HyperView User's Guide

Computed Results

Computed Results

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Computed Results

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Below is a list of results that are computed in HyperView:

•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:

computed_results_formula_a

where:

computed_results_formula1

computed_results_formula2

computed_results_formula3

In the case of a strain tensor, the shear components computed_results_formula4 are in the “Tensor shear Strain” format.  Various solvers output shear strains in one of the two formats:  “Engineering shear strain” and “Tensor shear strain”.  “Engineering shear strain” is twice that of “Tensor shear strain”.  All solver data that has shear strains in “Engineering shear strain” are converted to “Tensor shear strain” before calculating the principals.  This includes some solutions from NASTRAN, Abaqus, and ANSYS.

•vonMises Stress =

computed_results_formula5

where:

computed_results_p1, computed_results_p2, computed_results_p3 represent the principal stresses as calculated above for a stress tensor.

•vonMises Strain =

computed_results_formula6

where:

computed_results_p1, computed_results_p2, computed_results_p3 represent the principal strains as calculated above for a strain tensor.

computed_results_v is the Poisson ratio set to a default value of 0.5.

•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:

Pr = -(StressX + StressY + StressZ) / 3.0.

•Intensity - is the absolute difference between Major and Minor stresses:

Intensity = abs (P1-P3)

•Max Shear - is the maximum shear stress/strain:

Max shear = abs(P1(major) - P3(minor))/2

•Tresca - is computed as the Maximum of the following:

abs(P1-P2), abs(P1-P3), abs (P2-P3)

•Lodeparam xi =

[(27/2) *(P1+pressure) * (P2+pressure) * (P3+pressure)] / (vonMises* vonMises * vonMises);

•Lodeparam theta =

1 – [2 * Pi * arccos(lodeparamxi)];

•Triaxility =

-pressure/VonMises

References

VonMises Strain Calculation - Papers

Yu 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.