Nonlinear Hysteresis Behavior Research Articles

Effect of Nonlinear Hysteresis Details of Isolation System on In-Structure Response Spectra

To evaluate the seismic safety of components in a structure, an in-structure response spectrum (ISRS) must be obtained, and this also applies to seismically isolated structures. The main variables for designing seismic isolators are effective stiffness and effective damping, which can be given as the characteristic strength and secondary stiffness in seismic isolators for nonlinear behaviors. Many studies on the ISRS of isolated structures have been conducted to evaluate the effects of these two variables of isolators, but the effect of other variables related to the hysteresis curve of isolators also needs to be studied. This study focused on the effect of the initial stiffness of isolators on an ISRS because there were no clear criteria for determining the initial stiffness in isolator design standards, which has an effect on the ISRS that cannot be ignored. As a result, the initial stiffness contributed significantly to the ISRS not only at the natural frequency of the structure but also at low frequencies. An analysis was also performed in terms of the uncertainty of each variable. The sharpness of the yield point in the hysteresis curve was implemented using the Bouc–Wen model, and its impact was analyzed. In addition, the frequency content of the ISRS depending on the seismic intensity, which can considerably change the nonlinear hysteresis behavior, was examined. Through this study, although secondary stiffness and characteristic strength are the most important characteristics of seismic isolation design, it was confirmed that other variables also have a significant impact on the frequency content of an ISRS. Based on this study, the considerations when developing the ISRS of an isolated structure can be established.

Test, Modeling, and Vibration Control of a Novel Viscoelastic Multi-Dimensional Earthquake Isolation and Mitigation Device

Earthquakes contain complex components in both the horizontal and vertical directions. However, most vibration control strategies work only in a single direction. The existing multi-dimensional isolation devices usually have complex designs and low damping ratios; hence, the stability of structures that incorporate the devices is currently insufficient. This study designs a novel multi-dimensional isolation and mitigation device based on viscoelastic damping technology (VE-MDIMD). The device consists of a core bearing and several cylindrical dampers, providing vibration control capacity in both the horizontal and vertical directions and a strong uplift resistance. To evaluate the device’s performance, a series of dynamic tests are conducted on the cylindrical damper utilized in the device. The results show that the damper’s mechanical properties exhibit a pronounced dependence on the frequency and amplitude, and its hysteresis curves become obviously nonlinear with increased deformation. Subsequently, to describe the behavior of the VE-MDIMD, a mechanical model is established which combines the construction of the device and the characteristics of the damper. Considering the limitations of existing models in fully capturing the nonlinear behavior of the damper, a novel multi-scale model is proposed based on the microstructure of viscoelastic material. The experimental verification confirms that the model can accurately capture the frequency and amplitude dependence, as well as the nonlinear hysteresis behavior, of the damper. Finally, the effectiveness of the VE-MDIMD is evaluated through the dynamic analysis of an actual structure. The arrangement of the device in the structure is optimized based on a multi-objective genetic algorithm available in Matlab (R2019b) and OpenSEES (Version 3.0.0). The results demonstrate the device’s superiority in controlling both horizontal and vertical vibrations in the superstructure.

Enabling accurate simulations of the nonlinear magnetic hysteresis behavior in ferromagnetic materials

In this work, a stable node - based smoothed finite - element method algorithm is developed to address the lower accurate issues in the simulation of the magnetic hysteresis behavior in ferromagnetic materials, in which the inverse vector Jiles - Atherton model is intimately coupled. The improvement of the accuracy for hysteresis issues is achieved by linking the stable node - based smoothed finite - element method in the framework of the Newton - Raphson iteration and the Jiles - Atherton model. The optimal relaxation coefficient method is introduced to address the natural strong nonlinearity of the Jiles - Atherton model and to ensure the convergence of the model. The algorithm is validated against the experimental results, and several examples are presented for simulations of the ferromagnetic hysteresis issues to illustrate both the accuracy and expandability in the practical scenarios of ferromagnetic materials.

