Review on shear thickening fluid and its applications in vibration reduction

Shear thickening fluid (STF) is a nano-smart material that exhibits an instantaneous increase in viscosity when subjected to specific external loads. Notably, its viscosity response does not necessitate external energy input, making it widely applicable in vibration control, energy absorption, and vibration reduction. This paper first presents an introduction and analogy to the evolution of the thickening mechanism of STF. It then discusses factors that influence the rheological properties of STF, including the dispersed phase, dispersion medium, additives, and external environment. Furthermore, it explores various calculation models of STF in engineering applications, considering their advantages, disadvantages, and applicability. The paper later reviews the progress of STF utilization in vibration reduction and energy consumption, specifically focusing on improving mechanical properties in STF sandwich panels. Finally, it delves into the feasibility of STF application in vibration control by detailing the dynamic mechanical properties and applicability of vibration reduction equipment and calculation models based on STF.


Introduction
Shear thickening fluid (STF) is a non-Newtonian fluid that consists of a concentrated suspension formed by the uniform dispersion of nanoparticles in a dispersion medium.The rheological behavior of STF is relatively complex.Figure 1(a) shows that at lower shear rates, the viscosity of STF decreases slightly, allowing for easy flow.However, at high shear rates surpassing the critical shear rate, the viscosity response rapidly increases, causing some highly concentrated STFs to exhibit solid-like characteristics and decreased flowability [1,2].Based on the rheological properties of STF, shear thickening behavior can be categorized into continuous shear thickening (CST) and discontinuous shear thickening (DST).As illustrated in figure 1(b), CST is characterized by a rapid but relatively insignificant increase in viscosity when the shear rate exceeds the critical value.This behavior is commonly observed in colloidal dispersions of STFs.Conversely, DST is characterized by a substantial increase in viscosity by orders of magnitude once the shear rate exceeds the critical value.DST is often observed in examples such as cornstarch in water, densely packed suspensions of hard particles, and micelle solutions.Furthermore, the shear thickening behavior of STF exhibits reversibility [3].As the force is removed, the viscosity decreases and the STF promptly returns to its initial state.
The preparation of STF often involves mechanical stirring, ball milling, or ultrasonic dispersion methods to achieve an even mixing of the dispersed phase particles and the dispersed medium.Due to the long preparation time of STF, a small amount of dispersant is typically added during the process to facilitate faster and more uniform particle dispersion in solutions such as N-aminoethyl-γ-amino propyl trimethoxy silane.Silica (SiO 2 )-based STF, composed of nano-silica particles suspended in a polyethylene glycol solution, is a commonly used STF in laboratory settings.Presently, gas phase and sol-gel methods are the primary means of synthesizing SiO 2 spherical particles.The gas phase method finds widespread use in industrial production, resulting in fumed SiO 2 with a diverse range of particle sizes and particle agglomeration, reducing in the shear thickening effect of STF.In contrast, the sol-gel method involves the hydrolysis of ethyl orthosilicate and the condensation of silicic acid to produce SiO 2 with a narrower particle size distribution.However, the sol-gel method exhibits low economic benefits and slow industry progress due to the low yield and high cost of ethyl orthosilicate.Conversely, fumed SiO 2 proves more cost-effective and offers a broader range of applications.Other dispersed phases employed in STF synthesis include polystyrene ethyl acrylate particles, polymethyl methacrylate particles, and calcium carbonate particles, while dispersion media encompass glycerol, ethylene glycol, and dioctyl phthalate.Adjusting the mass fraction of the dispersed phase in the solution allows scholars to prepare highperformance STF.

Shear thickening mechanism
The microscopic origin of shear thickening in STFs has always been a prominent research area.This paper presents four main mechanisms that explain the phenomenon of shear thickening: the order-disorder transition (ODT) theory, particle cluster theory, particle jamming theory, and the contact rheology model.

Order-disorder transition theory
In the 1970s, Hoffman [20] utilized light diffraction technology to observe the particle changes preceding and following shear thickening in suspensions, as depicted in figure 3(a).Subsequently, he proposed the ODT theory as a mechanism for shear thickening.The ODT theory, postulated by Hoffman, hypothesized the following: First, the suspended particles adopt a hexagonal-packed spherical configuration; Second, the spheres flow solely within a two-dimensional plane; Lastly, upon undergoing shear, attractive and repulsive forces, in addition to applied shear force fields, arise between the suspension's spheres.Consequently, the ODT theory maintains that during the flow process, the hexagonal-packed spheres overtake one another, leading to a continuous increase in relative velocity on the sphere surfaces and, consequently, an increase in shear stress.The force between spheres is overcome upon surpassing a specific critical shear stress value.Consequently, spheres arrange themselves in a disordered state, hindering one another and eventually increasing in suspension viscosity.Additionally, Hoffman [21,22] observed the phenomenon of layered orientation within the concentrated suspension, confirming the presence of an ordered layered structure in the suspension system and supporting the ODT theory.Furthermore, Chow and Zukoski [23] and Boersma et al [24] substantiated the disordering of particles during shear thickening via small-angle neutron scattering technology, providing further corroboration of the ODT theory (figure 3

