I was looking for some reasons, why someone would choose the BB-model instead of a Prony series. In the "Mechanics of Solid Polymere" Bergström states that the BB-model" can overcome some of the main issues with linear viscoelasticity related to both large strain deformations and strain amplitude dependence of the dynamic properties (E’ and E’’)." Are these problems purely of a practical nature or can one explain them theoretically?
Obviously the BB-model uses a nonlinear dampener. Therefore one needs a large number of Prony terms to describe similar material behavior, which can be harder to fit.