NiTi Shape Memory Alloy Wires Research Articles

Combined effects of grain size and training on fatigue resistance of nanocrystalline NiTi shape memory alloy wires

The structural fatigue life of nanocrystalline NiTi wires with grain size ranging from 53 nm to 125 nm was improved by stress-controlled mechanical training and the percentage of the improvement increased with grain size. The structural fatigue life decreased with the increased grain size for the untrained samples. After training, the structural fatigue life increased with grain size. The generation and movement of dislocations during training contributed to lattice rotation, improving orientation intensity of 〈111〉 parallel to drawn direction texture. The reduction of fatigue striation spacing revealed training-induced plastic deformation and enhanced 〈111〉 texture contributed to hindering crack propagation.

Superelasticity degradation of NiTi shape memory alloy in wide ranges of temperature and loading level: Experimental observation and micromechanical constitutive model

In this work, cyclic tension-unloading tests with different peak strains (10%-18%) in the temperature range from 313 K to 393 K are performed to investigate the effects of temperature and loading level on the cyclic deformation behavior of NiTi shape memory alloy (SMA) wires. Experimental results demonstrate that the superelasticity degradation occurs during the cyclic deformation process, and such phenomenon aggravates with the rise of ambient temperature and loading level, which can be attributed to the complex interactions among the martensite transformation (MT), austenite plasticity (AP), martensite plasticity (MP) and the transformation-induced plasticity (TRIP). Then, a micromechanical cyclic constitutive model is proposed based on the framework of irreversible thermodynamics and Eshelby's inclusion theory. The martensite (M) phase is treated as mobile inclusions with alterable eigenstrain embedded in the austenite (A) phase matrix. The volume fractions of the M-phase, A-phase, and A-M interface-phase are introduced. The non-uniform stress fields in the three phases are estimated by employing the Mori-Tanaka's homogenization scheme and interfacial operator. The driving forces of the four types of the inelastic deformation mechanisms, MT, AP, MP, and TRIP are derived based on the proposed new Helmholtz free energy, instantaneous growth hypothesis of M domains, and the energy dissipation inequality. The inheritances of the plastic deformation induced by the movement of A-M interfaces during the repeated MT and its reverse are incorporated. Finally, to validate the predictive capability of the proposed model, the predicted results for the superelasticity degradation of NiTi SMA with various peak strains at different ambient temperatures are compared with the experimental ones. Moreover, the dominant plastic deformation mechanisms and the effects of AP, MP, TRIP on the cyclic deformation of NiTi SMA are discussed.

Uncovering the rate of the martensitic transformation in superheated shape memory alloy wires

The martensitic transformation in shape memory alloys is known to be very fast. However, its rate in bulk materials that serve in common actuator applications is still an open question. In this study, the martensitic transformation is induced by a high-voltage microsecond superheating pulse in a polycrystalline NiTi shape memory alloy wire and its rate is tracked using time resolved X-ray diffraction by synchrotron radiation. The study employs a novel experimental technique that allows for multi-frame time-resolved detection with a temporal resolution below 1 µs, demonstrating an order-of-magnitude improvement compared to previous time-resolved synchrotron studies. Results show that the transformation begins at the moment the wire temperature reaches the transformation temperature and the transformation rate follows the rate of heating, completing most of the process within approximately 1 µs. Yet, part of the transformation continues at much slower time scales of several tens of microseconds.

Fabrication and Mechanical Property Evaluation of Peripheral Stent Made from Shape Memory Alloys

This study proposes to design and fabricate the peripheral stent using NiTi shape memory alloy wires by braiding technique. The 0.2 mm diameter NiTi wire was attached to the automatic braiding machine and fabricated the braided stent under the different height of circular rod holder. Heat-treatment was carried out at 450°C, 500°C, 550°C and 600°C for 10 and 20 minutes, respectively. Then transformation temperature, the shape of cell area, and mechanical properties were evaluated. The results show that complete superelasticity can be confirmed under body temperature in stent prototypes with heat-treatment temperature over 500°C irrespective of heat-treatment time. The prototype with the height of circular mold of 70 mm shown a good braiding pattern with high kink resistance. The radial force shown no significant difference at any section along the length profile. It is noted that stent with the height of circular mold at 70 mm, carrier speed of 30 rad/sec and take-up speed of 4.86 mm/s which shown radial resistive force (ROF) of 2.44 ± 0.05 N/mm, and chronic outward force (COF) of 0.533 ± 0.03 N/mm which is sufficient for vessel expansion.

