Tensor module

Functions for working with tensors

dislocation_tools.tensor.numerical_ab_contraction(a, b, t)

Return a contraction of the fourth order tensor t and the vectors a and b

See equation 13-162 in Hirth & Lothe’s book [1]

In component notation

\[(ab)_{ij} = a_{i}c_{ijkl}b_{l}.\]

This function performs the contraction numerically.

References

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

dislocation_tools.tensor.symbolical_ab_contraction(a, b, t)

Return a contraction of the fourth order tensor t and the vectors a and b

See equation 13-162 in Hirth & Lothe’s book [1]

In component notation

\[(ab)_{ij} = a_{i}c_{ijkl}b_{l}.\]

This function performs the contraction symbolically.

References

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

dislocation_tools.tensor.tensor2voigt(t)

Convert a fourth order tensor into a Voigt matrix.

Parameters

t (array-like:) – elastic stiffness tensor in 3x3x3x3 array representation

Returns

v – elastic stiffness in 6x6 (Voigt-) matrix representation

Return type

numpy.ndarray

dislocation_tools.tensor.voigt2tensor(v)

Convert a Voigt matrix into a fourth order tensor.

Parameters

v (array-like) – elastic stiffness in 6x6 (Voigt-) matrix representation

Returns

t – elastic stiffness tensor in 3x3x3x3 array representation

Return type

numpy.ndarray