self.wn.T) self.w = tensors.Skew(self.wn) self.dmodel = crystaldamage.WorkPlaneDamage() self.nfunc = crystaldamage.SigmoidTransformation(self.c, self.beta) self.sfunc = crystaldamage.SigmoidTransformation(self.c, self.beta) self.dmodel = crystaldamage.PlanarDamageModel(self.dmodel, self.nfunc, self.sfunc, self.L) self.model = kinematics.DamagedStandardKinematicModel( self.emodel, self.imodel, self.dmodel) self.fspin = self.model.spin(self.S, self.d, self.w, self.Q, self.H, self.L, self.T, history.History()) self.fixed = self.model.decouple(self.S, self.d, self.w, self.Q, self.H, self.L, self.T, history.History())
def test_add(self): self.assertEqual(tensors.Skew(self.A + self.B), self.TA + self.TB) self.assertEqual(tensors.Skew(self.A - self.B), self.TA - self.TB)
def diff_history_skew(fn, w0): dfn = lambda w: np.array(fn(tensors.Skew(uskew(w)))) return differentiate(dfn, w0.data)
def diff_symmetric_skew(fn, w0): dfn = lambda w: fn(tensors.Skew(uskew(w))).data return tensors.SymSkewR4(differentiate(dfn, w0.data))
def test_transpose(self): self.assertEqual(tensors.Skew(self.A.T), self.TA.transpose())
def test_matrix_matrix(self): self.assertEqual(tensors.Skew(np.dot(self.A, self.B)), self.TA*self.TB)
def test_w_p(self): self.assertEqual( tensors.Skew(np.zeros((3, 3))), self.model.w_p(self.S, self.Q, self.H, self.L, self.T, self.fixed))
def setUp(self): self.WS1 = np.array([ [-8.3567359 , -5.39728818, -8.00844442, -8.33365112, -0.97903364, -8.23943149], [-6.97125417, 4.34802055, 7.06281056, -1.57511617, 7.83359933, -9.37625432], [-6.0799489 , -6.0309543 , 3.68575895, 8.84296976, 6.55799427, -9.22029379]]) self.WS1_full = common.wws2ts(self.WS1) self.TWS1 = tensors.SkewSymR4(self.WS1) self.WS2 = np.array([ [-8.80662663, 0.46179936, -5.49454144, 7.91618428, 5.34053953, -6.68997405], [ 4.15874971, -4.59781751, 7.43746813, 8.99981425, -0.97692573, 2.5075246 ], [ 9.53201007, -8.03524224, 0.94329443, -6.44415877, -9.92911741, 3.51742689]]) self.WS2_full = common.wws2ts(self.WS2) self.TWS2 = tensors.SkewSymR4(self.WS2) self.SW = np.array([ [ 5.43434005, -6.55983214, 0.29737664], [-4.77472172, -8.51287287, -3.19380185], [ 4.43407952, -6.02555614, 5.87786914], [ 1.89488869, -5.65383917, 8.83717547], [-7.18030867, 1.56100537, -9.83238641], [-4.52369317, -3.07284914, -7.54966999]]) self.SW_full = common.ws2ts(self.SW) self.TSW = tensors.SymSkewR4(self.SW) self.SS = np.array([ [ 5.99159801, -2.24342348, 0.26667281, -0.95466199, 3.98931478, -0.10846981], [ 1.86468226, -4.32391908, -7.82738638, -7.45008989, 5.89874777, 0.45820648], [-5.92565398, 2.4862829 , -6.02112389, 6.75455965, 4.65183463, 9.96900579], [ 0.60378883, -3.72189328, -7.63388446, -5.76559403, -0.3119789 , -1.1527258 ], [ 4.56813135, -6.06783828, -6.18341368, 8.06169686, -9.56928844, 9.08114655], [-8.25516614, 6.30663846, 7.2084381 , -7.38280703, -5.96279902, 8.9935982 ]]) self.SS_full = common.ms2ts(self.SS) self.TSS = tensors.SymSymR4(self.SS) self.R = np.array([[[[-8.03675620e+00, 2.58575052e+00, 2.44069661e+00], [ 4.75021663e+00, 1.24463394e+00, -8.69751301e-01], [-1.46310894e+00, -1.15053235e+00, -3.75342982e+00]], [[-7.64033956e+00, 4.19956720e+00, -4.87644982e+00], [ 1.06577507e+00, 8.94272637e+00, 6.57264250e-01], [-4.22613258e+00, -5.08830314e+00, 1.57718186e+00]], [[-4.02243082e+00, -4.75463781e+00, -8.88662152e+00], [-1.30383950e+00, -1.98063574e+00, -3.18963544e+00], [-7.52071674e+00, 1.08931933e+00, 2.86988431e+00]]], [[[ 5.28621060e+00, -6.83799668e+00, 8.98005935e+00], [-7.92741122e+00, 5.75699425e-01, 1.66782544e+00], [ 2.60041984e+00, -1.04476986e-02, -6.12424787e+00]], [[-3.73727368e+00, 6.59764771e+00, -1.18045587e+00], [ 4.08567441e+00, 2.66148943e+00, -6.82495588e-01], [-1.64417262e+00, 5.33119298e+00, 8.11045988e-03]], [[-5.90193883e+00, -2.63316107e+00, 5.61381825e+00], [-6.08591194e+00, 8.77285539e+00, -7.15230533e+00], [ 3.15093096e+00, 1.41350149e+00, 1.11702016e+00]]], [[[-9.61472764e-01, -1.91492497e+00, 9.48275324e+00], [ 6.68841134e+00, 3.23412041e+00, -3.41944541e+00], [-9.80203467e+00, 6.58425335e+00, -2.16548636e+00]], [[ 6.63950740e+00, 3.91551441e+00, -8.98229111e+00], [ 9.84606756e+00, -8.16145090e+00, 8.41929062e-01], [-1.93839620e+00, 7.44485127e+00, -2.70832414e+00]], [[ 9.79265531e+00, -1.18212395e+00, -5.39433704e+00], [ 4.87152614e+00, 9.47287450e+00, 5.53838514e+00], [ 9.30443367e+00, 1.27090319e+00, 1.60409739e+00]]]]) self.TR = tensors.RankFour(self.R) self.S = np.array([[4.1,2.8,-1.2],[3.1,7.1,0.2],[4,2,3]]) self.S = 0.5*(self.S + self.S.T) self.TS = tensors.Symmetric(self.S) self.scalar = 5.2 self.G = np.array([[ 9.50640677, 1.79084726, -2.8877036 ], [-1.63159958, 2.52866904, -8.71585042], [ 5.01859685, -8.7324075 , -0.42919134]]) self.TG = tensors.RankTwo(self.G) self.W = np.array([[-9.36416517, 2.95527444, 8.70983194], [-1.54693052, 8.7905658 , -5.10895168], [-8.52740468, -0.7741642 , 2.89544992]]) self.W = 0.5 * (self.W - self.W.T) self.TW = tensors.Skew(self.W)
def test_scalar_mult(self): self.assertEqual(tensors.Skew(self.s*self.A), self.s * self.TA) self.assertEqual(tensors.Skew(self.A / self.s), self.TA / self.s)