Development of a new dynamic hysteresis model for magnetorheological dampers with annular-radial gaps considering fluid inertia and compressibility

Modeling the inherent non-linear dynamic hysteresis behavior of magnetorheological (MR) fluid dampers is a fundamental necessity for their practical implementation. Quasi-static models, have been developed under very low frequency and small amplitude excitation conditions, are only beneficial in the early stages of MR dampers design and are sufficient for manufacturing requirements. These models, however, have failed to predict the non-linear hysteresis behavior of MR dampers (i.e., force-displacement and force-velocity characteristics) under low to moderate ranges of frequency and displacement amplitudes. The main contribution of the present work is to formulate a novel physic-based dynamic model to predict the non-linear behavior of MR dampers featuring an annular-radial bypass valve under different applied currents, and low to moderate input excitations. The proposed model incorporates unsteady fluid behavior and the fluid compressibility effect on the hysteretic response without relying on experimental data to evaluate the model parameters. To derive the model, the velocity profile and the pressure drop have been derived by solving the fluid momentum equation via the Laplace transform technique and Cauchy residue theory. The continuity equation has been employed for considering the compressibility contribution to hysteretic response based on the variation of bulk moduli. The predicted results for the force-displacement and force-velocity behavior of the MR damper were subsequently compared with the experimental results. Results suggest the effectiveness of the proposed model for predicting the dynamic hysteresis characteristics of the annular-radial MR fluid dampers under the relatively sufficient variation of mechanical and magnetic loading conditions considered.

A novel parametric model for nonlinear hysteretic behaviours with strain-stiffening of magnetorheological gel composite

Magnetorheological (MR) gels are a new class of MR composite materials that can effectively address the issue of particle agglomeration in MR fluids, enhancing the controllability of materials in engineering applications. In this study, a novel parametric model was developed to track the nonlinear hysteretic behaviours with strain-stiffening of the MR gel. The model parameters were identified using the measurement data pertaining to five current levels (0A, 0.2A, 0.5A, 0.8A, and 1A) under a strain amplitude of 10% and a frequency of 0.1 Hz. The fruit fly optimisation algorithm (FOA) was used to determine the optimal solution for the model parameters. The model parameters were generalised with respect to the loading current, and the reliability of the generalised model was verified. The results of the study demonstrate that the proposed model outperforms two classical models, the Bouc–Wen model and viscoelastic–plastic model, in capturing the nonlinear and strain-stiffening behaviour of MR gels, particularly for higher current excitations. This study has potential applications in predicting the nonlinear hysteresis behaviour of automotive dampers, and provides a theoretical basis for the semi-active control of suspensions.

Underwater dynamic hysteresis modeling and feedforward control of flexible caudal fin actuated by macro fiber composites

Underwater bionic robotics and vehicles that use flexible structures as power sources have attracted considerable attention. Thus, the underwater dynamic behaviors of the flexible structure of a variable cross-section actuated by smart actuators must be further investigated. In this study, underwater dynamic hysteresis modeling and feedforward compensation of a flexible caudal fin driven by macro fiber composites (MFC) at different frequencies were investigated. The MFC-actuated flexible caudal fin is considered a Euler–Bernoulli beam. A revised hydrodynamic function governed by the thickness of the viscous layer and the gap-to-width ratio of the cross-section was developed. Then, a characteristic-frequency-dependent extended transform function model is proposed for the hydrodynamic response of a non-uniform beam. An asymmetric hysteresis model is presented to characterize the rate-independent hysteresis behavior of the MFC actuators. Further, the underwater dynamic equation of the MFC-actuated caudal fin with hysteresis is obtained by connecting the two established models in series. Experiments demonstrate the dynamic behavior between the underwater responses of the caudal fin and the input voltages have an ellipse-like shape and vary in shape and size with oscillating frequency. The ellipse-like dynamic hysteresis loop first grows, reaching its maximum at the resonant frequency, and then decreases, because of the frequency-dependent dynamic behavior. Meanwhile, a phase shift of approximately 90°between the input voltage and underwater dynamic response was observed at the resonant state. Furthermore, the experimental results demonstrate that the proposed model can describe the nonlinear underwater dynamic hysteresis behavior of the proposed caudal fin at different frequencies. The trajectory tracking performances are remarkably improved over a broad frequency range with the proposed compensator. Consequently, the effectiveness of the proposed dynamic model and compensation method was demonstrated. These results are helpful for robotic fish or autonomous underwater vehicles propelled by oscillating foils actuated by smart actuators, including MFC.

