Add material model documentation to svMultiPhysics user guide

[divya-adil]

Problem

Need documentation on available material models and how to use them

Solution

Introduce material modes, list available volumetric and isochoric models, strain energy functions and code snippets on how to use them.

Additional context

No response

Code of Conduct

• I agree to follow this project's Code of Conduct and Contributing Guidelines

[ktbolt]

@divyaadil23 GitHub Issues are used to communicate changes in repository content, provides a mechanism to record a history and review of proposed changes.

You should describe what you are going to do and provide a link to the repository where you are making changes so the Team can review them before you do a pull request.

[ktbolt]

Some equations (e.g. Holzapfel-Ogden model) are not rendering correctly.

[divya-adil]

@ktbolt With the Holzapfel Ogden model,

$$ \Psi_{iso} = \frac{a}{2b} \exp \left( b (\bar{I}_1 - 3) \right) + \sum_{i \in {f,s}} \frac{a_i}{2b_i} \chi (\bar{I}_{4i}) \left( \exp \left( b_i (\bar{I}_{4i} - 1)^2 \right) - 1 \right) + \frac{a_{fs}}{2b_{fs}} \left( \exp \left( b_{fs} \bar{I}_{8fs}^2 \right) - 1 \right) $$

does not render correctly. The expression has 3 terms on the RHS. If I only put term 1 or only term 3 on RHS, it renders correctly.

$$ \Psi_{iso} = \frac{a}{2b} \exp \left( b (\bar{I}_1 - 3) \right) $$

$$ \Psi_{iso} = \frac{a_{fs}}{2b_{fs}} \left( \exp \left( b_{fs} \bar{I}_{8fs}^2 \right) - 1 \right) $$

Only term 2 does not render correctly, and terms 1 + term 3 does not render.

$$ \Psi_{iso} = \sum_{i \in {f,s}} \frac{a_i}{2b_i} \chi (\bar{I}_{4i}) \left( \exp \left( b_i (\bar{I}_{4i} - 1)^2 \right) - 1 \right) $$

$$ \Psi_{iso} = \frac{a}{2b} \exp \left( b (\bar{I}_1 - 3) \right) + \frac{a_{fs}}{2b_{fs}} \left( \exp \left( b_{fs} \bar{I}_{8fs}^2 \right) - 1 \right) $$

There is a similar problem with the Guccione model. The latex expressions for both seem to be correct and they render correctly when I preview locally, but not when I go live or type them here on Github. I'm pretty sure I am missing something silly. Do you have any idea why this is happening?

[ktbolt]

@divyaadil23 The documentation using MathJax which is not 100% like LaTeX; I don't have much experience with this. The README https://github.com/SimVascular/simvascular.github.io has a bit about LaTeX.

Have a look at the equations in the other sections to see how they are written.

[divya-adil]

@ktbolt all equations render correctly now. You can find my branch here. Any feedback on the content is welcome!

[ktbolt]

@divyaadil23 Thanks for getting this into a good initial stage!

I'll take over now and make my own edits.