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A Review of the Class of Bouc-Wen Differential Models for Simulating Mechanical Hysteresis Phenomena

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Mathematical Applications in Continuum and Structural Mechanics

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 127))

Abstract

One of the most popular hysteretic models used in many areas of engineering, especially the civil one, is the Bouc-Wen model. Although this model is able to simulate several types of hysteretic phenomena, it cannot describe some typical phenomena, such as cyclic degradation of strength and stiffness, pinching effect, and so on. For this reason, many researchers have proposed several variants of the original Bouc-Wen model. We present a review of the Bouc-Wen model and its most significant enhanced versions, utilizing the same technical terminology for all models in order to clarify and to shed some light on the number and physical significance of the parameters that the models require as input. Sensitivity analyses are also illustrated with respect to the input parameters.

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References

  • Ahmad N, Ali Q, Ashraf M, Khan AN, Alam B (2012) Performance assessment of low-rise confined masonry structures for earthquake induced ground motions. Int J Civil Struct Eng 2(3):842–859

    Article  Google Scholar 

  • Alibert JJ, Seppecher P, dell’Isola F (2003) Truss modular beams with deformation energy depending on higher displacement gradients. Math Mech Solids 8(1):51–73

    Google Scholar 

  • Altenbach H, Bîrsan M, Eremeyev VA (2012) On a thermodynamic theory of rods with two temperature fields. Acta Mech 223(8):1583–1596

    Article  MathSciNet  MATH  Google Scholar 

  • Andreaus U, Spagnuolo M, Lekszycki T, Eugster SR (2018) A Ritz approach for the static analysis of planar pantographic structures modeled with nonlinear Euler-Bernoulli beams. Contin Mech Thermodyn 30(5):1103–1123

    Article  MathSciNet  MATH  Google Scholar 

  • Ascione L, Berardi V, Feo L, Fraternali F, Tralli AM (2017) Probabilistic assessment of historical masonry walls retrofitted with through-the-thickness confinement devices. Proc AIMETA

    Google Scholar 

  • Baber TT, Noori MN (1985) Random vibration of degrading, pinching systems. J Eng Mech 111(8):1010–1026

    Google Scholar 

  • Baber TT, Noori MN (1986) Modeling general hysteresis behavior and random vibration application. J Vibr Acoust Stress Rel Des

    Google Scholar 

  • Baber TT, Wen YK (1981) Random vibration of hysteretic, degrading systems. J Eng Mech Div 107(6):1069–1087

    Article  Google Scholar 

  • Badoni D, Makris N (1996) Nonlinear response of single piles under lateral inertial and seismic loads. Soil Dyn Earthq Eng 15(1):29–43

    Article  Google Scholar 

  • Bahn BY, Hsu CTT (1998) Stress-strain behavior of concrete under cyclic loading. ACI Mater J 95:178–193

    Google Scholar 

  • Bai XX, Cai FL, Chen P (2019) Resistor-capacitor (RC) operator-based hysteresis model for magnetorheological (MR) dampers. Mech Syst Signal Process 117:157–169

    Article  Google Scholar 

  • Banon H, Veneziano D (1982) Seismic safety of reinforced concrete members and structures. Earthq Eng Struct Dyn 10(2):179–193

    Article  Google Scholar 

  • Barchiesi E, dell’Isola F, Laudato M, Placidi L, Seppecher P (2018) A 1d continuum model for beams with pantographic microstructure: asymptotic micro-macro identification and numerical results. In: Advances in mechanics of microstructured media and structures. Springer, pp 43–74

    Google Scholar 

  • Barchiesi E, Eugster SR, dell’Isola F, Hild F (2020) Large in-plane elastic deformations of bi-pantographic fabrics: asymptotic homogenization and experimental validation. Math Mech Solids 25(3):739–767

    Google Scholar 

  • Bouc R (1967) Forced vibrations of mechanical systems with hysteresis. In: Proceedings of the fourth conference on nonlinear oscillations, Prague

    Google Scholar 

  • Bouc R (1971) Modèle mathématique d’hystérésis. Acustica 21:16–25

    MATH  Google Scholar 

  • Broccardo M, Alibrandi U, Wang Z, Garrè L (2017) The tail equivalent linearization method for nonlinear stochastic processes, genesis and developments. In: Risk and reliability analysis: theory and applications. Springer, pp 109–142

