Classification and Unified Modeling of Complex Mechanical Hysteresis Phenomena


Mechanical systems and materials adopted in different engineering fields exhibit complex hysteretic responses in the input-output plane. The hysteretic behavior is typically established based on the relationship between the input and output variables. For instance, it can be referred to as rate-independent if the output variable only depends on the input one and rate-dependent if the output variable depends, fully or partially, on the variation rate of the input one. Due to the huge nature and number of these responses, their identification and modeling are usually challenging and only performed when necessary.

Rate-independent hysteretic mechanical systems and materials have been the research focus in recent years. They may have generalized displacement or generalized force as input or output variables. Various complex shapes and geometries of hysteresis loops define the behavior of different systems and materials. For example, the nonlinear behavior of materials like magnesium alloy bars and spring connectors is defined by asymmetric hysteresis loops, whereas the one of masonry walls and negative stiffness devices is characterized by S-shaped hysteresis loops. Likewise, flag-shaped hysteresis loops usually describe the behavior of timber walls and shape memory alloys.

Many uniaxial phenomenological models have been developed to simulate such complex responses. Among them, differential models are commonly used because of their high accuracy and ability to reproduce hysteresis loops made of curves rather than a sequence of straight lines. However, existing hysteretic models have several shortcomings that limit their applications: they cannot model decoupled loading and unloading phases, use parameters with unclear experimental and/or theoretical significance, and only simulate some complex hysteresis loops. Therefore, addressing such limitations is necessary to improve the efficiency of these models.

Herein, Dr. Nicolò Vaiana and Professor Luciano Rosati, from the Department of Structures for Engineering and Architecture of the University of Naples Federico II (Italy), developed a novel scheme for classifying complex hysteresis loops followed by the formulation of a unified approach for modeling such rate-independent hysteretic responses. The proposed classification was based on the analytical properties of the curves bounding the hysteresis loops. A generalized class of uniaxial phenomenological models was used to derive a single rate-independent hysteretic model, denominated Vaiana-Rosati Model (VRM). The work is currently published in the prestigious international journal Mechanical Systems and Signal Processing.

The Italian researchers demonstrated several important advantages of the new single rate-independent hysteretic model over the existing ones due to its exponential nature. It could evaluate the output variables in closed form, achieving higher computational efficiency, which was 1.5% of the time required by other models. It employed two sets of parameters to allow for uncoupled modeling of the loading and unloading phases. Additionally, it was easy to implement and required a simple procedure for identifying the parameters having clear experimental and/or theoretical interpretations.

In summary, Dr. Nicolò Vaiana and Professor Luciano Rosati developed a novel classification method and hysteretic model for classifying and modeling complex uniaxial rate-independent hysteretic responses. The model accuracy was successfully validated against experimental and numerical results. The model could accurately reproduce the complex experimental hysteresis loops retrieved in the literature. The results of the nonlinear time history analysis agreed well with those obtained using the Charalampakis-Tsiatas model. In a statement to Advances in Engineering, the authors explained that their findings would provide new insights into the hysteretic behavior of mechanical systems and materials used in aerospace, biomedical, civil, mechanical, and naval engineering applications.

About the author

Dr. Nicolò Vaiana

Nicolò Vaiana received the M.S. in Building Engineering and Architecture from the University of Calabria (Italy) in 2013. He obtained the Second Level International Master in Emerging Technologies for Construction (2015) and the Ph.D. in Structural, Geotechnical, and Seismic Engineering (2017) at the University of Naples Federico II (Italy). He spent one academic year (2015-2016) at University of California at Berkeley as visiting student researcher, under the supervision of Professor F.C. Filippou, and two academic years (2017-2019) at University of Naples Federico II as post-doctoral researcher. Currently, he is Assistant Professor in Structural Mechanics and Dynamics at the Department of Structures for Engineering and Architecture of the University of Naples Federico II (Italy) where he works in the research group coordinated by Professor L. Rosati. Starting from 19 September 2022, he is Visiting Professor at the ISAE-Supméca – Institut supérieur de mécanique de Paris. His main research topics are: computational techniques, experimental dynamics, nonlinear dynamics, hysteretic models, hysteretic mechanical systems and materials.

About the author

Prof. Luciano Rosati

Graduated with honors in Mechanical Engineering as well as Civil Engineering and Transportation, Ph.D. in Structural Engineering. Winner of a NATO-CNR scholarship in the Department of Aeronautics at Imperial College under the supervision of Prof. Mike Criesfield. Full Professor of Mechanics of Solids and Structures at the University of Naples Federico II since November 1st, 2001. Member of the National Secretariat of the SSD ICAR/08 – Mechanics of Solids and Structures (2004-2010). Coordinator since 2012 to 2018 of the Ph.D. in Structural Engineering, Geotechnics, and Seismic Risk of the University of Naples Federico II. Coordinator of Area 08 of the National University Council (CUN), since 2015 to 2020. President of the Società Italiana di Scienza delle Costruzioni (SISCO) since February 2021. Director of the Interdepartmental Centre for Cultural Heritage (CIBeC) since March 2021. Author of over one hundred scientific papers published in national and international journals and conference proceedings.


N. Vaiana, L. Rosati (2023). Classification and unified phenomenological modeling of complex uniaxial rate-independent hysteretic responsesMechanical Systems and Signal Processing, 182: 109539.

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