2D Elastoplasticity FEM

[rishabharora236-cell]

This update introduces 2D J2 plasticity implementation for quadrilateral meshes.

Key Changes:

New Files:

Added a new example script implementing J2 plasticity for a 2D quad mesh.

Added a new loss function module for element-level computation (currently supports only quad meshes).

Modified Files:

FEM utilities: Updated to include computations at the Gauss point level for elastoplastic behavior.

Solver module: Added a new function that supports solving with history-dependent parameters.

fe_loss.py: Adjusted existing functions to handle optional history parameters without breaking backward compatibility. This may appear a bit messy since I prioritized maintaining compatibility with existing functions rather than introducing entirely new ones. A cleaner refactor can also be done.

[RezaNajian]

@rishabharora236-cell

Thanks a lot for your work on introducing the 2D elastoplasticity (J2) implementation — this is a great addition to the framework and a significant step forward. I went through the code in detail and refactored/cleaned several parts to improve structure, readability, and maintainability.

All relevant element-level and history-dependent computations have now been moved into:

• mechanical_elastoplasticity.py
• fe_nonlinear_residual_based_solver_with_history_update.py

The example script has also been moved into a dedicated elastoplasticity/ folder for better project organization and overall cleanliness.

✔ Follow-up actions

Please take a look at mechanical_2d_elastoplasticity.py and update the code after line 98 to align with the new structure.

Additionally, it would be great if you could address the following items:

1. Add a Unit Test
   Please provide a unit test for the newly introduced mechanical_elastoplasticity loss function so we can properly validate behavior and avoid regressions.

2. Improve Example Readability
   Please reorganize and polish mechanical_2d_elastoplasticity.py to make it more readable and structured, especially for new users exploring elastoplastic simulations.

3. Extend to 3D and Additional Element Types
   As a next step, please consider extending the implementation to:

   • 3D elements
   • Other element types (triangles, hexahedra, etc.)

   The structure in mechanical_elastoplasticity.py was designed to allow these extensions naturally.

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Thanks again for your contribution — your work is helping shape a robust and extensible elastoplastic FEM module! Let me know if you need any support with the follow-up tasks.