Mathematical formula for hysteresis For my final year project, I need to design a lab to generate a hysteresis loop. But I have no idea how to do it.
Is there any mathematical function or any code or any article which would help me to generate the shape of the curve?
Can anyone help me with this?
Thank You
 A: Not sure this is of any help but hysteresis occurs when the free energy has more than one minimum, so the system get "stuck" in one or the other, this means that in one direction you'll get different results than in the other (coming back).
If the system was given infinite time it would have reached the global minimum. 
If by lab you mean something like maple/matlab simulation, you need to let it find the minimum NUMERICALLY, setting it to start the search each time from the previous point. Go in one direction and then the other. You'll get a loop. If you'll do it analytically you'll just get the global minimum.
not sure that was the question, hope I somewhat helped.
A: I think you can get a basic hysteresis just with mechanical motion. It's actually one of the models used in strength of materials to explain some of the observed effects once you go out of the elastic range of deformation.
Imagine a spring attached to a dashpot. Give the dashpot some static friction coefficient. What we want essentially is that below some force F, the dashpot doesn't move. Above some force F it moves with some resistance. Then you can make a graph of force versus displacement. For small displacements the spring is doing the work and you get a line with a constant slope. Once you displace your system enough to reach the critical force value though, the force remains constant while displacement continues to increase(as long as your system is displaced slowly anyway). If you then reverse displacement, the force on the dashpot goes below the critical value. 
This is called elasto-plastic behavior. What I described was the simplest model. You can make the model more complicated, like getting a spring in series with a dashpot and spring in parallel. Then before you reach the critical load value your graph will have one slope from the first spring constant. After the critical force is reached, the graph follows the slope determined by the two springs in parallel. This may be a little less of a headache if you get it working because unlike in the first case, you won't have a situation where a constant force leads to steadily increasing displacement.
A: In 2008, Dennis Bernstein from the University of Michigan, et. al. wrote an excellent tutorial article in IEEE Control Systems Magazine that classifies and categorizes various friction models and how they can be used to model the behavior of hysteresis in a dynamic system model. The article provides a good tutorial, and also equations you can directly adapt to your purpose.
