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This paper mainly carries out the preliminary work for the design of an innovative threeway seismic isolator based on the metallic pseudo rubbersilicon rubber (MPRSR) composite. First, the MPRSR composite was prepared by adding the SR, a highmolecular polymer, to the MPR, and several MPRSR specimens of different molding densities were prepared. Next, the specimens were subjected to compression and shear tests under quasistatic and dynamic loads, respectively. Several tests were carried out to reflect how these behaviors are affected by load amplitude, cycle count, loading frequency and molding density. The mechanical properties and damping features between the specimens were compared and analyzed in details. On this basis, the author examined the mechanical properties and SI mechanism of the MPRSR composite. The results show that the MPRSR composite has good recoverability under compressive and shear deformations: the composite can recover even if 40% of it has been deformed under compression and 80% under shear load; the hysteretic energy dissipation ability of the composite increases with the molding density; the loading frequency and cycle number have basically no impact on the compressive hysteretic behavior of the composite. To sum up, the MPRSR enjoys good stiffness and energy dissipation ability, and serves as an excellent material for anticorrosion, antioxidant threeway seismic isolator.
metallic pseudo rubbersilicon rubber (MPRSR) composite, threeway seismic isolator, compression, shear, hysteretic behavior
Since the 1960s, seismic isolation (SI) has been widely studied and applied in buildings. It is generally agreed that the SI is the most mature and effective means to reduce the structural seismic damage for lowrise buildings and bridges [12]. The laminated rubber bearing is by far the most popular and welldeveloped SI devices [34]. Following the Great Hanshin earthquake in 1995, an obvious vertical seismic effect has been found in buildings under the action of nearfield ground motions, especially in bridges and other largespan structures [59]. However, most of the available seismic isolators only dampen the horizontal seismic response of structures. As a result, it is highly necessary to develop a simple SI device that isolates seismic motions in both horizontal and vertical directions. Against this backdrop, this paper proposes to design a novel threeway SI device using metallic pseudo rubbersilicon rubber (MPRSR) composite, and explores the mechanical properties of the MPRSR composite in all three directions.
The metallic pseudo rubber (MPR) is an elastic porous material. It is usually prepared in three steps: winding thin metal wires into spring coils, weaving the spring coils into a mesh, and pressing the mesh into the MPR. In the MPR, the metal wires interlaced with each other, forming a network structure like the macromolecular structure of rubber. As its name suggests, the MPR enjoys a rubberlike elasticity [1012]. Under external load, friction, slippage, compression and deformation will occur between steel wire spring coils. A large amount of energy is thus dissipated, exerting a damping effect. According to the experimental data in previous literature, the MPRSR composite element based on Cr18Ni9Ti austenitic stainlesssteel wires has low tensile strength and shear stiffness, and cannot fully dissipate the vibration energy of a structure under a heavy load [1318]. The silicon rubber (SR) is a linear highmolecular weight polyorganosiloxane, featuring good hightemperature resistance and excellent damping performance. The mechanical properties of the SR are stable in a wide range of temperatures (50~200℃) [1920].
This paper mainly carries out the preliminary work for the design of a threeway seismic isolator based on the MPRSR composite. Specifically, MPRSR specimens of different molding densities were prepared by adding the SR, a highmolecular polymer, and the curing agent into the MPRs, which differ in molding density, at a fixed mix ratio. The prepared MPRSR specimens were subjected to a compressive test and a twoway shear test under quasistatic and dynamic loads, respectively. Based on the test results, the author analyzed the influence laws of factors like loading amplitude, number of load cycles, and loading frequency on the compressive and shear hysteretic behaviors of the MPRSR composite, and examined the hysteretic energy dissipation and deformation recovery of the material. The research results lay a solid basis for setting up the constitutive model of the composite material and developing a novel threeway seismic isolator based on the composite.
As shown in Figure 1, the MPR specimens were prepared in three steps: (1) Draw the fine metal wires and wind them into spring coils; (2) Weave the spring coils into a mesh, and fold the mesh into multiple layers, forming a blank; (3) Place the blank into a mold and punch it into the desired shape. The details on the processing techniques of the MPR are available in relevant literature [2122]. Our MPR specimens were made of 0Cr18Ni9Ti austenitic stainlesssteel wires, with the diameter of 0.2mm. The outer diameter of spring coil was set to 1.7mm. The blank was molded under the pressure of 5t/cm^{2}, and tempered at 400℃ [2327]. The serial numbers and geometric dimensions of the specimens are listed in Table 1. The molding density is an important parameter of each MPR specimen. It refers to the ratio of the specimen density to the density of the raw material.
