JulianKarlBauer / JulianKarlBauer/mechkit
Add "completely symmetric" fourth-order tensors to notation.ExplicitConverter
- Dominant language
- Python
- Stars
- 14
- Forks
- 8
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Description
Exchange of completely symmetric tensors, such as fiber orientation tensors of fourth order in a
minimal, i.e., nearly redundancy-free notation is a common task for engineers working with short fiber reinforced composites.
Support of
```
tensors =
con = mechkit.notation.ExplicitConverter()
con.convert(
inp=tensors, source="tensor", target="exchange", quantity="fiber_orientation"
)
```
with "exchange", e.g., being
```
[
N_1111, N_2222, N_3333,
N_2233, N_1133, N_1122,
N_1123, N_2223, N_3323,
N_1113, N_2213, N_3313,
N_1112, N_2212, N_3312,
]
```
See also equations (38) to (40) in
[Variety of fiber orientation tensors, Bauer and Böhlke 2021](https://journals.sagepub.com/doi/full/10.1177/10812865211057602)
It is clear, that, e.g., N_3333 could be omitted, as only 14 components are independent, but
not omitting it, will enable usage for, e.g., diffusion-weighted magnet resonance tomography tensors of fourth order,
which have no normalized trace.
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