8. Principal Stresses and von Mises stress

This section is really about adding bells and whistles or polish to our solver in the form of Principal Stress and von Mises stress distribution plots. We’ll start off with a brief review of principal stresses. If you want to dig a little deeper on the topic before taking on this section - jump down to the appendix where I cover Principal Stresses in more detail. 

After reviewing principal stresses in theory - we’ll use our existing stress field data to calculate the principal stresses and orientation of the principal planes. We’ll then visualise both the magnitude and orientation information. 

After this we’ll take a break from coding and discuss the von Mises failure theory. Once we have the concepts and key equations in hand, we’ll use our principal stress fields to calculate the von Mises stress field. 

This basically concludes our hard-core solver development. We’ll have some tweaks to make in the next section but once this section is complete you can congratulate yourself on building a very nice piece of analysis software.