Figure 1. Preparation of the MPR composite
Table 1. Parameters of the MPR specimens
Parameters Specimens 
Outer diameter of stainlesssteel wire mm 
Molding density 
Mass g 
Dimensions mm 
Loading pattern 
MPR I 
0.2 
0.23 
28 
25×25×25 
Compression and shear 
MPR II 
0.2 
0.25 
30 
25×25×25 
Compression and shear 
MPR III 
0.2 
0.27 
33 
25×25×25 
Compression and shear 
The mechanical properties of the MPRSR composite were tested on an Instron FastTrack 8801 servohydraulic fatigue testing system in a mechanics lab of Harbin Institute of Technology. The testing system can apply a cyclic load (≤100kN) at the maximum frequency of 50Hz. During the tests, the load was applied by controlling the specimen deformation. The forces and deformation of the specimen were collected by the force sensor and displacement sensor on the testing system, and converted into stress and strain according to the dimensions of the specimen. Each specimen was subjected to a cyclic compressive load in the punching direction (OZ in Figure 1(c)), and then cyclic shear loads in the two directions perpendicular to the punching direction (OX and OY in Figure 1(c)). The measured data were analyzed to evaluate the compressive and shear strengths of the specimen in the three directions. The photos of the specimen and testing system in the tests are displayed in Figures 2(a) and 2(b), respectively.
Figure 2. Specimen and testing system of MPRSR compression and shear tests
Firstly, quasistatic compressive loads were applied cyclically to MPRSRs I, II and III, which differ in molding density. The loads were applied in the punching direction of the MPR. The deformation was controlled within 6mm (24%), allowing the specimen to recover. During the test, each specimen was compressed unidirectionally at a constant speed (5mm/min), with a strain amplitude of 2%, 5%, 10%, 15%, and 20%, respectively. The cyclic loading was repeated five times for each strain amplitude, and the specimen under one cyclic loading was selected for quasistatic failure test. The recoverability of the specimen was tested under two strain amplitudes, namely, 30% and 40%.
Figures 3(a), (b) and (c) are the stressstrain hysteresis curves of MPRSRs I, II and III under different strain amplitudes, respectively. It can be seen that, with the growing strain amplitude, the elastic modulus of the composite increased, and the loading segment of each curve exhibited an obvious feature of strain hardening. This feature is very useful to develop a seismic isolator based on the MPRSR. The recoverability of such an isolator increases with the deformation, which is conducive to dissipating the energy of civil structures.
Moreover, the greater the deformation amplitude, the plumper the hysteresis curve of each MPRSR specimen, indicating a good ability of hysteretic energy dissipation. The main reason lies in that: when the deformation is small, the metal wires have not overcome the friction between them, slowing an unobvious slip; as the deformation amplitude grows, the slip between the metal wires become obvious, dissipating more energy.
Figure 3. Stressstrain hysteresis curves of the three specimens under quasistatic compression
It can also be seen that the cycle number has little impact on the stressstrain hysteresis features of each MPRSR specimen. Under each working condition, the stressstrain curves of almost all cycles were highly repeatable. The only exception is the stressstrain curve of the second cycle, which shows a slight stress degradation compared to that of the first cycle. This means the MPRSR has stable stressstrain features under compression, despite the growing number of loading cycles.
According to the test results, no specimen suffered from residual deformation, even if the strain amplitude reached 20%. Thus, the MPRSR composite boasts excellent elasticity and can recover from large deformation. These properties make the composite a desirable material for SI devices.
