# Computed Results

A listing of results that are computed in HyperLife.

- Principal Stress and Principal Strain
- For a given stress/strain tensor S, the three principals are obtained as the roots of the cubic equation below:
- vonMises Stress
- =
- vonMises Strain
- =
- Signed vonMises
- The sign of the signed vonMises is determined by the sign of that principal which has the biggest absolute value.
- Pressure
- The pressure is generated by the average of the 3 normal stresses:
- Intensity
- The absolute difference between Major and Minor stresses:
- Max Shear
- The maximum shear stress/strain:
- Tresca
- Computed as the Maximum of the following:
- Lodeparam xi
- =
`[(27/2) *(P1+pressure) * (P2+pressure) * (P3+pressure)] / (vonMises* vonMises * vonMises);`

- Lodeparam theta
- =
`1 – [(2/Pi) * arccos(lodeparamxi)];`

- Triaxiality
- =
`-pressure/VonMises`

- Absolute Max Principal
- The largest of the three principal stresses or strains in absolute terms is contoured, preserving the sign. In other words, Absolute Max Principal is the extreme of the three principal stresses (or strains).

## References

VonMises Strain Calculation - PapersYu Yang, Wang Ningfei, ZhangPing, Three-dimensional Damage Analysis of Free Loading Solid Propellant Grains Subjected to Low Temperature Loading. School of Mechano-Electronics Engineering, Beijing Institute of Technology, Beijing 100081, China.