    Google Scholar 

  • Caggegi C, Sciuto D, Cuomo M (2018) Experimental study on effective bond length of basalt textile reinforced mortar strengthening system: contributions of digital image correlation. Measurement 129:119–127

    Article  Google Scholar 

  • Carboni B, Lacarbonara W, Brewick PT, Masri SF (2018) Dynamical response identification of a class of nonlinear hysteretic systems. J Intell Mater Syst Struct 29(13):2795–2810

    Article  Google Scholar 

  • Colombo A, Negro P (2005) A damage index of generalised applicability. Eng Struct 27(8):1164–1174

    Article  Google Scholar 

  • Contrafatto L, Cuomo M (2002) A new thermodynamically consistent continuum model for hardening plasticity coupled with damage. Int J Solids Struct 39(25):6241–6271

    Article  MATH  Google Scholar 

  • Contrafatto L, Cuomo M, Fazio F (2012) An enriched finite element for crack opening and rebar slip in reinforced concrete members. Int J Fract 178(1–2):33–50

    Article  Google Scholar 

  • di Cosmo F, Laudato M, Spagnuolo M (2018) Acoustic metamaterials based on local resonances: homogenization, optimization and applications. In: Generalized models and non-classical approaches in complex materials 1. Springer, pp 247–274

    Google Scholar 

  • De Angelo M, Spagnuolo M, D’annibale F, Pfaff A, Hoschke K, Misra A, Dupuy C, Peyre P, Dirrenberger J, Pawlikowski M (2019) The macroscopic behavior of pantographic sheets depends mainly on their microstructure: experimental evidence and qualitative analysis of damage in metallic specimens. Contin Mech Thermodyn 31(4):1181–1203

    Google Scholar 

  • dell’Isola F, Seppecher P, Alibert JJ, Lekszycki T, Grygoruk R, Pawlikowski M, Steigmann D, Giorgio I, Andreaus U, Turco E et al (2019a) Pantographic metamaterials: an example of mathematically driven design and of its technological challenges. Contin Mech Thermodyn 31(4):851–884

    Google Scholar 

  • dell’Isola F, Turco E, Misra A, Vangelatos Z, Grigoropoulos C, Melissinaki V, Farsari M (2019b) Force-displacement relationship in micro-metric pantographs: experiments and numerical simulations. Comptes Rendus Mécanique 347(5):397–405

    Google Scholar 

  • Demetriades GF, Constantinou MC, Reinhorn AM (1993) Study of wire rope systems for seismic protection of equipment in buildings. Eng Struct 15(5):321–334

    Article  Google Scholar 

  • Dimian M, Andrei P (2014) Noise-driven phenomena in hysteretic systems. Springer

    Google Scholar 

  • Dobson S, Noori M, Hou Z, Dimentberg M, Baber T (1997) Modeling and random vibration analysis of SDOF systems with asymmetric hysteresis. Int J Non-Linear Mech 32(4):669–680

    Article  MATH  Google Scholar 

  • Drucker DC (1957) A definition of stable inelastic material. BROWN UNIV PROVIDENCE RI, Tech. rep

    Google Scholar 

  • Duhem P (1897) Die dauernden aenderungen und die thermodynamik. i. Zeitschrift für Physikalische Chemie 22(1):545–589

    Google Scholar 

  • Eremeyev V, Morozov N (2010) The effective stiffness of a nanoporous rod. Dokl Phys 55:279–282

    Article  MATH  Google Scholar 

  • Fedele R, Sessa S, Valoroso N (2012) Image correlation-based identification of fracture parameters for structural adhesives. Technische Mechanik-Europ J Eng Mech 32(2–5):195–204

    Google Scholar 

  • Foliente GC (1995) Hysteresis modeling of wood joints and structural systems. J Struct Eng 121(6):1013–1022

    Article  Google Scholar 

  • Fujimura K, Der Kiureghian A (2007) Tail-equivalent linearization method for nonlinear random vibration. Probab Eng Mech 22(1):63–76

    Article  Google Scholar 

  • Graesser E, Cozzarelli F (1991) Shape-memory alloys as new materials for aseismic isolation. J Eng Mech 117(11):2590–2608