Effect of hydrogen on super-elastic behavior of NiTi shape memory alloy wires: Experimental observation and diffusional-mechanically coupled constitutive model

NiTi shape memory alloys (SMAs) are inevitably in contact with hydrogen in specific service environments, which can degrade their mechanical behaviors. In this work, the effect of hydrogen on the super-elasticity of NiTi SMA orthodontic wires is investigated experimentally and theoretically. Firstly, cathodic hydrogen charging was performed for the wires at a current density of 10A/m2 with various charging times (2.5min, 5min, 7.5min and 10min) and charging lengths (20 mm, 40 mm, 60 mm and 80 mm) in 0.5 mol/L H2SO4+2 g/L CH4N2S electrolyte solution at room temperature. Then, ex-situ tension-unloading tests were carried out shortly after the hydrogen charging. The stress-strain responses showed a two-step martensite transformation (MT), i.e., the start stress of MT for the region with hydrogen charging is much larger than that without hydrogen charging. Based on the experimental observations, a diffusional-mechanically coupled constitutive model is constructed. Elastic strain, transformation strain, transformation-induced plasticity (TRIP) and hydrogen swelling deformation are considered. The effect of hydrogen on the thermo-mechanical behavior of NiTi SMA is taken into account by introducing the hydrogen concentration (HC)-dependent critical temperatures of MT and slip resistance of TRIP. The thermodynamic driving forces of MT and TRIP are derived from the constructed Helmholtz free energy and dissipation inequality. The balance equation of hydrogen diffusion is obtained by the chemical potential and Fick's diffusion law. To obtain the overall response of the wire with a heterogeneous HC field, a scale transition rule is proposed. The capability of the proposed model to describe the super-elasticity of NiTi SMA with various hydrogen charging times and charging lengths is validated by comparing the predicted results with the experimental ones.

Study on the effect of double-sided laser welding of NiTi shape memory alloys wire

NiTi shape memory alloys (SMAs) have essential applications in intelligent system design and development due to their flexibility in integration through welding or joining techniques. In this work, both single-sided laser welding and doublesided laser welding processes were used for the welding of NiTi SMAs wire. Then, the macro-morphology, microstructure, phase transformation behavior, mechanical performance, fracture surface characteristics, and cyclic tensile properties of the samples obtained under the two welding processes were investigated. The results showed that there were dendrites and equiaxed grains in the fusion zone (FZ) of the double-sided welding samples, without obvious welding defects. Although the phase transformation temperature in the FZ of the samples obtained by the two processes was significantly increased, the temperature rise of the double-sided welded samples was relatively lower. The tensile strength and elongation of the double-sided welded samples were higher, and all the samples had a ductile fracture. The residual strains of the 1st to 15th cycle tests revealed that the double-sided welded samples exhibited significant improvements in functional fatigue properties compared to the residual strains of the single-sided welded samples. The improved performance of laser-welded NiTi SMAs obtained from this work could benefit these alloys for welding integration applications in smart system design and production.

Cyclic degeneration of elastocaloric effect for NiTi shape memory alloy: Experimental observation and constitutive model