Particle cluster theory
Following the proposal of the ODT theory, scholars proceeded to investigate the phenomenon of shear thickening using small-angle neutron scattering technology.Their research demonstrated that shear thickening was often observed alongside the occurrence of ODT.However, it is essential to note that shear thickening does not always imply the presence of ODT [25,26].ODT represents only one form of variation in the internal structure of suspension systems; an alternative form occurs when particles aggregate to form particle clusters.Using Stokesian dynamics, Brady and Bossis [27,28] simulated the rheological behavior of the suspension and discovered that the rise in viscosity resulted from particle aggregation to form clusters.Based on these findings, they introduced the particle cluster theory.According to the theory of particle clusters, when shear thickening occurs, the Brownian motion inside the suspension intensifies, and the resulting fluid lubrication force exceeds the repulsive force between particles, which promotes particle aggregation, cluster formation, and the overall increase of suspension viscosity, as shown in figure 4(a).Phung et al [29] used fluid dynamics to simulate the non-equilibrium behavior of hard particles in shear suspension and observed that the suspension showed apparent internal fluid lubrication force at higher shear rates, resulting in the formation of large, non-dense particle clusters, which ultimately affected the flow of the suspension.Their research provides more evidence for the particle cluster theory.Additionally, Cheng et al [30] utilized fast confocal microscopy in conjunction with synchronous force measurement to objectively observe microparticles and provide empirical evidence for the validity of the cluster theory (figure 4(b)).

Particle jamming theory
Particle cluster theory can explain the behavior of CST, but it fails to explain the behavior of (DST) with a significant increase in viscosity [31].DST frequently occurs in high-concentration suspension systems.Recently, scholars have proposed the 'Jamming' mechanism as a theory to explain this behavior [32][33][34][35][36].According to the Jamming theory, when a suspension is sheared, the particles come into contact and aggregate in a confined space, leading to local blockage, an increase in viscosity, and a transition from a liquid to a solid state.Lootens et al [37] examined a suspension of SiO 2 particles with a rough surface and utilized a confocal microscope to observe the changes before and after shearing.Figure 5(a) depicts the state of expansion and blockage in the suspension, providing objective evidence for the validity of the Jamming theory.Numerous scholars have provided explanations for the occurrence of jamming.Brown et al [1] believed that the limit of DST behavior corresponds to the particle-blocking state.Fall et al [33] employed magnetic resonance imaging to investigate the rheological properties of high-concentration corn starch suspensions.The conclusions drawn from the analysis indicate that the limited space within the system is a probable cause of DST. Figure 5(b) displays the dimensionless velocity distribution in the gap, as determined through magnetic resonance measurements.Furthermore, Farr et al [38] proposed a 'fabric' model of load-bearing stress, predicting fluid blockage in an infinite system for hard sphere dispersed systems with a volume fraction exceeding 0.63.

Contact rheology model
The CST and DST behavior of STF can be explained by the particle cluster theory and the Jamming theory, respectively.Fernandez et al [39] proposed a contact rheology model based on contact dynamics and rheology to investigate the transition of STF from CST to DST due to the different lubrication mechanisms between particles.According to the contact rheology theory, the fluid lubrication force only plays a dominant role when the normal contact force between particles is small.The destruction of the fluid film between particles, the increase in contact between particles, and the leading role of the contact force and friction between them occur when the normal contact force between particles is large.Mari et al [40] conducted numerical simulations of the contact network during the shear thickening process, as depicted in figure 6.The gray and red parts represent frictionless and frictional contacts, respectively.It can be seen from the figure that the frictional contact appears on the small force chain along the compression axis at a low shear rate.At the high shear rate, the viscosity increases obviously, the friction contact appears in large quantities, and the contact network presents the phenomenon of blockage.In figure 6(a), the contact network of CST gradually becomes dense, demonstrating a continuous dense collective.In contrast, figure 6(b) illustrates that during DST, the contact network is similar to the viscosity change, and the transition from sparse to dense is not continuous.According to Steo et al [41], contact friction is crucial in DST.Before achieving the critical shear stress, the suspension experiences low viscosity where no contact and friction occur.Once the critical shear stress is surpassed, the suspension enters a high-viscosity state, resulting in shear blockage.Numerous scholars have verified the relationship between contact friction and the shear thickening of suspensions through experiments or numerical calculations [42][43][44][45].

Factors of shear thickening fluid
Various factors affect STF's rheological properties [46,47].Early studies on the rheological properties of STF primarily focused on the change in the critical shear rate during the onset of shear thickening.While studying the required shear rate provides a fundamental understanding of the rheological behavior of STF, additional research is necessary to achieve comprehensive knowledge in this field.Thus, a comprehensive investigation of the influencing factors on shear thickening performance is necessary to understand the shear thickening effect of STF fully.First, examining the impact of the dispersing phase and medium is crucial, including particle volume fraction, size, length-diameter ratio, and particle size distribution.Second, enhancing the performance of STF can be achieved by adding small amounts of additives, such as cellulose nanofibers and carbon nanotubes.Furthermore, the rheological properties of STF are significantly influenced by the external environment, including temperature, magnetic fields, and electric fields.

