von mises stress formula is incorrect

[xujunjiedsfd]

Describe the bug
SU2 gets the equivalent stress in plane stress problem using the following formula:

template<class T>
static su2double VonMisesStress(unsigned short nDim, const T& stress) {
if (nDim == 2) {
  su2double Sxx = stress[0], Syy = stress[1], Sxy = stress[2];

  su2double S1, S2; S1 = S2 = (Sxx+Syy)/2;
  su2double tauMax = sqrt(pow((Sxx-Syy)/2, 2) + pow(Sxy,2));
  S1 += tauMax;
  S2 -= tauMax;

  return sqrt(S1*S1+S2*S2-2*S1*S2);
}

But I think there is a mistake.According to the formula of Von Mises stress：
https://ansyshelp.ansys.com/public/a...iv_Stress.html
The code should be ：

return sqrt(S1*S1+S2*S2-S1*S2);

Please let me know if my understanding is incorrect. Thank you.

[pcarruscag]

Can you do some comparisson with your reference code?

[xujunjiedsfd]

Can you do some comparisson with your reference code?

OK，but....why?Incorrect formula, incorrect result.
return sqrt(S1*S1+S2*S2-2*S1*S2);

return sqrt(S1*S1+S2*S2-S1*S2);

[pcarruscag]

Because the link you shared does not work.
And since you already debugged everything you could post some comparisson with your reference code and open a pull request with the fix.
Otherwise I'll need to verify what you are saying when I get some time.

[xujunjiedsfd]

Because the link you shared does not work. And since you already debugged everything you could post some comparisson with your reference code and open a pull request with the fix. Otherwise I'll need to verify what you are saying when I get some time.

Hi, the link is von Mises stress formula in the Ansys manual. Of course, you can also find this formula in other materials mechanics references.
https://ansyshelp.ansys.com/public/account/secured?returnurl=//////Views/Secured/corp/v242/en/wb_sim/ds_Equiv_Stress.html

In two-dimensional, 𝜎_3=0:

So,the code should be ：
return sqrt(S1*S1+S2*S2-S1*S2);
I validated the Linear Elasticity case [https://su2code.github.io/tutorials/Linear_Elasticity/] using Ansys.The simulation shows that after the code is modified, the SU2 simulation results are consistent with the results from Ansys Mechanical.

[pcarruscag]

Thank you, so this is just for plane stress, plane strain is fine the way it is?

[xujunjiedsfd]

Thank you, so this is just for plane stress, plane strain is fine the way it is?

My pleasure.Case of plane strain also calls this function（\SU2_CFD\include\numerics\elasticity\CFEAElasticity.hpp）
static su2double VonMisesStress(unsigned short nDim, const T& stress)
In fact, all 2D cases of calculating the von Mises stress are affected by this function.

[pcarruscag]

Right, but in plane strain sigma_3 is not 0, only tau_xz and tau_yz are 0 right?

[xujunjiedsfd]

Yes,the calculation of von Mises stress for plane strain problem using the 3D formula is：
return sqrt(0.5*(pow(Sxx - Syy, 2) + pow(Syy - Szz, 2) + pow(Szz - Sxx, 2) + 6.0*(Sxy*Sxy+Sxz*Sxz+Syz*Syz)));
which Syz = 0, Sxz = 0, Szz = ν(Sxx + Syy) .
When calculating the von Mises stress for plane stress problem,set Szz,Syz,Sxz to 0.