def Evaluate(self, mechTest, stretchBound):
# Evaluate
# print('W = ', self._W)
# print('dW = ', self._dW)
l = self.DefineFunctionsInStretches(mechTest)
# print('W(uniaxial) = ', self._W)
# print('dW(uniaxial) = ', self._dW)
self.stretches = np.linspace(stretchBound[0], stretchBound[1], s)
self.W_v, self.dW_v, self.H_v, self.sigma_v = Evaluate.Functions(l, self.stretches, self._W, self._dW, self._H, self._sigma)
value = Evaluate.SinglePoint(self._W, l, 5.0)
P, dWoffset = [], 0.
P, dWoffset = Postulates.verify(l, self.stretches, self._W, self._dW, self._H, self._sigma)
print(P)
print(dWoffset)
return self.stretches, self.W_v, self.dW_v, self.H_v, self.sigma_v, P, dWoffset
def Evaluate(self, mechTest, stretchBound):
''' All '''
self._W = self.W
self._dW = self.dW
self._H = self.H
self._sigma = self.sigma
l, l_l1, l_l2, l_l3 = MechanicalTests.Uniaxial()
self.Substitute(self.mu, self._muC)
self.Substitute(self.alpha, self._alphaC)
self.Substitute(self.l1, l_l1)
self.Substitute(self.l2, l_l2)
self.Substitute(self.l3, l_l3)
self.stretches = np.linspace(stretchBound[0], stretchBound[1], s)
self.W_v, self.dW_v, self.H_v, self.sigma_v = Evaluate.Functions(l, self.stretches, self._W, self._dW, self._H, self._sigma)
''' Compression '''
self._W = self.W
self._dW = self.dW
self._H = self.H
self._sigma = self.sigma
l, l_l1, l_l2, l_l3 = MechanicalTests.Uniaxial()
self.Substitute(self.mu, self._muC)
self.Substitute(self.alpha, self._alphaC)
self.Substitute(self.l1, l_l1)
self.Substitute(self.l2, l_l2)
self.Substitute(self.l3, l_l3)
stretchesC = np.linspace(stretchBound[0], 1.0, s/2)
# W_vC, dW_vC, H_vC, sigma_vC = Evaluate.Functions(l, stretchesC, self._W, self._dW, self._H, self._sigma)
f_W = lambdify(l, self._W, "numpy")
W_vC = f_W(stretchesC)
# print("stretchesC",stretchesC.shape)
# print("W_vC",W_vC.shape)
''' Tension '''
self._W = self.W
self._dW = self.dW
self._H = self.H
self._sigma = self.sigma
l, l_l1, l_l2, l_l3 = MechanicalTests.Uniaxial()
self.Substitute(self.mu, self._muT)
self.Substitute(self.alpha, self._alphaT)
self.Substitute(self.l1, l_l1)
self.Substitute(self.l2, l_l2)
self.Substitute(self.l3, l_l3)
stretchesT = np.linspace(1.0, stretchBound[1], s / 2)
# W_vT, dW_vT, H_vT, sigma_vT = Evaluate.Functions(l, stretchesT, self._W, self._dW, self._H, self._sigma)
f_W = lambdify(l, self._W, "numpy")
W_vT = f_W(stretchesT)
# print("stretchesT",stretchesT.shape)
# print("W_vT",W_vT.shape)
# TODO Postulates (CORRECT since these is a combined tension compression test)
P, dWoffset = Postulates.verify(l, self.stretches, self._W, self._dW, self._H, self._sigma)
''' Join tests (W and stretches for now) '''
self.stretches = np.append(stretchesC, stretchesT)
self.W_v = np.append(W_vC, W_vT)
# print("stretches", self.stretches.shape)
# print("W_v", self.W_v.shape)
return self.stretches, self.W_v, self.dW_v, self.H_v, self.sigma_v, P, dWoffset
def verify(l, _lambdas, _W, _dW, _H, _sigma):
''' postulates '''
P1 = False
P2 = False
P3 = False
P4 = False
P5 = False
P6 = False
''' Resting state '''
print('Postulates @ Resting state:')
# W is zero
v = Evaluate.SinglePoint(_W, l, 1.0)
print(v)
if round(v, 4) == 0.0:
P1 = True
print(' W(1)={:.20f} is zero [{}]'.format(v, P1))
# dW is zero
v0 = Evaluate.SinglePoint(_dW[0], l, 1.0)
v1 = Evaluate.SinglePoint(_dW[1], l, 1.0)
v2 = Evaluate.SinglePoint(_dW[2], l, 1.0)
dWoffset = -v0
print(v0)
print(v1)
print(v2)
if round(v0, 4) == 0.0 and round(v1, 4) == 0.0 and round(v2, 4) == 0.0:
P2 = True
print(' dW(1)=[{:.4f},{:.4f},{:.4f}] is zero [{}]'.format(
v0, v1, v2, P2))
# diag(H) > 0
v0 = Evaluate.SinglePoint(_H[0, 0], l, 1.0)
v1 = Evaluate.SinglePoint(_H[1, 1], l, 1.0)
v2 = Evaluate.SinglePoint(_H[2, 2], l, 1.0)
if v0 > 0.0 and v1 > 0.0 and v2 > 0.0:
P3 = True
print(' diag(H)=[{:.4f},{:.4f},{:.4f}] is > 0 [{}]'.format(
v0, v1, v2, P3))
# det(H) > 0
H1 = np.zeros((3, 3))
for i in range(3):
for j in range(3):
H1[i, j] = Evaluate.SinglePoint(_H[i, j], l, 1.0)
v = np.linalg.det(H1)
if v > 0.0:
P4 = True
print(' det(H)={:.4f} is > 0 [{}]'.format(v, P4))
''' Deforming state '''
print('Postulates @ Deforming state:')
# W is non-negative
W_v, dW_v, H_v, sigma_v = Evaluate.Functions(l, _lambdas, _W, _dW, _H,
_sigma)
P5 = not any(v < 0 for v in W_v)
print(' W is non-negative [{}]'.format(P5))
# dW is monotonicly increasing
P6 = monotonic_increasing(dW_v[0])
print(' dW is monotonic increasing [{}]'.format(P6))
# print(_dW[0])
# axis = plt.subplot(121)
# plt.plot(_lambdas, W_v)
# axis.set_xlim([0, 5])
# axis.set_ylim([0, 4e7])
# axis = plt.subplot(122)
# plt.plot(_lambdas, dW_v[0]-dWoffset)
# axis.set_xlim([-5, 5])
# axis.set_ylim([-2e7, 2e7])
# plt.show()
# print(_lambdas)
# print(W_v)
# print(dW_v[0])
# input('break')
P = np.asarray([P1, P2, P3, P4, P5, P6])
return P, dWoffset