The equivalent damping ratio was introduced to compare the damping performance between specimens with different molding densities [28]:
$\zeta=\frac{W_{D}\left(a_{0}\right)}{4 \pi W_{S}}$ (1)
where, a_{0} is the deformation amplitude; W_{D}(a_{0}) is the mean area under the hysteresis curve (AUHC) at a_{0}; $W_{S}=\frac{1}{2} K a_{0}^{2}$ is the maximum elastic potential energy of the structure; K is the equivalent stiffness, which is approximated by the slope of the straight line connecting the start and end points of the forcedisplacement curve (Figure 4):
$K=\frac{F_{0}}{a_{0}}$ (2)
Figure 4. Calculation of the equivalent stiffness
The equivalent damping ratios of each of the three specimens were calculated for different strain amplitudes. The calculation results are recorded in Table 2.
Table 2. The equivalent damping ratios $\zeta$ of the MPRSR specimens
Strain amplitudes 
5% 
10% 
15% 
20% 

Equivalent damping ratio $\zeta$ 
MPRSR I (r=0.23) 
0.039 
0.037 
0.032 
0.026 
MPRSR II (r=0.25) 
0.055 
0.044 
0.037 
0.028 

MPRSR III (r=0.27) 
0.059 
0.045 
0.038 
0.033 
As shown in Table 2, at each strain amplitude, the equivalent damping ratio increased with the molding density of the MPRSR specimen.
Figure 5. The stressstrain hysteresis curves of specimens with different molding densities under quasistatic compression
To disclose the influence of molding density on damping performance, the stressstrain curves of the three specimens at the strain amplitude of 20% were compared (Figure 5). It can be seen that, under the same strain amplitude, the specimen with relatively high molding density had a high compressive stress, because the elastic modulus of the MPRSR composite is positively correlated with molding density.
Through Matlab computation, the AUHCs of MPRSRs I, II and III were obtained as 0.271, 0.402 and 0.506, respectively, at the strain amplitude of 20%. Obviously, the AUHC expanded with the growth in molding density. This is because the specimen of a high molding density has lots of metal wires per unit volume, i.e. the friction is high between the metal wires in the specimen. During the loading/unloading process, the metal wires spend much energy to overcome the frictional damping, which promotes the damping performance of the specimen.
To reveal the effects of loading/unloading frequency on compressive performance, the stressstrain hysteretic behaviors of the MPRSR composite were tested under dynamic cyclic loads of different amplitudes and frequencies. Four loading frequencies were adopted, namely, 0.1Hz, 0.5Hz, 1Hz, 3Hz and 5Hz. Under each loading frequency, four strain amplitudes were tested, including 5%, 10%, 15%, and 20%. The cyclic load was applied 20 times under each working condition.
Figures 6(a)~(d) present the stressstrain hysteresis curves of MPRSR I and MPRSR III under different loading frequencies and at the strain amplitudes of 15% and 20%, respectively. It can be seen that the loading frequencies exerted an insignificant impact on the stressstrain hysteretic behaviors of the MPRSR composite. Therefore, it is concluded that the compressive energy dissipation ability of the MPRSR composite does not change with the loading frequency.
To identify the limit of irrecoverable strain of the MPRSR composite, the MPRSR I specimen was applied 30% and 40% compressive strains, respectively. The compressive load was loaded and unloaded five times under each strain. Figures 7 and 8 display the stressstrain curves of the specimen at the compressive strains of 30% and 40%, respectively.
(a) Stressstrain curves of the MPRSR I at the strain amplitude of 15%
(b) Stressstrain curves of the MPRSR I at the strain amplitude of 20%
(c) Stressstrain curves of the MPRSR III at the strain amplitude of 15%
(d) Stressstrain curves of the MPRSR III at the strain amplitude of 20%
Figure 6. Stressstrain hysteresis curves of the specimens under different frequencies of dynamic compressive loads
Figure 7. Stressstrain hysteresis curves of the MPRSR I at the strain amplitude of 30%
Figure 8. Stressstrain hysteresis curves of the MPRSR III at the strain amplitude of 40%
As shown in the two figures, no obvious residual deformation was observed on the specimen at the strain amplitude of 30%; however, residual deformation appeared on the specimen at the strain amplitude of 40%, indicating that the strain is not fully recoverable. In addition, the residual deformation increased with the applied force. In the end, the stainlesssteel wires that make up the specimen were severely deformed, e.g. bulging and even breaking, and the specimen failed in the shape of a Chinese waist drum (bugled in the middle). According to our measurements, the residual strain of the specimen was about 20%.