Dispersion phase and dispersion medium
STF consists of the dispersion phase and medium, and their parameters significantly influence its rheological properties.The research on the influencing factors of rheological properties of STF mainly focuses on the volume fraction of dispersed phase particles.The shear rate-viscosity curves of suspensions containing precipitated calcium carbonate (PCC) and polyethylene glycol (PEG) at various particle volume fractions are depicted in figure 7(a).Figure 7(a) demonstrates that the viscosity of the suspension with a low volume fraction remains constant or slightly decreases during shearing.Conversely, as the volume fraction increases, the suspension's viscosity becomes more sensitive to the shear rate, gradually decreasing in the initial critical shear rate.The increase in particle volume fraction leads to greater susceptibility of particles in the suspension to the flow field exerted by neighboring particles.Consequently, hydrodynamic forces emerge among the particles, altering the rheological properties of the suspension and intensifying the likelihood of shear thickening.In addition, Barnes [48] suggested that as the particle volume fraction increases, the critical shear rate decreases, and the maximum viscosity of the system increases.The volume fraction of dispersed particles directly influences the system's critical shear rate and maximum viscosity, making it a crucial factor in shear thickening.
The particle size is an essential factor that affects the rheological properties of STF.It has been observed that as the particle size increases, the critical shear rate of STF decreases [48][49][50].This phenomenon can be explained by Gürgen et al [51], who noted that smaller particles exhibit high-velocity Brownian motion and a high surface charge density, allowing them to overcome the repulsive force between particles and cause aggregation, resulting in shear thickening.Barnes [48] conducted a study on STF with particle sizes ranging from 0.01 μm to 100 μm and proposed an inverse quadratic relationship between particle size and critical shear rate, as depicted in figure 7(b).Maranzano and Wagner [50] presented viscosity curves for different particle sizes at a fixed volume fraction (0.5), as illustrated in figure 7(c).These curves further confirmed the dependence of shear rate on particle size.Notably, the relationship between the critical shear stress and particle size in the suspension can be derived from the force balance between the repulsive force and the hydrodynamic compression force acting between two particles [50,52].This relationship is described by equation (1): Where a is the particle radius, T denotes temperature, κ is wave number, l b ≡ e 2 / (4πεε 0 K B T) represents Bjerrum length, Ψ 2 s = ψ s e / K B T is the dimensionless surface potential, ψ s is approximations for the surface potential, e is the electronic charge, K B is Boltzmann constant, ε is the permittivity of the vacuum and ε 0 is the permittivity of the solvent.The formula presented herein represents an inverse relationship between the critical shear stress and particle size.
The shape of particles significantly impacts shear thickening, with rod-shaped particles having the most pronounced effect on improving STF shear thickening [53].The effect of particle shape is closely related to particle aspect ratio, with higher aspect ratios resulting in increased viscosity of STF [48].Although higher aspect ratios reduce the maximum packing density and mutual attraction of particles in the system, a more significant aspect ratio increases the likelihood of contact with neighboring particles, making shear thickening more probable [54].Additionally, STF synthesized with high aspect ratio particles can display shear thickening behavior even at low volume fractions.
The dispersion medium's molecular weight and hydroxyl content strongly influence the viscosity and shear thickening behavior of STF.As solvent molecular weight increases, STF viscosity and shear thickening effect increase, causing the viscosity curve to shift upwards and the critical shear stress to decrease [55].Regarding hydroxyl content, more hydroxyl groups increase hydrogen bonding, causing STF to become less fluid and more susceptible to shear thickening.Jiang et al [56] prepared a suspension by mixing polymethyl methacrylate particles with a glycerin-water mixture and studied its rheological behavior under different glycerin-water ratios.They found that increasing the glycerol ratio weakened the hydrogen bonding interaction between particles and the medium, increased the volume fraction of the practical dispersion phase, and intensified the shear thickening phenomenon, as depicted in figure 7(d).Moreover, a stable shear-thickening system can only be prepared by precisely matching dispersed-phase particles and the dispersing medium.

