How to Calculate the Von Mises Strain

• 1). Assign the Principal Stresses to each of these designations:
  •1st Stress to {S1}
  •2nd Stress to {S2}
  •3rd Stress to {S3}
  
  If you do not have predetermined Principal Stresses for the material to be examined, you can calculate them from any point in the x, y or z direction from the principal axis. Principal Stresses work in combination from any point on the axis; the points you choose to calculate the Von Mises Strain for exist only within that area. You can recalculate with any points from any area created through reassigning the Principal Stresses to determine the effect of the strain on the potential for failure.
  
  
• 2). Using the following equation, substitute your Principal Stresses in the appropriate location.
  
  (S1-S2)^2 + (S2-S3)^2 + (S3-S1)^2 = 2Se^2
  
  For example, if your 1st stress was 4, the 2nd stress was 6 and your 3rd stress was equal to 8, the equation would then look like this:
  
  (4-6)^2 + (6-8)^2 + (8-4)^2 = 2Se^2
  
  Note: (4-6)^2 is to be read as "four minus six to the second power"
  
  
• 3). Now, solve the equation to determine the value of {Se}.
  
  
• 4). The value you discovered for {Se} is the Von Mises Stress or Strain; this is also known as the Equivalent Stress. The value of (Se), while the solution to the equation, is not the value that you are looking for to analyze the ductile failure of your material. There is one more step to perform to understand what the Von Mises Stress Value means to your material.
  
  
• 5). Assign your known yield stress to the following designation, {Sy}. Now, solve the following equation:
  Sy -- Se
  
  If {Se} is larger then {Sy} (the result of the equation producing a negative number), then your material, at the point at which the Principal Stresses were calculated, is considered to be in total failure.