Based on the cyclic tension-unloading tests with various peak strains (4%-12%), the effect of loading level on the cyclic deformation and evolution of elastocaloric effect (eCE) for NiTi shape memory alloy (SMA) wires was investigated. Experimental results show that the transformation ratchetting and degeneration of eCE simultaneously occur during the cyclic deformation, and these two phenomena aggravate with the increase of loading level. Although the refrigeration capacity (maximum temperature drop in the reverse phase transformation process) exhibits a positive relativity with loading level in the 1st loading cycle, it changes non-monotonically with the variation of loading level in the steady-state cycle, which can be attributed to the interaction between the phase transformation and plasticity deformation. Moreover, it is found that the phase transformation between austenite (A) and martensite (M) phases occurs as a two-step process involving an intermediate phase, rhombohedral (R) phase. Then, a thermo-mechanically coupled cyclic constitutive model is constructed based on the fundamental laws of irreversible thermodynamics. Besides the thermo-elastic deformation, four different inelastic deformation mechanisms, i.e., R phase transformation (RT), martensite transformation (MT), plasticity in A and R phases (ARP), transformation-induced plasticity (TRIP) and their interactions are considered in the proposed model. The volume fractions of R phase, M phase, martensite affecting zone (MAZ) and the free zone (FZ) of mixed A + R phases are introduced. The thermodynamic driving forces for the four considered inelastic deformation mechanisms, i.e., RT, MT, ARP and TRIP are derived by the energy dissipation inequality and a new proposed Helmholtz free energy. Internal heat generation caused by the mechanical dissipation and the latent heat of phase transformation, and the heat balance equation are obtained by applying the conservation law of energy. The forward and reverse inheritances of dislocation (i.e., plastic deformation) caused by the moving martensite interfaces during MT are addressed. Adopting a first-order approximation of the constitutive equations and lumped analysis of heat transfer, the proposed constitutive model for a material point is extended to describe the overall responses of the whole wire. Finally, the predicted results for the cyclic deformation of NiTi SMA and correspondent evolution of eCE are compared against the experimental ones to validate the capability of the proposed model.

Investigation into the Performance of NiTi Shape Memory Alloy Wire Reinforced Sn-Bi Self-Healing Metal Matrix Composite.

Self-healing materials have the potential to create a paradigm shift in the life cycle design of engineered structures, by changing the relation between material damage and structural failure, affecting structures’ lifetime, safety, and reliability. However, the knowledge of self-healing capabilities in metallic materials is still in its infancy compared to other material systems because of challenges in the synthesis of organized and complex structures. This paper presents a study of a metal matrix composite system that was synthesized with an off-eutectic Tin (Sn)-Bismuth (Bi) alloy matrix, reinforced with Nickel–Titanium (NiTi) shape memory alloy (SMA) wires. The ability to close cracks, recover bulk geometry, and regenerate strength upon the application of heat was investigated. NiTi wires were etched and coated in flux before being incorporated into the matrix to prevent disbonding with the matrix. Samples were subjected to large deformations in a three-point bending setup. Subsequent thermo-mechanical testing of the composites confirmed the materials’ ability to restore their geometry and recover strength, without using any consumable components. Self-healing was accomplished through a combination of activation of the shape memory effect in the NiTi to recover the samples’ original macroscopic geometry, closing cracks, and melting of the eutectic material in the matrix alloy, which resealed the cracks. Subsequent testing indicated a 92% strength recovery.

Experimental analysis of corrugated core sandwich panel with smart composite face-sheets under high-velocity impact

The present research work investigated on the behavior of corrugated core composite sandwich panel (CCCS) with composite face-sheets reinforced by pseudo-elastic NiTi shape memory alloy (SMA) wires subjected to high-velocity impact experimentally. The number of SMA wires, their location, and their pre-strain percentage are the parameters studied in this investigation. The sandwich specimens were made by woven glass fibers/epoxy composite face-sheets strengthened by the SMA wires and Aluminum corrugated core and prepared using the wet hand lay-up method. Their behavior is evaluated under high-velocity impact test by a gas gun impactor testing machine. According to the results obtained, a significant change in the amount of energy absorption of the specimens containing SMA wires is observed. By increasing the number of the SMA wires, the energy absorption by the specimen is increased, but by pre-straining the SMA wires, the effect in energy absorption is significant. Also, when the projectile hits the SMA wire in CCCS, better properties in energy absorption can be observed. The results show that the energy absorption increased from 117.247 J for the specimen without the SMA wire to 128.749 J for the six SMA wires specimen. On the other hand, by applying the pre-strain to the SMA wires, the residual stresses in the specimens and hence the energy absorption in the specimen with six SMA wires with 3% pre-strain increased to 142.57 J.

