check_S_and_B

dislocation_tools.backend.integral.check_S_and_B(S, B, m, n, c)

Check the matrices S and B of the integral formalism.

\(\mathbf{S}\) and \(\mathbf{B}\) can be computed both from Barnett and Lothe’s integral formalism, as well as from Stroh’s formalism, see equations (13-211), (13-213), (13-215), and (13-217) in Hirth and Lothe’s book [2]. This function checks \(\mathbf{S}\) and \(\mathbf{B}\) as obtained from the integral formalism by comparing them to the corresponding prediction from Stroh’s formalism.

Parameters

  • S (array-like) – matrix \(\mathbf{S}\), see equ. 13-211 in Hirth and Lothe’s book [2]

  • B (array-like) – matrix \(\mathbf{B}\), see equ. 13-213 in Hirth and Lothe’s book [2]

  • m (array-like) – x-direction of the dislocation coordinate system

  • n (array-like) – y-direction of the dislocation coordinate system

  • c (array-like) – 3×3×3×3 array representation of elastic stiffness, given in laboratory coordinates

References

  1. Barnett, D.M.; Lothe, J. Phys. Norvegica, 7 (1973)

  2. Hirth, J.P.; Lothe, J. Theory of Dislocations, 2nd Edition; John Wiley and Sons, 1982. pp 467

  3. Bacon, D. J.; Barnett, D. M.; Scattergood, R. O. Progress in Materials Science 1978, 23, 51-262.