    Google Scholar 

  • Greco F, Luciano R, Serino G, Vaiana N (2018) A mixed explicit-implicit time integration approach for nonlinear analysis of base-isolated structures. Annals Solid Struct Mech 10(1):17–29

    Article  Google Scholar 

  • Greco L, Cuomo M (2013) B-Spline interpolation of Kirchhoff-love space rods. Comput Methods Appl Mech Eng 256:251–269

    Article  MathSciNet  MATH  Google Scholar 

  • Hadad HA, Calabrese A, Strano S, Serino G (2017) A base isolation system for developing countries using discarded tyres filled with elastomeric recycled materials. J Earthq Eng 21(2):246–266

    Article  Google Scholar 

  • Hodgdon ML (1988) Mathematical theory and calculations of magnetic hysteresis curves. IEEE Trans Magn 24(6):3120–3122

    Article  Google Scholar 

  • Hossain MM, Browning R, Minkwitz R, Sue HJ (2012) Effect of asymmetric constitutive behavior on scratch-induced deformation of polymers. Tribol Lett 47(1):113–122

    Article  Google Scholar 

  • Jiles D, Atherton D (1983) Ferromagnetic hysteresis. IEEE Trans Magn 19(5):2183–2185

    Article  Google Scholar 

  • Jiles DC, Atherton DL (1984) Theory of ferromagnetic hysteresis. J Appl Phys 55(6):2115–2120

    Article  Google Scholar 

  • Kikuchi M, Aiken ID (1997) An analytical hysteresis model for elastomeric seismic isolation bearings. Earthq Eng Struct Dyn 26(2):215–231

    Article  Google Scholar 

  • Kreger ME, Abrams DP (1978) Measured hysteresis relationships for small-scale beam-column joints. Tech. rep., University of Illinois Engineering Experiment Station. College of

    Google Scholar 

  • Kwok N, Ha Q, Nguyen T, Li J, Samali B (2006) A novel hysteretic model for magnetorheological fluid dampers and parameter identification using particle swarm optimization. Sens Actuators, A 132(2):441–451

    Article  Google Scholar 

  • Kwok N, Ha Q, Nguyen M, Li J, Samali B (2007) Bouc-wen model parameter identification for a MR fluid damper using computationally efficient GA. ISA Trans 46(2):167–179

    Article  Google Scholar 

  • Liberatore D, Addessi D, Sangirardi M (2019) An enriched Bouc-Wen model with damage. Europ J Mech-A/Solids 77(103):771

    MathSciNet  MATH  Google Scholar 

  • Lima C, Angiolilli M, Barbagallo F, Belletti B, Bergami A, Camata G, Cantagallo C, Di Domenico M, Fiorentino G, Ghersi A, et al (2018) Nonlinear modeling approaches for existing reinforced concrete buildings: The case study of de gasperi-battaglia school building in norcia. In: Conference on Italian concrete days. Springer, pp 82–95

    Google Scholar 

  • Loh CH, Mao CH, Huang JR, Pan TC (2011) System identification and damage evaluation of degrading hysteresis of reinforced concrete frames. Earthq Eng Struct Dyn 40(6):623–640

    Article  Google Scholar 

  • Losanno D, Sierra IEM, Spizzuoco M, Marulanda J, Thomson P (2019a) Experimental assessment and analytical modeling of novel fiber-reinforced isolators in unbounded configuration. Compos Struct 212:66–82

    Article  Google Scholar 

  • Losanno D, Spizzuoco M, Calabrese A (2019b) Bidirectional shaking-table tests of unbonded recycled-rubber fiber-reinforced bearings (rr-frbs). Struct Control Health Monit 26(9)

    Google Scholar 

  • Losanno D, Palumbo F, Calabrese A, Barrasso T, Vaiana N (2021) Preliminary investigation of aging effects on recycled rubber fiber reinforced bearings (RR-FRBs). J Earthq Eng, 1–18

    Google Scholar 

  • Marmo F, Rosati L (2012a) Analytical integration of elasto-plastic uniaxial constitutive laws over arbitrary sections. Int J Numer Meth Eng 91(9):990–1022

    Article  MathSciNet  Google Scholar 

  • Marmo F, Rosati L (2012b) An improved flexibility-based nonlinear frame element endowed with the fiber-free formulation. European congress on computational methods in applied sciences and engineering (ECCOMAS 2012). Viena, Austria, pp 1–17

