stress analysis in Finite Element Analysis

Here are some notes about stress analysis in the field of Finite Element Analysis:

 

Stress is simply a measurement of the internal forces in a body,  as a result of the externally applied loads. 

 

Force is a vector - it has both magnitude and direction. As a result, stress actually has direction as well. So what happens when you have complex (multi-directional) loading? Your stress inside your part will have components in each of these different directions. 

Assume a part centered at the origin. If you pull on it only in the direction of the X-axis, it will only have stress values normal to that direction. However, if you also pull on it in the Y-direction, it has stress normal to X from the original force in the X-direction, but also stress normal to Y from the Y-direction force. In addition, an angled force load with respect to geometry will causes the material try to slide past, and shear the part. This contributes to what are called shear stresses.

 

As a result of this, looking at a 3-D part we can actually have up to 3 different stress normal directions, as well as up to 3 different shear directions (X on Y, Y on Z, and X on Z). This means we can in theory have 6 different stress values. That's a lot to try to calculate or interpret!

 

Here we will explain why Von mises stress is so important. We need to find a way to combine these six individual principal and shear stresses into a single resolved stress value, to which we can compare. The resolved stress will have a direction as well as magnitude. Maybe we don't particularly care about the direction, but we need to know what the magnitude of this is to make sure this part isn't breaking. This is where Richard Elder von Mises comes into play.

 

Von Mises is credited with coming up with what is arguably the most accepted yield criterion (way of resolving these stresses). He designed an equation that takes in each shear and principal stress value, and in turn spits out a single "von Mises stress value" which can be simply compared to a yield strength of the material. If it's greater than the yield strength, the part is failing according to his criteria. If it is less, then the part is said to be within the yield criteria, and is not failing. The equation for von Mises stress is shown below.

 

   ( where the sigmas (σ) correspond to normal stress values, and the taus (τ) are the shear stress values. )

 

Notes: There is no inherent set of units in ABAQUS. It is up to the user to decide on a consistent set of units and use that units. Typical sets of units : 

 

Original URL : http://blog.design-point.com/blog/2013/january/solidworks-simulation-what-is-von-mises-stress-part-1-of-2.aspx