Multi-Scale Modeling of Dielectric Polarization in Polymer/Ferroelectric Composites

Ferroelectric materials are attractive fillers for polymer composites due to their high and non-linear dielectric constants. In this study, the dielectric response of the epoxy/BaTiO3 composite is obtained by a Sawyer–Tower measurement. In addition, we propose a multiscale computational approach that allows simulation of the polarization behavior of polymer/ferroelectric composites on the timescale above 100 ms, which is several orders of magnitude longer than previous studies. The model is free of ad hoc parameters and therefore can simulate the polarization characteristics from first-principles. Both in experiments and simulations, non-linear hysteresis behavior was observed in the epoxy/BaTiO3 composite even when the electric field across the BaTiO3 is more than an order of magnitude lower than the coercive field. The computational results suggested that this originates from the domain wall motion in BaTiO3. Some practical implications drawn from the computational results are discussed.

Deep learning model for prediction of non-linear cyclic hysteresis of seismic isolation devices: Full-scale experimental validation

Recurrent neural networks predicting the non-linear hysteresis behavior of specific triple pendulum bearing (TPB) and lead rubber bearing (LRB) seismic isolation devices, are developed, and tested in this paper. Experimental datasets of full-scale isolators were derived from a shake-table test program of a five-story building specimen, performed at the Hyogo Engineering Research Center of Miki, Japan. Data measured during several table motions of different amplitudes, frequency content, and durations, are appropriately processed to construct a substantial TPB/LRB dataset of 158/55 samples. A comprehensive framework is proposed to process the data, to optimize the network architecture, and to train, validate, and to test the machine learning models. The comparisons with reference experimental data showed that developed models could predict the two-dimensional hysteresis behavior of studied isolators with a very good accuracy. The R2 value of the TPB/LRB model was of 0.83/0.96 on new unseen dataset. The illustration of representative predictions showed the power of a single model to capture different and irregular hysteresis patterns, performed by a typical isolator under variable and realistic loading conditions and that can't be described by conventional analytical models. The generalization capability of these surrogate models on such a substantial data, revealed the benefit of applying machine learning to solve complex structural engineering problems.

Modeling and identification of nonlinear hysteresis behavior of piezoelectric actuators using a computationally efficient phenomenological model and modified cuckoo search algorithm

Hysteresis, an intrinsic characteristic of piezoelectric (PZT) actuators, has been demonstrated to dramatically reduce the capability and stability of the system. This paper proposes a novel computationally efficient model to describe nonlinear and hysteresis behaviors of PZT actuators. First of all, the model parameters are analyzed to investigate their effects on the output response. Then, a modified cuckoo search algorithm is used to identify the model parameters, without falling into the local optimum problems through introducing adaptive egg discovery probability and step length control factor. Further, the performance of the proposed model is validated using experimental data, via the comparison with classical Bouc-Wen and Prandtl-Ishlinskii hysteresis models. Finally, the rate-dependence of the parameters of proposed model is analyzed, which contributes to a generalized hysteresis model for the compensation control application of PZT actuators.