    Google Scholar 

  • Marmo F, Rosati L (2013) The fiber-free approach in the evaluation of the tangent stiffness matrix for elastoplastic uniaxial constitutive laws. Int J Numer Meth Eng 94(9):868–894

    Article  MathSciNet  MATH  Google Scholar 

  • Marmo F, Serpieri R, Rosati L (2011) Ultimate strength analysis of prestressed reinforced concrete sections under axial force and biaxial bending. Comput Struct 89(1–2):91–108

    Article  Google Scholar 

  • Mayergoyz ID (2003) Mathematical models of hysteresis and their applications. Academic Press

    Google Scholar 

  • Menegotto M (1973) Method of analysis for cyclically loaded RC plane frames including changes in geometry and non-elastic behavior of elements under combined normal force and bending. In: Proc. of IABSE symposium on resistance and ultimate deformability of structures acted on by well defined repeated loads, pp 15–22

    Google Scholar 

  • Nejadsadeghi N, De Angelo M, Drobnicki R, Lekszycki T, dell’Isola F, Misra A (2019) Parametric experimentation on pantographic unit cells reveals local extremum configuration. Exp Mech 59(6):927–939

    Google Scholar 

  • Noël JP, Kerschen G (2017) Nonlinear system identification in structural dynamics: 10 more years of progress. Mech Syst Signal Process 83:2–35

    Article  Google Scholar 

  • Nuzzo I, Losanno D, Caterino N, Serino G, Rotondo LMB (2018) Experimental and analytical characterization of steel shear links for seismic energy dissipation. Eng Struct 172:405–418

    Article  Google Scholar 

  • Nuzzo I, Losanno D, Caterino N (2019) Seismic design and retrofit of frame structures with hysteretic dampers: a simplified displacement-based procedure. Bull Earthq Eng 17(5):2787–2819

    Article  Google Scholar 

  • Özdemir H (1976) Nonlinear transient dynamic analysis of yielding structures[ph. d. thesis]. PhD thesis, University of California

    Google Scholar 

  • Park R, Paulay T (1975) Reinforced concrete structures. John Wiley & Sons

    Google Scholar 

  • Pellecchia D, Sessa S, Vaiana N, Rosati L (2020) Comparative assessment on the rocking response of seismically base-isolated rigid blocks. Proc Struct Integrity 29:95–102

    Google Scholar 

  • Pideri C, Seppecher P (1997) A second gradient material resulting from the homogenization of an heterogeneous linear elastic medium. Continuum Mech Thermodyn 9(5):241–257

    Article  MathSciNet  MATH  Google Scholar 

  • Placidi L, Barchiesi E, Misra A (2018) A strain gradient variational approach to damage: a comparison with damage gradient models and numerical results. Math Mech Complex Syst 6(2):77–100

    Article  MathSciNet  MATH  Google Scholar 

  • Placidi L, Misra A, Barchiesi E (2019) Simulation results for damage with evolving microstructure and growing strain gradient moduli. Continuum Mech Thermodyn 31(4):1143–1163

    Article  MathSciNet  Google Scholar 

  • Ramberg W, Osgood WR (1943) Description of stress-strain curves by three parameters. Nat Adv Committ Aeron

    Google Scholar 

  • Sengupta P, Li B (2013) Modified Bouc-wen model for hysteresis behavior of RC beam-column joints with limited transverse reinforcement. Eng Struct 46:392–406

    Article  Google Scholar 

  • Sengupta P, Li B (2014) Hysteresis behavior of reinforced concrete walls. J Struct Eng 140(7):04014,030

    Google Scholar 

  • Serpieri R, Sessa S, Rosati L (2018) A MITC-based procedure for the numerical integration of a continuum elastic-plastic theory of through-the-thickness-jacketed shell structures. Compos Struct 191:209–220

    Article  Google Scholar 

  • Sessa S (2010) Multiobjective non-linear random vibration analysis for performance-based earthquake engineering. Reliability and optimization of structural systems-proceedings of reliability and optimization of structural systems pp 185–192

    Google Scholar 

  • Sessa S, Valoroso N (2017) Kriging interpolation strategy for finite-element-based surrogate responses of DCB delamination tests. In: Risk and reliability analysis: theory and applications. Springer, pp 453–461

