  While it is widely used to represent hysteresis phenomena with
unidirectional-oriented loops, we study in this paper the use of Preisach
operator for describing hysteresis behavior with multidirectional-oriented
loops. This complex hysteresis behavior is commonly found in advanced
materials, such as, shape-memory alloys or piezoelectric materials, that are
used for high-precision sensor and actuator systems. We provide
characterization of the Preisach operators exhibiting such input-output
behaviors and we show the richness of the operators that are capable of
producing intricate loops.
