Backend package

This package contains backends for computing the displacement field

dislocation_tools.backend.stroh

Implements Stroh theory

dislocation_tools.backend.integral

Implements the integral method

dislocation_tools.backend.stroh Module

Implements Stroh theory

Functions for computing the displacement field using Stroh’s formalism [1]. The variables of the elastic problem are given similar names as in Refs. [2] and [3].

References

  1. Stroh, A.N. J. Math. Phys., 41: 77 (1962)

  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.

Functions

calculate_displacements_from_eigensystem(…)

Compute the displacements from the solution of the sextic equations.

solve_sextic_equations(m, n, c)

Compute the eigenvalues and eigenvectors of the problem.

dislocation_tools.backend.integral Module

Implements the integral method

Functions for computing the displacement field using the integral formalism [1]. The variables of the elastic problem are given similar names as in Refs. [2] and [3].

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.

Functions

calculate_cylindrical_coordinates(…)

Calculate cylindrical coordinates

calculate_displacements_with_numerical_integrals(…)

Compute the displacements with integral formalism and numerical math

calculate_displacements_with_symbolical_integrals(…)

Compute the displacements with integral formalism and symbolical math

check_S_and_B(S, B, m, n, c)

Check the matrices S and B of the integral formalism.

generate_numerical_rotation_matrix(axis, angle)

Generate numeric rotation matrix for rotation about an axis by an angle

generate_symbolical_rotation_matrix(axis)

Generate symbolic rotation matrix for rotation about an axis by an angle

ufuncify_angular_function(…)

Convert a matrix of symbolical functions into numerical functions