Guidance on Implementing Custom SR2Invariants (e.g., Equivalent Stress)?

[zhangjunzheng136]

Hello NEML2 Developers,

Thank you for developing NEML2.

I am currently exploring how to implement custom material models, and I've run into a question. I see that the library provides the SR2Invariant model, which can compute standard invariants like VONMISES, I1, and I2. It's also possible to combine the scalar outputs of these models using ScalarLinearCombination to create some new forms.

However, for more complex, non-linear functions of a tensor, it seems difficult or impossible to define them purely within the .i file. For example, I would like to implement an equivalent stress:

where $F$ is the equivalent stress, $\sigma$ is the stress tensor, function tr() represents the trace of the SR2 tensor, $\mathbf{I}$ is the identity tensor, $\sigma_b$ is the back stress tensor, $h$ and $l$ are constant parameters, function sign() is the sign function, |...| is the absolute value function, and ||...||:

This equation seems difficult to implement solely in a .i file, as the methods provided by SR2Invariants are limited, and it also includes exponential calculations.

Could you provide some guidance on implementing more complex equations? such as:

1. Can I implement exponential calculations directly I might have missed in the .i file?
2. If this isn't possible in the .i file, which C++ files should I edit, and how should I edit them to implement the custom calculations?

Any advice or examples you could provide would be greatly appreciated. Thank you for your time and for this library.

Zhang Junzheng

[hugary1995]

I'd recommend you to implement this as a separate, custom model. We have a set of tutorials to walk you through this process: https://applied-material-modeling.github.io/neml2/tutorials-extension.html

In your equation, input variables are $\sigma$ and $\sigma_b$, output variable is $F$, and parameters are $h$ and $l$.

We have a template project serving as the boilerplate for hosting your own models: https://github.com/applied-material-modeling/neml2-custom-lib-template

Can I implement exponential calculations directly I might have missed in the .i file?

I didn't quite understand this question -- I don't see any exponentiation in your equation. Can you elaborate?

[zhangjunzheng136]

Thank you for your reply, and I will try the neml2-custom-lib-template for implementation, which seems to be very helpful.

In my equation, in $\left | \mathrm{tr}(\mathbf{\sigma} ) \right | ^l$, the absolute value of trace of the stress tensor, as a scalar, is raised to the power of $l$. My question was confusing "power" and "exponential".

[hugary1995]

Ah, I see. We have the pow overloads on Scalar:
https://applied-material-modeling.github.io/neml2/namespaceneml2.html#a1b3cd5e20f566b12a4c9d272c008a0f2
https://applied-material-modeling.github.io/neml2/namespaceneml2.html#aa344ed31387f8abf98705f7fa9e6ca12
depending on whether you want a batched exponent.

[zhangjunzheng136]

Thank you for your guide.

[zhangjunzheng136]

The template https://github.com/applied-material-modeling/neml2-custom-lib-template worked well. That's a good job.