Linear and nonlinear electro-elastic/electro-damping effect in ferroelectric ceramics

The linear piezoelectric and nonlinear hysteresis behaviors of ferroelectrics are well-known and have been extensively studied. However, less attention has been paid to the variations of their mechanical properties under electric loading. In this work, using tube and cylinder specimens, three independent elastic coefficients and related internal frictions of PZT-5H ferroelectric ceramics are measured using our proposed modified piezoelectric ultrasonic composite oscillator technique (M-PUCOT) under an electric field E3 along the poling direction. Results show that under low electric fields, the elastic coefficients s11E, s66E and all internal frictions decrease linearly with E3, whereas s44E increases linearly with E3. Based on these linear results, two fifth-order tensors are defined, i.e., linear electro-elastic and linear electro-damping tensor with the reduced symbol of pikl and qikl, among which p311, p366, p344 and q311, q366, q344 are obtained in this work. When the applied electric field exceeds the coercive field (∼500 V/mm), nonlinear electro-elastic/electro-damping effect dominates, resulting in reversed butterfly curves for s11E and s66E and butterfly curves for s44E. As to the internal frictions under large bipolar fields, they seem to be a superposition of the reversed butterfly curves and a peak or valley at the coercive field. The linear electro-elastic effect in ferroelectric ceramics is caused by the reversible domain wall motions while the nonlinear electro-elastic effect is caused by non-180° domain switching and is well reproduced by a statistical model. The linear and nonlinear electro-elastic/electro-damping results obtained in this work offer new insight into the electromechanical coupling behavior of ferroelectric materials.

Nonlinear bending behavior of a multilayer copper conductor in a dynamic power cable

Reciprocating bending behavior is the main factor leading to the fatigue failure of dynamic power cables. However, in the research on the reciprocating bending behavior of dynamic cables, only the mechanical properties of the armored steel wire has been considered thus far and the copper conductor is disregarded. In this paper, the nonlinear bending properties of multilayer helically wound copper conductors are studied by experiments and numerical simulation. The research can provide accurate data of nonlinear bending mechanical properties of copper conductor for hydrodynamic analysis of dynamic cable fatigue life. Firstly, the nonlinear bending hysteresis curves of copper conductors are obtained by a reciprocating bending experiment of copper conductor. Secondly three-dimensional finite element numerical simulations of the copper conductor’s bending behavior were also conducted. The numerical results from the finite element model were compared with the experimental data. Finally, sensitivity analysis of the structural parameters of the copper conductor was performed. The research shows that copper conductor has obvious nonlinear bending hysteresis behavior. The change of friction coefficient and radial extrusion pressure from the conductor’s outer sheath layer have obvious effects on the critical sliding curvature and bending hysteresis properties of nonlinear bending properties of copper conductors.

Static and Dynamic Mechanical Characterization of Polydimethylsiloxane (PDMS) under Uniaxial Tensile Loading

The present study is based on performing mechanical characterization of polydimethylsiloxane (PDMS) under tensile loading. PDMS samples are developed by mixing prepolymer and curing agent with 10:1 ratio. Mechanical characterization of the PDMS samples is carried out using static and dynamic mechanical testing methods. In particular, the material is characterized under monotonic loading, different strain rates, and force-controlled cyclic loading. The monotonic loading tests are performed at different grip tightening levels to optimize gripping that avoids slipping and reaches failure point. The strain rate dependency and cyclic loading tests are performed to study the viscoelastic behaviour of the material. Strain rate dependency tests are carried out at the strain rates of 6.7×10-3 s-1, 3.2×10-2 s-1, and 6.2×10-2 s-1. The hysteresis tests are performed at the force rates of 0.1 – 2 N/s. The obtained results show that fixing the testing specimen made of soft hyperviscoelastic material such as PDMS is challenging and can significantly affect its stress-strain behaviour and mechanical properties. A higher strain rate increases the stiffness of the material due to the viscoelastic nature of the material. Observing the stress-strain curves, with respect to the lowest strain rate case, the curve for 6.2×10-2 s-1 strain rate diverges at 40% strain compared to 3.2×10-2 s-1 strain rate curve that diverges at 80% strain. The material shows a nonlinear hysteresis behaviour and similar energy dissipation for the considered force-controlled cyclic loading cases.