Similar to the compression test, the shear test was also performed on the Instron FastTrack 8801 servohydraulic fatigue testing system. Each specimen was subjected to static and dynamic cyclic loads along two directions perpendicular to the punching direction (Figure 9). Then, the shear strength, shear deformation, hysteretic behavior and shear stiffness of the MPRSR composite were tested and computed at room temperature.
Each specimen was fixed onto the connecting piece of the shear fixture (Figure 10). Two symmetrical fixtures moved alternatively to complete the loading. To ensure that the specimen is deformed in the recoverable range, the strain amplitudes were set to 5%, 10%, 15% and 20% in turn, while the dynamic loading frequency was set to 0.1Hz, 0.5Hz, 1Hz and 3Hz, respectively. The waveform of the loading is a sine wave. Each specimen was applied 10 cycles of static load and 20 cycles of dynamic load.
Figure 9. Loading directions of the MPRSR composite
Figure 10. The fixture of the shear test
4.1 Influence of loading frequency on hysteretic behavior
The Instron FastTrack 8801 servohydraulic fatigue testing system was adopted for both static and dynamic testing, because the two test methods share the same mechanical principle. The only difference between them lies in the type of sensors [3640]. To verify whether loading frequency affects the shear performance of the MPRSR composite, the specimen MPRSR I was loaded at different frequencies: 0.1Hz, 0.5Hz, 1Hz and 3Hz. Figures 11 (a), (b), (c) and (d) show the shear stressstrain hysteresis curves of the specimen under strain amplitudes of 5%, 10%, 15% and 20%, respectively, at different loading frequencies.
As shown in Figure 11, the MPRSR composite basically had identical hysteresis curves under the same strain amplitude, despite the variation in the frequency of shear load. Therefore, the loading frequency of the shear force has a negligible influence on the shear performance, that is, the shear energy dissipation ability of the MPRSR composite does not change with the loading frequency. Therefore, the same frequency can be adopted for the dynamic shear test on MPRSRs II and III. Due to the presence of dry friction damping, the recoverability of the MPRSR composite might be asymmetry across the Yaxis under sine wave loading, which ultimately depends on the nature of the material.
(a) Hysteresis curves of the MPRSR I at the strain amplitude of 5%
(b) Hysteresis curves of the MPRSR I at the strain amplitude of 10%
(c) Hysteresis curves of the MPRSR I at the strain amplitude of 15%
(d) Hysteresis curves of the MPRSR I at the strain amplitude of 20%
Figure 11. Shear stressstrain curves of the MPRSR I under different loading frequencies
4.2 Influence of loading direction and cycle number on hysteretic behavior
The shear loading/unloading was carried out on MPRSRs I, II and III, respectively, in two mutually orthogonal directions (OX and OY), aiming to disclose how the specimens vary in the shear performance on the noncompressed surface. Figures 12 shows the shear stressstrain hysteresis curves of MPRSRs I, II and III at the loading frequency of 1Hz and the strain amplitude of 10%, respectively. It is easy to observe that the hysteresis curves of each specimen in the two directions were basically coincident, when the specimens were loaded in OX and OY directions. Therefore, the two mutually perpendicular noncompressed surfaces of the MPRSR composite have basically the same hysteretic behavior.
(a) Shear stressstrain curves of MPRSR I
(b) Shear stressstrain curves of MPRSR II
(c) Shear stressstrain curves of MPRSR III
Figure 12. Shear stressstrain curves of specimens along OX and OY directions
Figure 13 presents the shear hysteresis curves of MPRSRs I, II and III at the strain amplitude of 20% and loading frequency of 1Hz, after being loaded/unloaded for 10 cycles. It can be seen that the cycle number has virtually no impact on the hysteretic behavior of the MPRSR composite; no degradation was observed in energy dissipation ability; the stressstrain curves of all the cycles were repeatable. Hence, the MPRSR composite boasts very stable shear energy dissipation ability.
(a) Shear stressstrain hysteresis curves of MPRSR I
(b) Shear stressstrain hysteresis curves of MPRSR II
(c) Shear stressstrain hysteresis curves of MPRSR III
Figure 13. Shear stressstrain curves of specimens with different molding frequencies
The test results also show that the MPRSR composite has good elasticity in the shear directions; no residual deformation appeared when the strain reached 20%. Similar to the results of static shear loading, the loading segment in the shear stressstrain curve of the MPRSR composite was approximately linear, with an unobvious strain hardening effect.