Various additives
In addition to adjusting the parameters of the dispersion phase and dispersion medium, adding a small number of appropriate additives to the pre-configured STF can also enhance the shear thickening performance.The common additives are (1) Four types of surfactants: cationic, anionic, zwitterionic, and nonionic.(2) Charged or acid-alkaline particle or solution.(3) Nano-scale materials: nano cellulose fibers, graphene, carbon nanotubes, and other materials.(4) Micron particles: silicon carbide, montmorillonite, dichloride dioxide.
Ghosh et al [58] selected cellulose nanofibers (CNF) as an additive.Adding a small amount of CNF to STF resulted in a significant increase in peak viscosity and a decrease in critical shear rate.The reason is that many hydroxyl groups in CNF enhance the interaction between nanoparticles through hydrogen bonding.Figure 8(a) illustrates the mechanism diagram of CNF-enhanced shear thickening.Ge et al [59] introduced SiC nanowires into STF.Compared to pure STF, adding an appropriate amount of SiC nanowires significantly improved the initial viscosity and peak viscosity of STF, as shown in figure 8(b).However, adding additives also prolonged the thickening period of STF, as depicted in figure 8(c).Furthermore, Gürgen et al [60] suggested that the volume fraction of dispersion phase particles decreased after adding additives to the suspension system.When the shape of the additive particles differed from that of the dispersion phase particles, the expansion of water clusters became challenging, ultimately affecting the shear thickening performance.
Furthermore, the shear thickening performance of STF can be altered by changing the pH value of the system, as the surface charge of dispersed phase particles is influenced by the pH value, which in turn affects the force between the particles.Scholars have controlled the pH value of STF by introducing different acid-base solutions, thereby regulating its shear thickening property [61][62][63].Chen et al [61] examined the impact of pH on the shear-thickening behavior of polystyrene-ethylacrylate (PSt-EA) copolymer nanospheres.Their findings revealed that irrespective of whether acid or alkaline additives were used, the further the pH value of STF deviated from the neutral value of 7, the smaller the critical shear rate became, indicating a stronger shear thickening performance (figure 9(a)).Shan et al [64] explored the effect of pH value on fumed silica suspension and deduced that an increase in pH value led to an increase in critical shear rate and stress (figure 9(b)).Although the viscosity at a low shear rate increased with the rise of pH value, the shear thinning behavior outweighed this effect.

Application environment
The rheological properties of STF are influenced by ambient temperature [65].Previous studies have demonstrated that as temperature increases, the critical shear rate of STF also rises, resulting in delayed shear thickening, reduced critical viscosity, and decreased shear thickening effect (figure 10(a)) [66][67][68].The weakening of shear thickening at high temperatures can be attributed to two factors.Firstly, the hydrogen bonding between dispersion phase particles and dispersion medium weakens with temperature rise [69].Secondly, high temperature amplifies the repulsive forces between particles, hindering the formation of particle clusters [70].
External magnetic and electric fields impact certain special STFs, characterized by dispersion phases possessing conductive or magnetic properties or by adding conductive or magnetic substances after preparation.In recent years, scholars have begun studying the combination of STF with magnetorheological fluid (MRF) or electrorheological fluid (ERF), resulting in the development of magnetorheological shear thickening fluid (MRSTF) and electrorheological shear thickening fluid (ERSTF) [71][72][73][74][75].However, existing tests have shown that STFs with multiple functions generally compromise their shear thickening strength [76].Zhang et al [77] incorporated carbonyl iron particles into STF to prepare MRSTF.As the concentration of iron particles increased, the shear thickening effect of MRSTF diminished while the magnetorheological impact intensified.Li et al [78] compared the performance of MRSTF and STF under shearing.Without a magnetic field, the viscosities of MRSTF and STF were similar.However, upon applying a magnetic field, the viscosity of MRSTF increased, but the shear thickening effect weakened or even disappeared (figure 10(b)).The weakening of the shear thickening effect in MRSTF can be attributed to two factors.Firstly, as the concentration of iron particles in the system increases, the dispersed phase concentration decreases, leading to a decrease in viscosity.Secondly, the presence of carbonyl iron particles hinders the movement of the dispersed phase, making it challenging to form water clusters and reducing the shear-thickening effect.Shenoy et al [79] conducted a study on ERSTF and arrived at a similar conclusion.When an electric field is applied, the formation of particle clusters is inhibited, resulting in a weakened shear thickening effect.The reason is that the electric field induces particle polarization, produces polarization force, changes the force between particles, and increases the critical stress required to produce water clusters.

Viscosity model of shear thickening fluid
The constitutive model of STF highlights its material properties, with several literature sources introducing STF constitutive models [36,[80][81][82][83][84].The WC model [36] is widely acknowledged as the primary STF constitutive model.Though the constitutive model explains the nature of STF, the viscosity model is the more crucial element in engineering numerical calculations.Figure 11 illustrates the shear rate-viscosity curve of a typical STF.The figure shows that the viscosity of STF initially decreases and dilutes at low shear rates, then sharply rises as the shear rate increases to the critical shear rate, resulting in the thickening of the STF.Finally, in the late thickening stage, thinning reappears as the shear rate surpasses the critical value, leading to a decrease in viscosity.To describe the viscosity behavior of STF, several scholars have proposed various viscosity models [85].Gopalakrishnan and Zukoski [86] calculated viscosity by dividing it into two parts based on thermodynamics

Power law model
The thickening and thinning stages of STF adhere to the rheological features of the power-law fluid, thereby establishing a connection between viscosity and the shear rate of STF through a power-law function.Equation (2) represents the power law model.This simple and practical model can describe the viscosity of non-Newtonian fluids and is widely used for simulating the viscosity of STF [90].
Where η is the viscosity, K is the material-related constant, g  represents the shear rate, and n represents the power law index.After incorporating certain adjustments, including the initial viscosity, during the subsequent stage, the functional model exhibited increased accuracy, as depicted in equation (3).
Where a represents the adjustment parameter of the curve, K is the material-related constant, g  0 and g  max represent the initial and shear rates corresponding to the maximum viscosity, respectively.Although the power law model provides a straightforward calculation method, it solely captures the shearthickening behavior of STF and cannot accurately simulate the shear-thinning behavior.Wei et al [91] employed a power law model to fit the viscous-shear rate curve of STF, as depicted in figure 12.However, it is evident from figure 12 that this model solely represents the growth process of viscosity and fails to capture the shear thinning behavior at high shear rates or determine the peak viscosity of STF, rendering it unsuitable for numerical simulation.

