Ryan Krauss wrote:
We can work out the notations details and make sure it agrees with other SfePy docs for consistency.
matrices denoted by [], vectors by {}
Yes.
But I think a matrix is a second order tensor and a vector is a first order tensor so that the first equation should be:
1/2 \int E_{ij} \varepsilon_{i} \varepsilon_{j}
or something like that - at least for the 1D problem.
Am I thinking correctly?
There are two possible approaches: engineering (using just vectors and matrices) and "mathematical". The engineering approach employs usually symmetry, consider (in a pseudo-latex):
e_ij = 1/2 (du_i/dx_j + du_j/dx_i) - a symmetric second order tensor can be stored as {e} = [e_11, e_22, e_33, e_12, e_13, e_23] - a vector.
I would prefer working with proper tensors in the docs. The storage is just an implementation detail (yes, in sfepy we use this storage too).
r.