Make the "partial molar volume" a function of stoichiometry

[aabills]

Description

For many chemistries, notably high-nickel NMCs and graphite, the volume change associated with intercalation is a strong function of stoichiometry. Here, I have taken the r-averaged value for Ω and used it to calculate total stress. This accounts for the change without violating the initial model assumptions.

Type of change

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• Bug fix (non-breaking change which fixes an issue)

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (ebacf49) 99.59% compared to head (bf6e83b) 99.71%.

❗ Current head bf6e83b differs from pull request most recent head cfb467f. Consider uploading reports for the commit cfb467f to get more accurate results

Additional details and impacted files

@@             Coverage Diff             @@
##           develop    #2943      +/-   ##
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+ Coverage    99.59%   99.71%   +0.11%     
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  Files          257      273      +16     
  Lines        20639    19007    -1632     
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- Hits         20556    18952    -1604     
+ Misses          83       55      -28     

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[valentinsulzer]

Thanks!

There is already a parameter, t_change, for the electrode thickness change as a function of particle concentration. Should that be the same parameter?

[aabills]

They are closely related, but not the same. In most cases, t_change is a function of Omega, but t_change is more of a summary variable to monitor volume changes of the cell while Omega is used to calculate the stress within a particle. According to Appendix B of Ai 2020 (which based on comments is the paper around which pybamm's stress models are implemented), this is to avoid numerical difficulties.

For example, t_change in the Ai2020 parameter set for the positive electrode is Ω*c_s_max*stoich, but it is a more complicated function for the negative electrode.

[aabills]

I think we could get rid of t_change with this, but it would require us to change the parameter sets to be different from the papers from which they were created.

[aabills]

Closed in favor of #3576