Piecewise function model
Per the observed trends, the conventional viscosity curve of STF illustrated in figure 11 can be segregated into three distinct regions.Region I refers to the low shear rate with shear thinning behavior, where the initial viscosity is η 0 , and the viscosity at critical shear rate is η c , indicating the end of Region I. Region II corresponds to the shear thickening stage, which ranges from η c to η max and represents the ascending interval of viscosity.η max signifies the peak viscosity, while the corresponding shear rate is denoted as g  .
max Region III represents the high shear rates with shear thinning behavior.To address the limitations of the power-law model, Galindo-Rosales et al [89] proposed a piecewise function model, whose foundation is formed based on the formula of Cross [92], and analyzed the three regions with changing viscosity behavior in STF, as presented in equation (4).Where K I , K II and K III all have a time dimension and are responsible for the transition between the flat region and the power law in the three regions, respectively.g  c is critical shear rate.η I , η II and η III are dimensionless exponents related to the slope of the power law region.They employed the Levenberg-Marquardt algorithm to optimize the parameter fitting.The resulting fitting curve is illustrated in figure 13, demonstrating the favorable efficacy of this model.Shortly after Galindo-Rosale's segmentation model proposal, Tian et al [93] discovered that the formula was conditional.Specifically, the parentheses must be positive if η I , η II and η III are decimal in the formula.Consequently, they added the absolute value symbol to the parentheses of the initial formula and proposed a revised model, as demonstrated in equation (5).The graph in figure 14 indicates that the model is also well-suited for various temperature conditions.
n for for

h h dg dg h g dg h g dg
Equation ( 7) is the parameter calculation method in equation (6), where g  is the local shear rate, g  c is the critical shear rate corresponding to the viscosity transition, and δg  determines the shear rate range from the viscosity η 0 to the η 1 change.In addition, η 1 > η 0 , m and n ensure the continuity of viscosity.Figure 15(c) verifies the fitting effect of the Smoothed-Particle Hydrodynamics (SPH) inverse double-viscosity model.

Fractional order model
Using a fractional order model has proven effective in describing the behavior characteristics of non-Newtonian fluids [95,96].This model is highly precious in engineering applications due to its simplicity and the limited number of parameters required [97,98].Sun et al [99] developed a fractional derivative constitutive equation for non-Newtonian fluids by utilizing the fractional derivative of the velocity gradient, as demonstrated in equation (8).Where τ denotes the viscous shear stress, τ 0 represents the yield stress, u is the flow velocity, μ α is the fractional dynamic viscosity, du/dy is the velocity gradient, y is the direction perpendicular to the fluid flow and α is fractional derivative order.I 1− α , I 2− α represent the Riemann-Liouville fractional integral, as shown in equation (9).
Where Г is the gamma function.

Phenomenological model and artificial neural network model
The phenomenological model describes the hydrodynamic characteristics of STF.Amongst the existing models, Wei et al [91] proposed a simple STF viscosity prediction model, as shown in equation (11).
Where η 0 represents the initial viscosity of STF, η max represents the maximum viscosity, g  is shear rate, and k 1 , k 2 , w 1 and w 2 are the adjustment parameters of the fitted curve.As depicted in figure 17, they employed the nonlinear least square method to fit the model's parameters, demonstrating that it was highly superior to the power law model during the viscosity simulation test and effectively simulated the entire shear thickening process.Moreover, the functional model is continuous, suitable for numerical simulation and curve fitting, and broadly applicable in engineering.
The phenomenological model proposed by Wei et al [91] exhibits a remarkable capability to fit single-phase STF data accurately.However, when Gürgen et al [102] employed this model to investigate the rheological behavior of multiphase STF and assess the fitting accuracy of the model under varying temperatures, they observed that it was inadequate for describing multiphase STF, as illustrated in figure 18.Consequently, they developed a modified version of the phenomenological model, tailored specifically for polyphase STF, presented in equation (12).Where a , 1 a , 2 k 1 , k 2 , w 1 and w 2 are the adjustment parameters.The fitting results of the modified model are presented in figure 19, demonstrating its ability to describe the rheological behavior of multiphase STFs accurately.
Furthermore, Lin et al [103] employed logic, power, and exponential functions to simulate shear thinning and failure behavior, employed a logistic growth model to account for the shear thickening region, and developed a phenomenological model, as demonstrated in equation (13).Figure 20(a) illustrates the corresponding fitting curve.
Polyphase STF exhibits complex non-Newtonian behavior, and obtaining a theoretical model to predict its rheological behavior necessitates time-consuming, often tedious experiments.An alternative approach is using an artificial neural network (ANN) model, which generates mappings based on the relationship between experimental inputs and outputs.The ANN model offers an easier prediction of the rheological behavior of STF [104].Arora [105] developed a parameter-less ANN model and successfully forecasted the shear rate-viscosity curve of STF using it.Figure 20(b) portrays the ANN prediction alongside the corresponding experimental data.Remarkably, the results exhibit a promising correlation coefficient, validating the high prediction accuracy achieved by the ANN model.