4.3 Influence of strain amplitude on hysteretic behavior
Figures 14(a), (b) and (c) are the hysteresis curves of MPRSRs I, II and III at different strain amplitudes, when the loading frequency is 1Hz. For each specimen, the most representative curve was selected from the hysteresis curves in the ten loading/unloading cycles. It can be seen that, with the growth in strain amplitude, the AUHC of each specimen was on the rise, indicating that the composite consumed an increasingly high amount of energy. This trend can be explained as follows: when the deformation is small, the metal wires have not overcome the friction between them, slowing an unobvious slip; as the deformation amplitude grows, the slip between the metal wires become obvious, dissipating more energy.
(a) Shear stressstrain hysteresis curves of MPRSR I
(b) Shear stressstrain hysteresis curves of MPRSR II
(c) Shear stressstrain hysteresis curves of MPRSR III
Figure 14. Shear stressstrain curves of the three specimens along the OX direction at different strain amplitudes and the loading frequency of 1Hz
Since the loading segment of each stressstrain curve is almost linear, the equivalent shear stiffness can be approximated from the elastic hysteresis curve obtained through the test:
$K_{S}=\frac{F_{S 2}F_{S 1}}{a_{2}a_{1}}$ (3)
where, a_{1} and a_{2} are the maximum horizontal displacements in the negative and positive directions, respectively; F_{S1} and F_{S2} are the shear forces corresponding to a_{1} and a_{2}, respectively. The calculation process of the equivalent shear stiffness is illustrated in Figure 15.
Figure 15. The equivalent shear stiffness
Then, the equivalent damping ratios of MPRSRs I, II and III at different strain amplitudes can be computed by formula (1):
$\zeta=W_{D}\left(a_{0}\right) / 4 \pi W_{S}$ (4)
4.4 Influence of molding density on hysteretic behavior
Table 3 lists the relationship between equivalent shear stiffness, equivalent damping ratio and strain amplitude for the three specimens with different molding densities. It can be seen that the equivalent shear stiffness of each MPRSR specimen exhibits a rising trend with the growth in the molding density. Under the same strain amplitude, the higher the molding density, the greater the equivalent shear stiffness. This is because the specimen of a high molding density has lots of metal wires per unit volume. When the deformation amplitude is the same, numerous metal wires rub against each other in such a specimen, pushing up the friction between wires and thus the shear stiffness. This means the SI effect of the MPRSR composite along the shear directions increases with its molding density.
It can also be seen from Table 3 that, with the increase in the strain amplitude, the shear stiffness of each specimen exhibited a slightly decline, indicating that the shear strain has a limited impact on the lateral shear stiffness. Overall, the equivalent damping ratio is negatively correlated with the strain amplitude.
Table 3. The relationship between equivalent shear stiffness, equivalent damping ratio and strain amplitude for the three specimens with different molding densities

MPRSR I (Molding density: 0.23) 
MPRSR II (Molding density: 0.25) 
MPRSR III (Molding density: 0.27) 

Strain amplitude 
Equivalent stiffness (kN/mm) 
Equivalent damping ratio $\zeta$ 
Equivalent stiffness (kN/mm) 
Equivalent damping ratio $\zeta$ 
Equivalent stiffness (kN/mm) 
Equivalent damping ratio $\zeta$ 
5% 
0.043 
0.142 
0.041 
0.145 
0.036 
0.147 
10% 
0.039 
0.119 
0.035 
0.128 
0.032 
0.131 
15% 
0.035 
0.108 
0.032 
0.112 
0.030 
0.119 
20% 
0.028 
0.101 
0.030 
0.103 
0.027 
0.107 
4.5 Ultimate shear deformation
(a) Stressstrain hysteresis curves of MPRSR I at the strain amplitudes of 3070%
(b) Stressstrain hysteresis curves of MPRSR I at the strain amplitudes of 80%
Figure 16. Shear stressstrain curves of MPRSR I at large strain amplitudes
The next step is to test the resistance of the MPR/SR composite to ultimate shear deformation. For this purpose, MPRSR I were applied shear load with stepwise increase in strain amplitude. Figure 16(a) offers the hysteresis curves of MPRSR I at the strain amplitudes of 30%, 40%, 50%, 60% and 70%. It can be observed that the specimen could fully recover from the strain amplitude of 70%, revealing the stable elastic performance of the specimen. When the strain further increased to 80% (Figure 16(b)), the AUHC gradually decreased with the growth in cycle number, strain degradation started to appear, and the specimen had obvious residual deformation after unloading. Hence, the recoverable ultimate deformation of the specimen was about 80%. This means the MPR/SR has a strong resistance to shear damages in the directions other than the punching direction.
