@func
def sym_eig3x3(A, dt):
M_SQRT3 = 1.73205080756887729352744634151
m = A.trace()
dd = A[0, 1] * A[0, 1]
ee = A[1, 2] * A[1, 2]
ff = A[0, 2] * A[0, 2]
c1 = A[0, 0] * A[1, 1] + A[0, 0] * A[2, 2] + A[1, 1] * A[2, 2] - (dd + ee +
ff)
c0 = A[2, 2] * dd + A[0, 0] * ee + A[1, 1] * ff - A[0, 0] * A[1, 1] * A[
2, 2] - 2.0 * A[0, 2] * A[0, 1] * A[1, 2]
p = m * m - 3.0 * c1
q = m * (p - 1.5 * c1) - 13.5 * c0
sqrt_p = ops.sqrt(ops.abs(p))
phi = 27.0 * (0.25 * c1 * c1 * (p - c1) + c0 * (q + 6.75 * c0))
phi = (1.0 / 3.0) * ops.atan2(ops.sqrt(ops.abs(phi)), q)
c = sqrt_p * ops.cos(phi)
s = (1.0 / M_SQRT3) * sqrt_p * ops.sin(phi)
eigenvalues = Vector([0.0, 0.0, 0.0], dt=dt)
eigenvalues[2] = (1.0 / 3.0) * (m - c)
eigenvalues[1] = eigenvalues[2] + s
eigenvalues[0] = eigenvalues[2] + c
eigenvalues[2] = eigenvalues[2] - s
t = ops.abs(eigenvalues[0])
u = ops.abs(eigenvalues[1])
if u > t:
t = u
u = ops.abs(eigenvalues[2])
if u > t:
t = u
if t < 1.0:
u = t
else:
u = t * t
Q = Matrix.zero(dt, 3, 3)
Q[0, 1] = A[0, 1] * A[1, 2] - A[0, 2] * A[1, 1]
Q[1, 1] = A[0, 2] * A[0, 1] - A[1, 2] * A[0, 0]
Q[2, 1] = A[0, 1] * A[0, 1]
Q[0, 0] = Q[0, 1] + A[0, 2] * eigenvalues[0]
Q[1, 0] = Q[1, 1] + A[1, 2] * eigenvalues[0]
Q[2, 0] = (A[0, 0] - eigenvalues[0]) * (A[1, 1] - eigenvalues[0]) - Q[2, 1]
norm = Q[0, 0] * Q[0, 0] + Q[1, 0] * Q[1, 0] + Q[2, 0] * Q[2, 0]
norm = ops.sqrt(1.0 / norm)
Q[0, 0] *= norm
Q[1, 0] *= norm
Q[2, 0] *= norm
Q[0, 1] = Q[0, 1] + A[0, 2] * eigenvalues[1]
Q[1, 1] = Q[1, 1] + A[1, 2] * eigenvalues[1]
Q[2, 1] = (A[0, 0] - eigenvalues[1]) * (A[1, 1] - eigenvalues[1]) - Q[2, 1]
norm = Q[0, 1] * Q[0, 1] + Q[1, 1] * Q[1, 1] + Q[2, 1] * Q[2, 1]
norm = ops.sqrt(1.0 / norm)
Q[0, 1] *= norm
Q[1, 1] *= norm
Q[2, 1] *= norm
Q[0, 2] = Q[1, 0] * Q[2, 1] - Q[2, 0] * Q[1, 1]
Q[1, 2] = Q[2, 0] * Q[0, 1] - Q[0, 0] * Q[2, 1]
Q[2, 2] = Q[0, 0] * Q[1, 1] - Q[1, 0] * Q[0, 1]
return eigenvalues, Q
这里当norm 为0的时候会出错，计算应力张量的时候初始数值都是0，有没有啥办法解决？