Vibration reduction application of shear thickening fluid
STF exhibits sensitivity to external loads and is capable of absorbing energy upon impact, with its shear thickening behavior being reversible [107,108].Additionally, STF functions as a damping material, offering damping effects in both shear and extrusion modes [109].Consequently, STF holds significant potential for applications in vibration damping and energy absorption.The subsequent sections will delve into the various applications of STF in vibration damping and energy absorption, including STF sandwich structures, STF dampers, and other related applications.

Sandwich structure
Fluid damping offers continuous energy dissipation, and incorporating adaptive materials into composite structures enhances the ability to control vibration and stiffness.STF damped sandwich structures represent a novel technology for vibration reduction, characterized by high stiffness, lightweight design, and excellent resistance to deformation [110].
The first investigation into STF damped sandwich beams was conducted by Fischer [111].This study replaced a three-layer polyvinyl chloride (PVC) sheet sandwich beam consisting of epoxy resin with an STF material, as depicted in figure 21(a).Through vibration beam tests, Fischer demonstrated the considerable vibration reduction capabilities of the STF sandwich beams he produced [112], as illustrated in figures 21(b) and (c).These structures' vibration-damping mechanism stems from the STF material's shear thickening induced by the relative motion between the PVC sheets within the sandwich.Consequently, the resonant frequency and damping of the structure increase.Wang et al [113] provided a visualization of this vibration-damping mechanism for STF sandwich beams in figure 21(d).Their research suggested that during shear thickening, the hydrogen bonds between PEG-400 molecules in the STF material and the ether-hydrogen bonds formed by PEG on the surface of SiO 2 are broken, resulting in the formation of particle chains through the combination of PEG-400 molecules and SiO 2 particles.Consequently, the elastic modulus and equivalent damping of the sandwich structure are significantly improved.Furthermore, Wang et al [113] proposed a novel shear strain model for the sandwich damping layer.They believed that the damping layer thickens with a fixed strain amplitude, but the damping capacity of the structure does not increase as the STF content increases.In contrast to the previous studies, Wei et al [114] developed a dynamic model for sandwich beams with an STF core, theoretically investigating the dynamic characteristics of this structure under forced excitation.The author reached the following conclusions: The natural frequency of STF sandwich beams is more sensitive to excitation amplitude than conventional forms, and the natural frequency is not fixed when stimulated by different cycles, as illustrated in figure 22(a).
Sandwich materials possess several advantageous properties, such as high energy absorption, lightweight characteristics, and high specific stiffness, rendering them suitable as impact-resistant and energy-absorbing components [5,10,115].Incorporating highly adaptive STF materials into sandwich structures has demonstrated the potential for significantly enhancing structural strength and facilitating vibration control [9,116,117].Gürgen and Sofuoğlu [118] successfully infused silica-based STF into the core layer of polystyrene foam and significantly improved the vibration reduction performance of the traditional sandwich structure.In a separate study, Tan et al [119] constructed a simple STF core sandwich plane plate using pure aluminum on the front and back.STF filled the middle, and polymethyl methacrylate (PMMA) sealant was applied at the edges.By   subjecting the sandwich plate to projectile impact, they observed that the absorption of energy by the STF sandwich plate increased with faster impact speeds.
Due to its excellent vibration damping and energy absorption properties, honeycomb structures are commonly employed in STF sandwich constructions [120].By incorporating STF into the honeycomb core of a sandwich panel, Fu et al [121] achieved a remarkable increase in energy absorption compared to the original panel, as illustrated in figure 22(b).Upon increasing the initial impact velocity, they observed that the energy absorption of the STF-filled sandwich composite exhibited a rapid rise during low-velocity impacts.However, under high-energy conditions, the capacity of STF to absorb all the energy became insufficient, resulting in direct destruction of the bottom of the composite due to the impact force.To address this issue, researchers have sought to enhance the impact resistance of STF composite materials by thickening the STF core.Warren et al [122] conducted ultra-high-speed impact tests on honeycomb sandwich panels, as depicted in figure 22(c), revealing superior impact mitigation effects of STF sandwich panels compared to those filled with polyethylene glycol (PEG).Additionally, Wu et al [123] constructed a sandwich panel with STF filled pyramidal lattice truss core.They subjected it to loading tests using an improved split Hopkinson pressure bar (SHPB), as showcased in figure 22(d).The results of the tests indicated that, in comparison to an empty pyramidal lattice truss core sandwich panel, the STF-filled sandwich panel exhibited significantly enhanced dynamic energy absorption capabilities, with a compressive strength effect surpassing the combined effects of the empty and water-filled panels, thus demonstrating the phenomenon of '1 + 1 > 2'.
In conclusion, sandwich structures filled with STF exhibit the ability to respond to external loads without requiring additional energy input.This characteristic enables them to dampen vibrations and absorb energy effectively, making them suitable for implementation as lightweight structural components in aircraft and automobiles.Furthermore, their potential extends to applications such as wind vibration resistance and adaptive structural control in prefabricated buildings in the future.