    Google Scholar 

  • Sessa S, Serpieri R, Rosati L (2017) A continuum theory of through-the-thickness jacketed shells for the elasto-plastic analysis of confined composite structures: theory and numerical assessment. Compos B Eng 113:225–242

    Article  Google Scholar 

  • Sessa S, Marmo F, Rosati L, Leonetti L, Garcea G, Casciaro R (2018) Evaluation of the capacity surfaces of reinforced concrete sections: eurocode versus a plasticity-based approach. Meccanica 53(6):1493–1512

    Article  Google Scholar 

  • Sessa S, Marmo F, Vaiana N, De Gregorio D, Rosati L (2019a) Strength hierarchy provisions for transverse confinement systems of shell structural elements. Compos B Eng 163:413–423

    Article  Google Scholar 

  • Sessa S, Marmo F, Vaiana N, Rosati L (2019b) Probabilistic assessment of axial force-biaxial bending capacity domains of reinforced concrete sections. Meccanica 54(9):1451–1469

    Article  MathSciNet  Google Scholar 

  • Sessa S, Vaiana N, Paradiso M, Rosati L (2020) An inverse identification strategy for the mechanical parameters of a phenomenological hysteretic constitutive model. Mech Syst Signal Process 139(106):622

    Google Scholar 

  • Shih MH, Sung WP (2005) A model for hysteretic behavior of rhombic low yield strength steel added damping and stiffness. Comput Struct 83(12–13):895–908

    Article  Google Scholar 

  • Sierra IEM, Losanno D, Strano S, Marulanda J, Thomson P (2019) Development and experimental behavior of HDR seismic isolators for low-rise residential buildings. Eng Struct 183:894–906

    Article  Google Scholar 

  • Sireteanu T, Giuclea M, Mitu AM, Ghita G (2012) A genetic algorithms method for fitting the generalized bouc-wen model to experimental asymmetric hysteretic loops. J Vib Acoust 134(4)

    Google Scholar 

  • Sivaselvan MV, Reinhorn AM (2000) Hysteretic models for deteriorating inelastic structures. J Eng Mech 126(6):633–640

    Google Scholar 

  • Song J, Der Kiureghian A (2006) Generalized Bouc-wen model for highly asymmetric hysteresis. J Eng Mech 132(6):610–618

    Google Scholar 

  • Song J, Kiureghian AD, Sackman JL (2007) Seismic interaction in electrical substation equipment connected by non-linear rigid bus conductors. Earthq Eng Struct Dyn 36(2):167–190

    Article  Google Scholar 

  • Tomaževič M, Lutman M (1996) Seismic behavior of masonry walls: modeling of hysteretic rules. J Struct Eng 122(9):1048–1054

    Article  Google Scholar 

  • Turco E, Giorgio I, Misra A, dell’Isola F (2017) King post truss as a motif for internal structure of (meta) material with controlled elastic properties. Royal Soc Open Sci 4(10):171,153

    Google Scholar 

  • Turco E, Misra A, Pawlikowski M, dell’Isola F, Hild F (2018) Enhanced Piola-Hencky discrete models for pantographic sheets with pivots without deformation energy: numerics and experiments. Int J Solids Struct 147:94–109

    Google Scholar 

  • Vaiana N, Spizzuoco M, Serino G (2017) Wire rope isolators for seismically base-isolated lightweight structures: experimental characterization and mathematical modeling. Eng Struct 140:498–514

    Article  Google Scholar 

  • Vaiana N, Sessa S, Marmo F, Rosati L (2018) A class of uniaxial phenomenological models for simulating hysteretic phenomena in rate-independent mechanical systems and materials. Nonlinear Dyn 93(3):1647–1669

    Article  Google Scholar 

  • Vaiana N, Sessa S, Marmo F, Rosati L (2019a) An accurate and computationally efficient uniaxial phenomenological model for steel and fiber reinforced elastomeric bearings. Compos Struct 211:196–212

    Article  Google Scholar 

  • Vaiana N, Sessa S, Marmo F, Rosati L (2019b) Nonlinear dynamic analysis of hysteretic mechanical systems by combining a novel rate-independent model and an explicit time integration method. Nonlinear Dyn 98(4):2879–2901