Characterization and modeling of the ratcheting behavior of unidirectional off-axis composites

The ratcheting behavior of unidirectional carbon/epoxy composites under cyclic off-axis loading with non-zero average stress was investigated, with a focus on the influence of peak stress (stress ratio R = 0) and fiber orientation. The experimental results show that nonlinear hysteresis and ratcheting behaviors heavily depend on fiber orientation and loading stress. Herein, the evolutionary features of the nonlinear hysteresis behavior and ratcheting deformation of the material are discussed. Furthermore, a creep damage-coupled viscoplastic cyclic constitutive model based on the nonlinear hysteresis behavior and cyclic creep is proposed to simulate the ratcheting behavior of carbon fiber composites under different stress levels and with various fiber orientations. The proposed model can adequately predict the nonlinear response during loading, hysteresis behavior during unloading and reloading, and ratcheting phenomena after a large number of cycles.

A new hysteresis model for magneto–rheological dampers based on Magic Formula:

This paper investigates a novel model based on the Magic Formula and the Pan’s model to effectively predict the inherent nonlinear hysteresis behavior of magneto–rheological (MR) dampers. In the pr...

An elasto-plastic constitutive model for frozen soil subjected to cyclic loading

Upon employing the theoretical frame of breakage mechanics for geological materials and homogenization, a new elasto-plastic constitutive model is proposed to investigate the dynamic mechanical behaviors and volumetric strain of frozen soil under cyclic loading. In this model, using a mesoscopic method to formulate the breakage of frozen soil by idealizing it as a binary medium, assuming respectively the unbroken state as bonded element and the damage state as frictional element. During the loading process, the evolution of the nonuniform deformation and ice cementation breakage is described by the local strain concentration coefficient and breakage ratio, respectively. The dynamic triaxial compression test data for different confining pressures, coarse particle contents, and dynamic deviatoric stress amplitudes are utilized to confirm the suitability of the new elasto-plastic constitutive model. In the results, the model presented the stress-strain curves and volumetric strain curves of frozen soil under cyclic loading which captured the basic dynamic characteristics, such as nonlinear variation, hysteresis behaviors, and plastic strain accumulation behaviors. Herein, the extensive experimental validation shows the applicability of the proposed model.

Predictive Control with Dynamic Hysteresis ‎Reference ‎Trajectory: Application to a Structural Base-‎Isolation ‎Model

Over the last decades, in the field of control engineering, Model Predictive Control (MPC) has been successfully ‎employed in many industrial processes. This due to, among other aspects, its capability to include constrains within ‎the design control formulation and also its ability to perform on-line optimization. For instance, in the civil ‎engineering field, different MPC approaches have been well developed to formulate active control algorithms able ‎to reduce civil structural responses to earthquakes. Thus, in this paper, a customized version of a conventional ‎Predictive Control (PC) strategy is proposed to mitigate the displacement on a base-isolated system with a ‎nonlinear hysteresis behavior, that is excited by a seismic event. The proposal consists of including a dynamic ‎hysteresis system into the control scheme to generate a reference trajectory that will softly drive the base-isolated ‎structure to a rest status. The proposed control scheme is evaluated through numerical experiments, and then its ‎performance is compared with respect to the conventional Predictive Control methodology. According to the ‎numerical experiments, the approach here presented results more efficient than the conventional method due to ‎the use of a suitable linear model of the structural system plus a new Driver Block with dynamic hysteresis within ‎the Predictive Control scheme‎.

Fano-Resonant Hybrid Metamaterial for Enhanced Nonlinear Tunability and Hysteresis Behavior.

Artificial resonant metamaterial with subwavelength localized filed is promising for advanced nonlinear photonic applications. In this article, we demonstrate enhanced nonlinear frequency-agile response and hysteresis tunability in a Fano-resonant hybrid metamaterial. A ceramic cuboid is electromagnetically coupled with metal cut-wire structure to excite the high-Q Fano-resonant mode in the dielectric/metal hybrid metamaterial. It is found that the significant nonlinear response of the ceramic cuboid can be employed for realization of tunable metamaterials by exciting its magnetic mode, and the trapped mode with an asymmetric Fano-like resonance is beneficial to achieve notable nonlinear modulation on the scattering spectrum. The nonlinear tunability of both the ceramic structure and the ceramic/metal hybrid metamaterial is promising to extend the operation band of metamaterials, providing possibility in practical applications with enhanced light-matter interactions.

