Functions to compute some tensor-related quantities usual in continuum mechanics.
Encapsulates functions to convert various stress tensors in the symmetric storage given the deformation state.
Given the space dimension, return the symmetric storage size.
The deviatoric part (deviator) of a tensor.
The indices for converting the symmetric storage to the full storage.
The non_diagonal indices for the full vector storage.
The indices for converting the full storage to the symmetric storage.
Get the full 4D tensor with major/minor symmetries from its 2D matrix representation.
Parameters: | t2s : array
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Returns: | t4 : array
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The volumetric part of a tensor.
Given a symmetric stress tensor, compute the von Mises stress (also known as Equivalent tensile stress).
Notes
\sigma_V = \sqrt{\frac{(\sigma_{11} - \sigma_{22})^2 + (\sigma_{22} - \sigma_{33})^2 + (\sigma_{11} - \sigma_{33})^2 + 6 (\sigma_{12}^2 + \sigma_{13}^2 + \sigma_{23}^2)}{2}}
Prepare matrices for transforming tensors into cylindrical coordinates with the axis ‘z’ in a given origin.
Parameters: | coors : array
origin : array of length 3
mode : ‘axes’ or ‘data’
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Returns: | mtx : array
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Given the symmetric storage size, return the space dimension.
Notes
This function works for any space dimension.
Transform vector or tensor data components between orthogonal coordinate systems in 3D using transformation matrix M, that should express rotation of the original coordinate system to the new system denoted by \bullet' below.
For vectors:
\ul{v}' = M \cdot \ul{v}
For second order tensors:
\ull{t}' = M \cdot \ull{t} \cdot M^T \mbox{or} t_{ij}' = M_{ip} M_{jq} t_{pq}
For fourth order tensors:
t_{ijkl}' = M_{ip} M_{jq} M_{kr} M_{ls} t_{pqrs}
Parameters: | data : array, shape (num, n_r) or (num, n_r, n_c)
coors : array
mode : one of [‘cylindrical’]
mtx : array
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Returns: | new_data : array
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