Damper
An STF damper is a novel passive device for structural vibration control, utilizing the shear thickening effect of intelligent material STF.This technology offers numerous advantages, including rapid response, strong adaptability, and energy-independent operation [124][125][126][127][128]. Its working principle relies on the movement of a piston within the damper chamber, causing the STF to be pushed through the annular gap between the piston and the cylinder wall.Consequently, the shear thickening of the STF occurs, leading to a significant increase in viscosity, thereby absorbing energy and damping structural vibrations.
The STF damper can be categorized into two forms based on the type of piston: single rod and double rod.The structure of a single rod damper is more complex as it requires the addition of a gas compensator.Figure 23(a1) illustrates a single-rod STF damper designed by Zhou et al [129], while its dynamic performance is displayed in figure 23(a2).Yeh et al [125] investigated the performance of a self-made single-rod STF damper under cyclic loading.Their findings indicated that the STF damper exhibits nonlinear characteristics that can be adjusted according to vibration speed.Zhao et al [127] successfully applied STF dampers to rotor systems, allowing its nonlinear damping to control unbalanced vibrations, which presents distinct advantages.Significantly, at high dynamic loading speeds, STF dampers demonstrate higher damping capabilities and energy absorption rates [130].
Compared to single-rod STF dampers, double-rod STF dampers offer a simpler structure and can avoid the influence of additional chambers on shear thickening performance.The performance of the double-rod gap damper is affected by the excitation conditions and the annular gap.Zhou et al [128] conducted tests on the response of double-rod STF dampers under varying excitation frequencies and amplitudes using a fatigue testing machine.The results indicated that increasing the excitation frequency and amplitude led to higher damping force and greater energy consumption by the dampers.Wei et al [124]developed a double-rod STF damper, as depicted in figure 23(b1), and investigated the impact of annular gap and excitation conditions on the damper's performance.Figure 23(b2) showcases the force-velocity characteristics of the damper for different annular gaps.The findings revealed that beyond a critical value, the damping force decreases when the excitation amplitude (frequency) exceeds this threshold, and decreasing the annular gap progressively increases in the damping force.Although double-rod STF dampers demonstrate favorable vibration damping performance, Lin et al [17] discovered that their performance weakens under long-term cyclic loads.The internal temperature of the damping cylinder significantly increases during cyclic loading, causing a rise in the internal STF temperature, which weakens the shear-thickening effect and leads to a logarithmic decrease in the damping force.
For the development of multifunctional STF, Yang et al [131] utilized MRSTF technology to create an internal electromagnet semi-active damper, as depicted in figure 23(c1).The results of the loading tests conducted on this damper are illustrated in figure 23(c2).Analysis of figure 23(c2) reveals that the performance of the MRSTF is akin to that of the MRF when the external magnetic field is stimulated.The MR effect of the MRSTF damper becomes more apparent, while the shear thickening effect gradually diminishes with an increase in the concentration of iron particles.Moreover, it is worth noting that STF can effectively serve as an adaptive passive damper in microelectromechanical systems [132].
Establishing the dynamic model of the STF damper is essential to improve its performance further.Zhang et al [130] proposed an equivalent linear model and presented fitting results in figure 24(a).The model adequately captures the linear characteristics.However, the model fails to accurately describe the nonlinear characteristics of the STF damper caused by the shear thickening phenomenon.Zhou et al [129] extended the equivalent linear model by introducing a power law model to describe the output force of the STF damper.They established a comparable nonlinear model to enable performance prediction.The fitting curve is shown in figure 24(b).In addition, Wei et al [133] developed a mechanical model of STF dampers based on phase transition theory.Figure 24(c) demonstrates that at the instant of shear thickening, the water cluster can be classified as one phase (S phase) and the floating suspended particles under shear stress as another phase (F phase).Presently, the dispersed water cluster has two phases in opposite directions (F+ and F− phases), as described by Wei.Based on this phase transition theory, Wei et al [133] proposed a dynamic model in the form of differential equations, as shown in equation (14), to simulate the nonlinear behavior of STF dampers.where ρ, ξ, α, β and γ denote the system parameters, η represents the external load of the STF damper, τ represents the shear stress, and ẗand t  are the second derivative and the first derivative for time, respectively.Figure 24(d) illustrates the fitting curve of the mechanical model of the STF damper, which is proposed using the phase transition theory.The fitting results align well with the experimental data.