Development, simulation, and validation of sliding self-centering steel brace with NiTi SMA wires

This study proposes an innovative sliding self-centering (SC) brace to reduce or eliminate residual deformation after strong earthquakes. The brace uses tension-only nickel and titanium (NiTi) shape-memory alloy wires to generate SC behavior and tension-only steel bars to provide energy dissipation, axial strength, and axial stiffness. The proposed sliding SC brace concept and details are outlined, and tests are conducted on variations of the proposed brace subject to cyclic loading to investigate their hysteretic behavior. The experimental results demonstrated that the proposed brace exhibited a double-flag-shaped hysteretic response, controlled axial strength, and preferable SC behavior. An important advantage is that the tension-only steel bars of the proposed brace exhibit a sliding hysteretic response, which can significantly reduce the number of NiTi shape-memory alloy wires and decrease the cost of the brace. The proposed sliding SC brace mechanisms and governing equations for practical engineering designs are presented. A cyclic restoring force model with a trilinear skeleton curve, which reflected the sliding characteristics and SC features, was proposed and calibrated using experimental results. Additionally, the finite element analysis results were aligned with the test results. Three main design parameters affecting the sliding SC brace energy dissipation and SC ability are addressed.

Experimental investigation of the effects of aging and cryogenic treatments on the mechanical properties of superelastic nickel-titanium shape-memory alloys

In this study, electropolishing and two different heat treatments were applied to wires made of superelastic nickel-titanium (NiTi) shape-memory alloy (SMA) and their mechanical properties and stress-induced deformations were investigated. In experimental studies, cryogenic and aging heat treatments were applied to NiTi SMA wire samples and tensile test experiments were carried out to determine the effect of the heat treatments on their mechanical properties. Following the tensile test experiments conducted at room temperature (23°C), the study investigated changes in the elemental composition, fracture modes, micro cracks, and phase structures and in the mechanical properties formed in the fracture region. Intermetallic phase structures (Ti2Ni, Ni3Ti, and Ni4Ti3) were observed in the X-ray diffraction (XRD) analyses. It was concluded that the aging heat treatment had directly affected the reduction in hardness. In particular, in samples without the aging heat treatment, a stress-induced decrease in the Ni and Ti ratios and an increase in the carbon (C) ratio were observed in the chemical composition of the fracture surface of the superelastic NiTi SMA wires. It was determined that the changes in the chemical composition caused by stress had affected the mechanical properties negatively. In the fractography of the NiTi SMA wires, the samples exhibited mostly ductile fracture behavior with small dimples.

The Longitudinal Compression Capacity of Hollow Concrete Cylinders Prestressed by Means of an SMA Wire.

This paper deals with the mechanical behavior of hollow concrete cylinders prestressed with nickel-titanium (Ni-Ti)-shape memory alloy (SMA) wires wound around them. Prestresses can be created by the thermal activation of the memory effect of SMA wire placed on the outer surface of concrete cylinders. In order to assess the stress level in concrete, a model was used to analyze the thermal stresses in the concrete shell resulting from a temperature gradient in the thickness. Another model was used to calculate the circular concentric loading applied by the wound wire resulting from the impairment of its memory effect by the concrete cylinder. Finally, longitudinal compression tests were performed on the prestressed hollow cylinders. Longitudinal and circumferential strains were measured using gauges located on the surfaces of the hollow cylinders. The tests were performed almost one year after the application of prestressing by means of Ni-Ti SMA wire, confirming that the residual stress in the wire remained present. It may therefore be concluded that the prestressing of concrete elements designed with the use of Ni-Ti SMA material is effective for a long time.

Effects of the angle between the spring arm on spring characteristics on the single coiled torsion spring using Ti-Ni shape memory alloy wire.

We have been investigated one-coil torsion springs using shape memory alloy (SMA) wire for application to welfare equipment (for example, lower limb orthoses), because one-coil torsion springs using SMA wire have small size and large displacement. It is known that the spring properties of a torsion spring depend on the shape of the spring, and design calculation method for springs made of normal metals have already been established. However, SMA has different characteristics from normal metals, and it is difficult to apply conventional design calculation methods. Therefore, we fabricated several SMA torsion springs with different the angle between the spring arm and investigated the effects of shape of the spring on the spring characteristics of SMA torsion springs by spring characteristic tests and fatigue tests. The experimental results show that increasing the angle between the spring arm improves the fatigue life of the SMA torsion springs but the spring generating force decreased. On the other hand, the functional degradation characteristics are independent of the angle between the spring arms.

