Extended classification and generalized Vaiana–Rosati model accounting for rate-independent hysteresis loops with evolving shape

Mechanical systems and materials may exhibit rate-independent hysteretic responses that involve generalized force–displacement hysteresis loops with varying shape. With the aim of proposing a unified phenomenological modeling approach to accurately reproduce them, we first classify such hysteresis loops into four categories according to the analytical properties of their limiting curves. Subsequently, we generalize a modeling approach, recently developed by the authors, to simulate the vast majority of experimental hysteresis loops with evolving shape. The proposed approach offers both analytical and differential formulations, allows for an uncoupled modeling of the generic loading and unloading phases by employing two distinct sets of nine parameter functions having a clear mechanical meaning, and requires a straightforward computer implementation. A meticulous model validation is carried out by adopting experimental hysteresis loops retrieved from the literature. Additionally, a numerical application is performed to show the agreement between the results provided by two solution procedures that exploit the analytical and differential formulations of the model, respectively, to analyze four different mechanical systems subjected to three types of external generalized forces.