COMSOL Tips & Tricks - Stress and Strain Variables

Published: Tue, 08/05/14

It is time for another COMSOL Tips & Tricks deposit.

If you are solving solid mechanics problems with COMSOL Multiphysics you may have noticed that in recent releases some stress and strain variables are now available in two different versions:  
  1. Original "legacy" version (e.g. solid.mises) and
  2. Gauss point evaluation version (e.g. solid.misesGp).

So, what is the difference between these two different variable definitions?  And, which one should I use?

If you are interested in qualitative behavior only or in making relative stress and strain comparisons for different modeling parameters, there will likely not be much difference which version you choose.  However, if you are interested in reporting absolute values of stresses or strains at particular points in your model, it is worth considering the difference.  The following image shows a contour plot of the percent difference between the solid.mises and solid.misesGp variables in a critical area on the surface of a bracket under a bending load.  Note the maximum difference is about 36%.

Why the difference?  In short, the newer Gauss point evaluation (available since v4.3) reports the stress values that have been extrapolated from the Gauss points rather than the nodes (the old way).  Without getting into too much of the "under-the-hood" details of how the finite element method works (see Note below), suffice it to say that the Gauss points are used during the solution process for the force calculation, and, for a nonlinear material, the Gauss points are the only locations where the constitutive law is actually satisfied.  In contrast, the Lagrange point evaluation (the original version) is an evaluation based on the derivative of the displacements at the nodes.

In general, this evaluation is not exactly consistent with the force calculations that are actually being performed numerically within the elements.  This inconsistency can be especially notable for non-linear models (e.g. plasticity modeling).  Furthermore, there is not any situation we are aware of where switching to the Gauss point evaluation has any downside.  For these reasons, we recommend that the Gauss point evaluation be used rather than the nodal evaluation (especially for non-linear models).  Here at AltaSim, we are now considering the original stress and strain definitions as a "legacy" form and recommend getting in the habit of using the variables with the "Gp" instead.

Note: For more information on the difference between Gauss points and Lagrange points, consider the COMSOL Knowledge Base article "Stress and Strain results at Gauss Points" Solution Number 1176.  

Until next time...

Jeff & Kyle

Phone: 614-861-7015