Investigation of the effect material responses parameter (alpha) on stress-strain behavior during loading and unloading of superelastic shape memory nitinol wire

Shape Memory Alloy (SMA) is able to recover big strains beyond an appropriate heating and/or mechanical loading procedure. Numerous uses being exploiting such notable characteristic and the NiTi wires are of particular attention to conduct the connections in various industrial states. The present research aims to achieve a numerical simulation of the superelastic conduct of the NiTi shape memory alloy wire, using Finite Element Method by employing commercial ANSYS 15.0 software. The influence of the material responses parameter (Alpha) on the stress–strain behavior during loading and unloading of superplastic shape memory NiTi wire has been investigated. Axisymmetric wire element is employed, and characteristic responses are analyzed by considering von Mises stress and von Mises strain curves at constant time for various values of Alpha parameter from during the bending process. The numerical simulations manifested the features of superelastic recovery, which is also in terms of time.

Seismic Performance of Ni-Ti SMA Wires Equipped in the Spatial Skeletal Structure

Nickel Titanium (Ni-Ti) Shape Memory Alloy (SMA) can be used to limit response of structure during external disturbances such as large seismic events. This paper presents a seismic performance study of Ni-Ti SMA wires equipped in the spatial skeletal structure. First, an improved Graesser-Cozzarelli (G-C) numerical constitutive model of the Austenitic phase of NiTi SMA wire is established. By contrast, the model based on uniaxial cyclic loading experimental tests is demonstrated as feasibility and validity. Next, a method consisting of a three-layer steel spatial skeletal structure model equipped with SMA wires is employed for simulation and experimental tests. According to the obtained constitutive numerical model, the simulation program of vibration control is written to simulate the effect of vibration control of seismic EL-centro wave. Furthermore, a shaking table experimental test was designed to verify the vibration control effect under the same action of seismic EL-centro wave. By comparison of the results of the numerical simulation and shaking table test, dynamic responses of the displacement and acceleration for different floors with control and without control was concluded. The superior superelastic properties of SMA wires used in passive control are investigated and the correctness of the constitutive numerical model are verified as well. The results show that such a comprehensive analysis integrates seismic-resistant behavior of Ni-Ti SMA wires in this type of structure. Besides, proposed method has broad application prospects to address the issues in passive control field of building structures.

In situ growth of submicron polypyrrole on NiTi alloy wire as electrodes for recoverable and flexible quasi-solid-state supercapacitors

In recent years, wearable and flexible supercapacitors have attracted extensive attention. High energy density supercapacitors based on shape-memory materials can meet the requirements of recoverability and fatigue resistance. We fabricate a symmetric wire-based shape-memory supercapacitor (SMSC) by depositing polypyrrole (PPy) on NiTi shape-memory alloy wire as electrodes. The SMSC exhibits high flexibility and excellent shape-memory performance, which can quickly recover to its original shape in a few seconds with almost constant capacitance when heated to the deformation temperature (approximately 60 °C) at arbitrary shapes of deformation. Furthermore, the SMSC displays an ultrahigh areal energy density of 60.0 μWh cm−2 and represents excellent capacitance stability after multiple deformation/recovery processes. Considering its outstanding flexible ability and excellent electrochemical performance, the wire-based SMSC shows infinite potential in the application of flexible and wearable electronics.

Cyclic testing of an innovative self-centering X-braced ductile shear panel

This paper presents an innovative seismic load-resisting component of braced ductile shear panel (BDSP) with self-centering ability. Tension-only nickel-titanium (NiTi) shape memory alloy (SMA) wires installed along the inclined segments are employed to facilitate the self-centering ability. Thin shear panel with pinching hysteretic feature is adopted to decrease the amount of SMA wires, and it provides sufficient lateral bearing capacity and lateral stiffness. A total of eight specimens at one-third scale tests were performed to investigate the hysteretic behavior and re-centering capacity under cyclic loading. The experimental results show that the adoption of SMA wires inside traditional BDSP component realized the desirable self-centering ability and retained moderate energy dissipation capacity with the equivalent viscous damping ratio in the range of 0.124–0.158. Compared to solid shear panel, the employment of slotted shear panel obtained a considerably pinching hysteretic loop and reduced the amount of SMA wires for providing the re-centering ability. The local buckling and damage were primarily focused on the shear panel. The self-centering BDSP specimens were used as replaceable fuse elements for realizing the repairability after an earthquake. The tension field inclination in the solid shear panel ranged from 18° to 33.5°, which was approximately consistent with the main diagonal direction according to observed experimental phenomenon. Furthermore, the surrounding flanges of shear panel did not play an important role on improving lateral strength. The average overstrength factor of the self-centering BDSP specimens was 1.49.

