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1import numpy as np

4# The indices of the full stiffness matrix of (orthorhombic) interest

5voigt_notation = [(0, 0), (1, 1), (2, 2), (1, 2), (0, 2), (0, 1)]

8def full_3x3_to_voigt_6_index(i, j):

9 if i == j:

10 return i

11 return 6 - i - j

14def voigt_6_to_full_3x3_strain(strain_vector):

15 """

16 Form a 3x3 strain matrix from a 6 component vector in Voigt notation

17 """

18 e1, e2, e3, e4, e5, e6 = np.transpose(strain_vector)

19 return np.transpose([[1.0 + e1, 0.5 * e6, 0.5 * e5],

20 [0.5 * e6, 1.0 + e2, 0.5 * e4],

21 [0.5 * e5, 0.5 * e4, 1.0 + e3]])

24def voigt_6_to_full_3x3_stress(stress_vector):

25 """

26 Form a 3x3 stress matrix from a 6 component vector in Voigt notation

27 """

28 s1, s2, s3, s4, s5, s6 = np.transpose(stress_vector)

29 return np.transpose([[s1, s6, s5],

30 [s6, s2, s4],

31 [s5, s4, s3]])

34def full_3x3_to_voigt_6_strain(strain_matrix):

35 """

36 Form a 6 component strain vector in Voigt notation from a 3x3 matrix

37 """

38 strain_matrix = np.asarray(strain_matrix)

39 return np.transpose([strain_matrix[..., 0, 0] - 1.0,

40 strain_matrix[..., 1, 1] - 1.0,

41 strain_matrix[..., 2, 2] - 1.0,

42 strain_matrix[..., 1, 2] + strain_matrix[..., 2, 1],

43 strain_matrix[..., 0, 2] + strain_matrix[..., 2, 0],

44 strain_matrix[..., 0, 1] + strain_matrix[..., 1, 0]])

47def full_3x3_to_voigt_6_stress(stress_matrix):

48 """

49 Form a 6 component stress vector in Voigt notation from a 3x3 matrix

50 """

51 stress_matrix = np.asarray(stress_matrix)

52 return np.transpose([stress_matrix[..., 0, 0],

53 stress_matrix[..., 1, 1],

54 stress_matrix[..., 2, 2],

55 (stress_matrix[..., 1, 2] +

56 stress_matrix[..., 2, 1]) / 2,

57 (stress_matrix[..., 0, 2] +

58 stress_matrix[..., 2, 0]) / 2,

59 (stress_matrix[..., 0, 1] +

60 stress_matrix[..., 1, 0]) / 2])