An inverse identification strategy for the mechanical parameters of a phenomenological hysteretic constitutive model


Constitutive models describe how different materials respond to different loadings and play essential roles in numerous engineering applications. Within the context of continuous hysteretic models, most of the traditional approaches present several drawbacks, including the need to fix the values of some parameters to improve their accuracy, which limits their computational accuracy and applications.

Recently, a new class of uniaxial constitutive models. Compared to most of the traditional models, including the popular Bouc-Wen, these new models exhibit several advantages making their application more convenient since its constitute parameters represent its physical parameters and can be obtained directly from the experiment. For instance, they are less complicated, fast, and do not require any differential equations. Despite the significant efforts devoted towards the development of effective constitutive models, most approaches are based on mechanical considerations and fitting of experimental curves that lacks the desired accuracy to measure and determine the degree of the errors, despite being effective for determining the parameters.

In an effort to address the above problem, a team of researchers at the University of Naples Federico II: Dr. Salvatore Sessa, Professor Luciano Rosati, Dr. Massimo Paradiso, and Dr. Nicolò Vaiana presented an inverse strategy for identifying the constitutive parameters of phenomenological hysteretic constitutive models. In their approach, two optimization procedures performed sequentially were employed to minimize the least square residual between the experimental curve and numeric response.  Moreover, the first trial of the identifying parameters was determined iteratively to ensure convergence to the global minimum. Their work is currently published in the journal, Mechanical Systems and Signal Processing.

This strategy was particularly used to identify the parameters of a hysteretic phenomenological model. Results showed that the proposed strategy is robust and highly convenient for parameter identification of differential models. Unlike analogous strategies, the proposed strategy exhibits several advantages: does not assume approximations, does not require limitation of any parameter values, and does not require any particular expertise. The authors observed that it was easy and straightforward to compute the suitable first trials, considered an essential step of the procedure, taking advantage of the fact that the parameter corresponds to the physical quantity characterized by the experiment. The feasibility of the proposed strategy was validated in numerical applications to identify the mechanical parameters of two theoretical and four experimental responses, and the results proved to be robust and effective.

In summary, the study presented an inverse strategy for the identification of constitutive parameters characterizing materials modeled by the phenomenological constitutive model. Despite being developed for the algebraic model, the procedure is versatile and can be extended to other constitutive models of the same family. Moreover, the effectiveness and efficiency of the algorithm were successfully tested through numerical applications. In a statement to Advances in Engineering, Dr. Salvatore Sessa, first author said the study findings will advance future research and development of constitutive models for various engineering applications.

An inverse identification strategy for the mechanical parameters of a phenomenological hysteretic constitutive model - Advances in Engineering

About the author

Dr. Salvatore Sessa graduated in civil engineering in 2005 at the University of Naples Federico II where he was also got a PhD in “Engineering of Materials and Structures” in 2009. In 2007-08 he was Visiting Scholar at the University of California, Berkeley where he studied Structural Reliability and Random Vibrations. He held several postdoc positions researching in inverse identification of cohesive fracture interfaces. In 2014 he returned to his alma mater as postdoc and therefore as Assistant Professor since 2016. In 2018 he obtained the Italian Academic Qualification for the position of Associate Professor of Continuum and Structural Mechanics.

His research activities concern nonlinear analysis of structures with particular focus on seismic analysis of reinforced concrete framed structures and dynamic analysis of masonry structures.


About the author

Dr. Nicolò Vaiana received the M.S. in Building Engineering and Architecture from the University of Calabria 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. He spent one academic year (2015-2016) at the University of California at Berkeley as Visiting Student Researcher, and two academic years (2017-2019) at the University of Naples Federico II as Post-Doctoral Researcher. Currently, he is Research fellow in Structural Mechanics and Dynamics at the University of Naples Federico II.

His main research topics are: computational techniques, experimental dynamics, nonlinear dynamics, hysteretic models, hysteretic mechanical systems and materials.

About the author

Mr. Massimo Paradiso received the BS degree in Civil Engineering in 2012 and the MS degree in Structural and Geothecnical Engineering in 2017 from University of Naples Federico II, where he is currently attending the Phd course in Structural Engineering, Geotechnics and Seismic Risk. In 2019-2020 he was visitor intern at Vanderbilt University where he conducted research activities about structural modeling in Soft Robotics.

His research interests include computational mechanics, finite element modeling, shear effects in beam theory and shear-torsion coupling. His current research is focused on geometrically exact formulations for beam finite elements.

About the author

Prof. Luciano Rosati graduated with honors in Mechanical Engineering in 1982 and in Civil Engineering in 1984 at the University of Naples Federico II where he got a PhD. In Structural Mechanics in 1989. In 1997 he spent a two-months granted research appointment at the Imperial College in London under the supervision of prof. M. Chrisfield. Since 2001 he is full professor of Structural Mechanics at the University of Naples Federico II where he has been carrying out teaching and research activities about finite elements, nonlinear analysis of structures and continuum mechanics, coordinating 15 research projects as principal investigator and serving as reviewer for several international journals.

He served as member of several committees including the Research Task Committee “Instructions for the Design, Cons of fiber-reinforced composites”, hosted by CNR. (National Research Council) and the Italian branch of the Natural Society of Philosophy.


Sessa, S., Vaiana, N., Paradiso, M., & Rosati, L. (2020). An inverse identification strategy for the mechanical parameters of a phenomenological hysteretic constitutive model. Mechanical Systems and Signal Processing, 139, 106622.

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