The Application of Ni-Ti SMA Wires in the External Prestressing of Concrete Hollow Cylinders.

An innovative method for prestressing structural elements through the use of shape memory alloys (SMAs) is gaining increasing attention in research as this method does not require the use of mechanical anchorages for tendons. The activation of the memory effect by means of temperature variations (Joule effect) in effect produces high stresses in SMA components attached to concrete components as reported in the literature. This paper presents the work performed for the purpose of prestressing concrete hollow cylinders with the use of nickel–titanium (Ni–Ti) SMA wires. In the tests, a variety of hollow cylinders were made using the same concrete mix and with the same wall thickness (20 mm), but with different external diameters (200 mm, 250 mm, and 300 mm). Their prestressing was achieved by the means of Ni-Ti SMA wires of different diameters (1 mm, 2 mm, and 3 mm) wrapped around the cylinders. Longitudinal and circumferential strain during the thermal activation of the SMA wires by Joule heating was measured using gauges located on the internal surface of the hollow cylinders. The experimental protocol, recorded observations, and discussion of the effectiveness of the prestressing of concrete elements as a function of the test parameters are included in the text in detail. Comments on the conditions for effective prestressing of concrete cylinders with SMA wires are proposed in the conclusions of the paper.

Mechanical Consequences of Dynamically Loaded NiTi Wires under Typical Actuator Conditions in Rehabilitation and Neuroscience.

In the field of rehabilitation and neuroscience, shape memory alloys play a crucial role as lightweight actuators. Devices are exploiting the shape memory effect by transforming heat into mechanical work. In rehabilitation applications, dynamic loading of the respective device occurs, which in turn influences the mechanical consequences of the phase transforming alloy. Hence in this work, dynamic thermomechanical material behavior of temperature-triggered phase transforming NiTi shape memory alloy (SMA) wires with different chemical compositions and geometries was experimentally investigated. Storage modulus and mechanical loss factor of NiTi alloys at different temperatures and loading frequencies were analyzed under force-controlled conditions. Counterintuitive storage modulus- and loss factor-dependent trends regarding the loading frequency dependency of the mechanical properties on the materials’ composition and geometry were, hence, obtained. It was revealed that loss factors showed a pronounced loading frequency dependency, whereas the storage modulus was not affected. It was shown that force-controlled conditions led to a lower storage modulus than expected. Furthermore, it turned out that a simple empirical relation could capture the characteristic temperature dependency of the storage modulus, which is an important input relation for modeling the rehabilitation device behavior under different dynamic and temperature loading conditions, taking directly into account the material behavior of the shape memory alloy.

Experimental and Numerical Analysis of the Mechanical Properties of a Pretreated Shape Memory Alloy Wire in a Self-Centering Steel Brace

As a stimulus-sensitive material, the difference in composition, fabrication process, and influencing factors will have a great effect on the mechanical properties of a superelastic Ni-Ti shape memory alloy (SMA) wire, so the seismic performance of the self-centering steel brace with SMA wires may not be accurately obtained. In this paper, the cyclic tensile tests of a kind of SMA wire with a 1 mm diameter and special element composition were tested under multi-working conditions, which were pretreated by first tensioning to the 0.06 strain amplitude for 40 cycles, so the mechanical properties of the pretreated SMA wires can be simulated in detail. The accuracy of the numerical results with the improved model of Graesser’s theory was verified by a comparison to the experimental results. The experimental results show that the number of cycles has no significant effect on the mechanical properties of SMA wires after a certain number of cyclic tensile training. With the loading rate increasing, the pinch effect of the hysteresis curves will be enlarged, while the effective elastic modulus and slope of the transformation stresses in the process of loading and unloading are also increased, and the maximum energy dissipation capacity of the SMA wires appears at a loading rate of 0.675 mm/s. Moreover, with the initial strain increasing, the slope of the transformation stresses in the process of loading is increased, while the effective elastic modulus and slope of the transformation stresses in the process of unloading are decreased, and the maximum energy dissipation capacity appears at the initial strain of 0.0075. In addition, a good agreement between the test and numerical results is obtained by comparing with the hysteresis curves and energy dissipation values, so the numerical model is useful to predict the stress–strain relations at different stages. The test and numerical results will also provide a basis for the design of corresponding self-centering steel dampers.