A State-of-the-Art Review of the Bouc-Wen Class Model of Hysteresis: Origin, Evolution and Current State

This paper presents a comprehensive review of the Bouc-Wen model for hysteresis, analyzing its historical development, mathematical formulations, and capacity to represent complex behaviors such as asymmetry, degradation, pinching, and two newly identified response patterns: s-shaped and flag-shaped curves. The phenomenological nature of the model is examined, highlighting the absence of a rigorous mathematical and physical foundation in many of its variations. A systematic survey of the available literature is conducted to assess the physical compatibility of the Bouc-Wen formulation and its derivatives, identifying cases where modifications align with fundamental mechanical principles and others that remain purely empirical. Additionally, trends, challenges, and gaps in existing implementations are discussed, providing insights into the model's evolution over the past two decades. Commentary on biaxial developments, stochastic dynamic implementation, and parameter identification of the model is presented. The review concludes by outlining potential research directions, emphasizing the need for enhanced physical consistency, improved parameter identification strategies, broader applications in structural and mechanical systems, and further generalization of the model through multi-representation capability.