    Article  MATH  Google Scholar 

  • Vaiana N, Sessa S, Paradiso M, Marmo F, Rosati L (2019c) An efficient computational strategy for nonlinear time history analysis of seismically base-isolated structures. In: Conference of the Italian association of theoretical and applied mechanics. Springer, pp 1340–1353

    Google Scholar 

  • Vaiana N, Sessa S, Paradiso M, Rosati L (2019d) Accurate and efficient modeling of the hysteretic behavior of sliding bearings. In: 7th international conference on computational methods in structural dynamics and earthquake engineering (COMPDYN 2019). Crete, Greece, pp 24–26

    Google Scholar 

  • Vaiana N, Marmo F, Sessa S, Rosati L (2020) Modeling of the hysteretic behavior of wire rope isolators using a novel rate-independent model. Nonlinear Dynamics of Structures. Springer, Systems and Devices, pp 309–317

    Google Scholar 

  • Vaiana N, Capuano R, Sessa S, Marmo F, Rosati L (2021a) Nonlinear dynamic analysis of seismically base-isolated structures by a novel opensees hysteretic material model. Appl Sci 11(3):900

    Article  Google Scholar 

  • Vaiana N, Losanno D, Ravichandran N (2021b) A novel family of multiple springs models suitable for biaxial rate-independent hysteretic behavior. Comput Struct 244(106):403

    Google Scholar 

  • Vaiana N, Sessa S, Rosati L (2021c) A generalized class of uniaxial rate-independent models for simulating asymmetric mechanical hysteresis phenomena. Mech Syst Signal Process 146(106):984

    Google Scholar 

  • Valoroso N, Fedele R (2010) Characterization of a cohesive-zone model describing damage and de-cohesion at bonded interfaces. sensitivity analysis and mode-i parameter identification. International Journal of Solids and Structures 47(13):1666–1677

    Google Scholar 

  • Valoroso N, Sessa S, Lepore M, Cricri G (2013) Identification of mode-i cohesive parameters for bonded interfaces based on DCB test. Eng Fract Mech 104:56–79

    Article  Google Scholar 

  • Valoroso N, Marmo F, Sessa S (2014) Limit state analysis of reinforced shear walls. Eng Struct 61:127–139

    Article  Google Scholar 

  • Valoroso N, Marmo F, Sessa S (2015) A novel shell element for nonlinear pushover analysis of reinforced concrete shear walls. Bull Earthq Eng 13(8):2367–2388

    Article  Google Scholar 

  • Visintin A (2013) Differential models of hysteresis, vol 111. Springer Science & Business Media

    Google Scholar 

  • Wang CH, Wen Yk (1998) Reliability and redundancy of pre-Northridge low-rise steel buildings under seismic excitation. na

    Google Scholar 

  • Wen Y (1980) Equivalent linearization for hysteretic systems under random excitation. ASME J Appl Mech

    Google Scholar 

  • Wen YK (1976) Method for random vibration of hysteretic systems. J Eng Mech Div 102(2):249–263

    Article  Google Scholar 

  • Xu J, Dolan JD (2009) Development of a wood-frame shear wall model in abaqus. J Struct Eng 135(8):977–984

    Article  Google Scholar 

  • Zamani SM, Vafai A, Aghakouchak A, Kazemi M (2012) Experimental investigation of steel frames with single bays of symmetrical y-shaped concentric bracings. Scientia Iranica 19(2):195–210

    Article  Google Scholar 

  • Zhang H, Foliente GC, Yang Y, Ma F (2002) Parameter identification of inelastic structures under dynamic loads. Earthq Eng Struct Dyn 31(5):1113–1130

    Article  Google Scholar 

  • Zuccaro G, Dato F, Cacace F, De Gregorio D, Sessa S (2017) Seismic collapse mechanisms analyses and masonry structures typologies: a possible correlation. Ingegneria Sismica 34(4):121–150

    Google Scholar 

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Pellecchia, D., Paradiso, M. (2021). A Review of the Class of Bouc-Wen Differential Models for Simulating Mechanical Hysteresis Phenomena. In: Marmo, F., Sessa, S., Barchiesi, E., Spagnuolo, M. (eds) Mathematical Applications in Continuum and Structural Mechanics. Advanced Structured Materials, vol 127. Springer, Cham. https://doi.org/10.1007/978-3-030-42707-8_7

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