According to the results of the above compression and share tests, the MPR/SR composite has relatively high bearing capacity and large compression modulus, under the compressive load in the punching direction. However, the shear modulus of the composite is relatively low in the other directions.
Table 4 lists the singlecycle secant moduli and equivalent damping ratios of MPRSRs I, II and III under the loading frequency of 1Hz and the strain amplitude of 20%. The data show that the equivalent damping ratio of the MPRSR composite under compression is smaller than that under shear deformation, and the secant modulus of the composite under compressive deformation is more than twice that under shear deformation. These results are favorable for developing a threeway SI device that withstands the vertical load of structures.
After the completion of all tests, each specimen was subjected to a failure test with large strain amplitude in the compression and shear directions. The recoverable ultimate deformations under compression and shear loads of each specimen were observed. The observations show that the MPRSR composite could recover from the ultimate compressive deformation of 40% and the ultimate shear deformation of 80%.
Table 4. Secant moduli and equivalent damping ratios of specimens under compressive and shear loads
Strain amplitude 20%, 1Hz 
MPRSR I (Molding density: 0.23) 
MPRSR II (Molding density: 0.25) 
MPRSR III (Molding density: 0.27) 

Secant modulus 
Equivalent damping ratio 
Secant modulus 
Equivalent damping ratio 
Secant modulus 
Equivalent damping ratio 

Compression 
3.527 
0.0289 
4.561 
0.0294 
5.596 
0.0385 
Shear 
1.043 
0.1153 
1.2683 
0.114 
1.33 
0.1168 
This paper prepares MPRSR specimens of different molding densities, and explores their compressive and shear hysteretic behaviors under quasistatic and dynamic loads, respectively. Several tests were carried out to reflect how these behaviors are affected by load amplitude, cycle count, loading frequency and molding density. The mechanical properties and damping features between the specimens were compared and analyzed in details. The main conclusions are as follows:
(1) When subjected to compressive deformation in the punching direction, the MPRSR composite carries obvious features of strain hardening in its stressstrain curve, revealing a certain capacity for hysteretic energy dissipation; the cycle number and loading frequency have no significant impact on the compressive stressstrain hysteretic behavior of the composite; under the same strain amplitude, the higher the molding density, the greater the secant modulus and recoverability, and the larger the equivalent damping ratio.
(2) When subjected to shear deformation in the punching direction, the MPRSR composite exhibits no obvious features of strain hardening in its stressstrain curve, showing a good energy dissipation ability; the cycle number and loading frequency have no impact on the shear stressstrain hysteretic behavior of the composite; under the same strain amplitude, the higher the molding density, the greater the secant modulus and the equivalent damping ratio; the shear stressstrain hysteretic behaviors of the composite are basically the same in the two directions (OX and OY) perpendicular to the punching direction, i.e. the composite enjoys similar shear performance in the two directions.
(3) The equivalent damping ratio of the MPRSR composite under compression is smaller than that under shear deformation, and the secant modulus of the composite under compressive deformation is more than twice that under shear deformation. These features are favorable for developing a threeway SI device that withstands the vertical load of structures.
This work is supported by Heilongjiang Provincial Natural Science Foundation for the general project “Seismic Failure Modes of FrameShear Structures in Energy Dissipators Based on Metal PseudoRubber/ Silicone Rubber” (Grant No.: E201401), and by the University Students Innovation and Entrepreneurship Training Program of Heilongjiang Province for the project “Mechanical Experiment and Seismic Isolation Analysis of Energy Dissipators Based on Metal PseudoRubber/ Silicone Rubber” (Grant No.: 201910225245).
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