Research on transient multi-field coupling model of GMM under variable pressure in embedded GMA

To improve the output performance of embedded giant magnetostrictive actuators (GMAs) for non-circular hole precision machining and to describe the transient nonlinear hysteresis behavior of giant magnetostrictive material (GMM), the magnetostrictive process of GMM is analyzed in detail in this paper. Based on the J–A model and the Gibbs free energy model, a transient multi-field coupling model of GMM is developed by considering the eddy current effect, compression stress variation, and ΔE effect. The simulation results show that the hysteresis loop area increases with increasing driving frequency. The strain of GMM increases first and then decreases with increasing preloading stress. If the stiffness of the deformable bar is too large, the stress of GMM will increase rapidly, thus hindering the elongation of GMM. The simulation process combines the magneto-mechanical coupling model and the dynamic model of embedded GMAs. The simulation results at different excitation frequencies are basically consistent with the experimental data, indicating that the proposed model can predict the output displacement well and provide a theoretical basis for the optimized design of magneto-mechanical coupling for high-performance embedded GMAs.

Springback behavior and a new chord modulus model of copper alloy during severe plastic compressive deformation

Abstract The copper alloy in the unloading process after severe plastic compressive deformation (SPCD) exhibits obvious nonlinear stress-strain relationship and hysteresis behavior, and generates severe springback deformation. The severe strain hardening and softening effects occurring in the SPCD and the anisotropy of the material will affect the springback behavior of the material. In this paper, the samples obtained along the different directions (rolling direction, short-thickness direction, transverse direction, and 45° direction) of copper alloy hot-rolled plates were used to perform the quasi-static single pass compression tests with different deformation ratios (0.25 %–90 %). The springback behavior of the copper alloy under the SPCD was investigated. The effects of the strain hardening, strain softening and anisotropy on the springback behavior of the material were revealed. The variation relationships of the instantaneous tangent modulus and the chord modulus in unloading with stress and strain at different deformation stages (elastic stage, yield stage, strain hardening stage, and strain softening stage) were analyzed. A new chord modulus in a power exponential form was proposed. According to the unloading characteristic of the SPCD, the Yoshida-Uemori chord modulus model and the QPE model were modified. The applicability and accuracy of the unloading chord modulus models for the SPCD were evaluated and compared by using the power exponential chord modulus model, the modified QPE chord modulus model, the modified Yoshida-Uemori chord modulus model, and the Yoshida-Uemori chord modulus model, respectively. Besides, based on the proposed chord modulus model in a power exponential form, a 1-D E T model in a power exponential form was also proposed to describe the nonlinear unloading process and the variation of the slope of the unloading curves after the SPCD. The results indicated that the springback behavior of SPCD is obviously different from those of small plastic compressive deformation and elastic compressive deformation. The proposed chord modulus model in a power exponential form can accurately predict the chord modulus and springback strain in the unloading after the SPCD.

Experimental and Numerical Investigation of Solar Panels Deployment with Tape Spring Hinges Having Nonlinear Hysteresis with Friction Compensation

In this work, experimental and numerical investigation on the deployment of solar panels with tape spring (TS) hinges showing complex nonlinear hysteresis behavior caused by the snap-through buckling was conducted. Subsequently, it was verified by comparing simulation results by multi-body dynamics (MBD) analysis with test results on ground-based deployment testing considering gravity compensation, termed zero-gravity (Zero-G) device. It has been difficult to predict the folding and unfolding behavior of TS hinges because their moment–rotation relationship showed a nonlinear hysteresis behavior. To realize this attribute, an algorithm that checks the sign of angular velocity of the revolute joints was used to distinguish folding from unfolding. The nonlinear hysteresis was implemented in terms of two path-dependent nonlinear moment–rotation curves with the aid of the expression function (a kind of user subroutine) in MBD software RecurDyn. Finally, it was found that the results of the deployment analysis were in excellent agreement with those of the test when the friction torques of the revolute joints were properly identified by an inverse analysis with the test frames, thus validating the MBD model.