Darren,
It's a tough one. Did you know that there is a biannual conference on the subject. This year it will be held in Paris (5th European Conference on Consitutive Models For Rubber (ECCMR).
Iwas givena similarproblem to the one are describing. I took a simple pragmatic approach and stayed in the time domain. My opinion is, how can we model a material in the frequency domain when we can'tdescribe its in the time domain. I worked in ADAMS and I think I produced a good model.
This is basically is how I described the hysteresis in the time domain (if I can explain it in words). Lets take a standard Maxwell Element (a spring & damper in series). As you know the dampers force is described bythe dampers constant multiplied by the velocity across the damper.
I suggest you change this description slightly by dividingthe (Constant x velocity) by a new constant (say Zeta) plus the velocity across the entire Maxwell Element (that's the damper and spring). Try different values for Zeta and see how the element behaves in response to different inputs (various frequency sinusiodal motion and stepped displacements).
You will find that this method produces a nice asymetric damping loop similar to the type we see when we measure filled rubber and is has stress relaxation which is dependent upon the value of the dividing constant. Now just add a non-linear parallel spring to describe the non-linear elastic component of the rubbers response.
Lots of peoplehave worked on this problem (butof course I think my solution is best!) I think you will be able to find my work if you type Paul Allen, Cranfield University and Tank Track Modelling in to Google.
Hopethis helps.
Are you publishing your work?
