FIX: Correct 2D Von Mises Stress Calculation in CFEAElasticity (#2603)

[ayush4874]

Issue:
As reported in Issue #2603, the 2D implementation of the Von Mises stress calculation in CFEAElasticity::VonMisesStress was mathematically incorrect.

The previous code implemented:
$$\sigma_{vm} = \sqrt{S_1^2 + S_2^2 - 2S_1S_2} = \sqrt{(S_1 - S_2)^2} = |S_1 - S_2|$$

This formula corresponds to the Tresca equivalent stress (twice the maximum shear stress), not the Von Mises stress.

Fix:
Updated the formula to the correct 2D Plane Stress Von Mises definition:
$$\sigma_{vm} = \sqrt{S_1^2 + S_2^2 - S_1S_2}$$

Verification:
Verified that the term -2*S1*S2 was the source of the discrepancy. The updated implementation now aligns with standard continuum mechanics definitions for plane stress.

[pcarruscag]

Thanks. Can you look into the plain strain case too?

[ayush4874]

@pcarruscag I have added support for Plane Strain as requested.

Implementation Details:

1. Updated VonMisesStress (CFEAElasticity.hpp):

   • Modified the function signature to accept Nu (Poisson's Ratio) and isPlaneStrain.
   • Used default arguments (Nu=0.0, isPlaneStrain=false) to ensure backward compatibility with other classes (like CFEALinearElasticity) that do not need these inputs.
   • Math: For Plane Strain, we now calculate the out-of-plane stress $S_{zz}$ before the Von Mises calculation:

   /*--- In Plane Strain, Szz is not zero. It is determined by Poisson's ratio. ---*/
   su2double Szz = 0.0;
   if (isPlaneStrain) {
     Szz = Nu * (Sxx + Syy);
   }
   // ... followed by general 3D Von Mises formula using Szz

2. Updated CFEASolver.cpp:

   • Now fetches the Poisson Ratio from the config (GetPoissonRatio(0)).
   • Checks the 2D formulation kind via GetElas2D_Formulation() to set the isPlaneStrain flag correctly.

[ayush4874]

@pcarruscag I have applied the requested changes:

1. Removed default arguments from VonMisesStress to enforce explicit handling of material properties everywhere.
2. Updated CFEALinearElasticity.cpp (and CFEANonlinearElasticity.cpp) to:
   • Retrieve the Poisson Ratio (Nu) and 2D Formulation from the config.
   • Calculate and store the 4th stress component ($S_{zz}$) for Plane Strain inside the element loop, as suggested.
   • Pass the explicit values to the Von Mises utility.
3. Added myself to AUTHORS.md.

Builds are passing locally. Ready for final review!

[pcarruscag]

I'll approve the tests to run, but there will be plenty of segmentation faults.

[pcarruscag]

If the 4th element of "stress" is Szz you don't need to pass Nu and isPlainStrain to this function.

[ayush4874]

@pcarruscag Done. I have refactored the implementation as requested to ensure memory safety.

1. Utility (CFEAElasticity.hpp): VonMisesStress is now a pure math function. It no longer accepts physics parameters (Nu, isPlaneStrain) and strictly expects a 4-component vector for 2D inputs (Sxx, Syy, Sxy, Szz).
2. Solvers (CFEALinearElasticity, CFEANonlinearElasticity, CFEASolver): The logic for calculating Szz (based on Plane Strain vs Plane Stress) has been moved explicitly to the caller side.

I updated all 3 call sites to pack the stress vector correctly before passing it to the utility, preventing any potential segfaults.