Other applications
Other researchers have looked into additional uses of STF in the realm of vibration reduction in addition to sandwich constructions and dampers.To lessen the impact and vibration of the bolted flange joint during operation, Guo et al [134] filled it with STF.They contrasted the junctions with and without substance by filling the flange joints with epoxy resin and STF, respectively.Figure 25(a) presents the experimental results.The figure shows that, in comparison to the original construction, the structural vibration is evidently controlled with the addition of STF or epoxy resin, with STF having a higher vibration-reduction impact.Furthermore, the epoxy resin can only reduce the amplitude to a certain level.In contrast, the addition of STF can reduce the structure's fundamental frequency and abolish the high-frequency oscillation, as illustrated in figure 25(b).Gürgen and Sofuoğlu [135] used STF to improve the vibration reduction performance of carbon fiberreinforced polymer (CFRP) tubes by increasing the natural frequency of the structure.Their research also discovered a good match between the damping ratio and the rheological parameters.The damping ratio increases, and the damping properties improve when shear thickening performance improves, as shown in figure 25(c).Additionally, Gürgen and Sofuoğlu [136] filled the STF film layer at the interface of the multi-layer cork structure, which improved the structure's vibration reduction performance without changing the composite material's thickness due to the cork's good vibration isolation performance and environmental protection.Their research concluded that the more layers of STF film and cork there were in the cork composite material, the more STF content, the better the structure's ability to dampen vibrations, as shown in figure 25(d).

Conclusion
This paper discusses the research progress of STF.The collective investigation of the shear thickening mechanism, performance influencing factors, calculation model, and applications of vibration reduction and energy absorption has led to a comprehensive understanding of STF.Nevertheless, as an energy-dissipating material, especially in adaptive vibration reduction and energy absorption, STF still presents significant challenges.The following issues need to be addressed for future advancements: (1) The theory underlying the shear thickening phenomenon remains controversial.The shear thickening behavior varies across different experimental conditions, making it impossible to explain all STFs using a single theoretical model.The understanding of the shear thickening mechanism has evolved from the early ODT theory to the widely employed particle cluster theory.The cluster theory predominantly accounts for colloidal suspension thickening (CST) behavior, whereas the thickening behavior of dense suspensions (DST) is defined by the theory of 'Jamming' or the contact rheology model.
(2) There are some limitations and challenges in the application of STF.First, temperature has a significant impact on the shear-thickening properties of STFs.The increase in temperature leads to the increase of the critical shear rate of STFs, thus reducing its shear thickening ability.Second, STF is commonly liquid and prone to overflowing when filled in composite materials.Structural deformation can lead to leakage of the STF, consequently reducing user comfort.Finally, during prolonged use of STF, the sedimentation of particles becomes a concern, reducing the shear thickening performance.
(3) Insufficient research has been conducted on polyphase and high-performance STFs.Depending on specific working scenarios, scholars should carefully select an appropriate dispersion phase, dispersion medium, and dispersant and employ additives to tailor the properties of STFs, thereby fully utilizing their advantageous performance characteristics.
(4) Due to the substantial friction between the solid and fluid layers within the STF sandwich structure, precise surface treatment of the sandwich structure is necessary.Furthermore, the shear-thinning behavior of STF does not contribute positively to vibration control.When employing an STF sandwich structure within a vibration-damping system, it is advisable to prevent the initiation of the shear thinning stage.
(5) Despite the advantages of STF in damping equipment, including no additional requirements, immediate response to external forces, low maintenance costs, and extended service life, and its potential to address issues of high costs and energy consumption in active vibration control, the development of a high- precision mechanical model for STF dampers is still lacking.The establishment of such a model proves challenging due to the consideration of multiple dynamic response characteristics, such as nonlinear deformation and variations in viscosity. (b)).

Figure 1 .
Figure 1.(a) The variation process of viscosity of typical STF with the shear rate; (b) Continuous shear thickening and discontinuous shear thickening [4].

Figure 9 .
Figure 9. (a) The viscosity curves of STF after adding different amounts of acid and alkali and the relationship between critical shear rate and PH value were studied [61]; (b) Viscosity curves of fumed silica suspensions with different PH values [64].

Figure 12 .
Figure 12.Comparison between the prediction of viscosity curve of power law function and experimental results [91]. h

Figure 14 .
Figure 14.Model fitting curves of STF with different concentrations at different temperatures [93].

Figure 16 (
a) shows the relationship between viscous shear stress and velocity gradient under different yield stresses and fractional derivative orders.It can be seen from the figure that different types of non-Newtonian fluids, including shear thickening fluids, can be clearly characterized by using this model.Using equation (8) as a foundation, Chang et al[100] developed a viscosity constitutive relation for non-Newtonian fluids within pipelines, which is presented in equation(10).

Where a 1 ,
a 2 , a 3 , b 1 , b 2 and b 3 denote the parameter of the logistic growth curve.The model demonstrates the capability to predict viscosity-shear rate curves of STFs under various material and temperature conditions.

Figure 21 .
Figure 21.(a) Schematic diagram of three-layer PVC sandwich structure [112]; (b) Effect of STF composition on the increase of relative damping of sandwich structures [112]; (c) Effect of STF composition to the rise of EI relative to sandwich structure [112]; (d) Damping mechanism diagram of STF sandwich beam [113].

Figure 22 .
Figure 22.(a) Effects of different excitation amplitudes on natural frequencies of sandwich beams [114]; (b) Impact load-displacement curve of sandwich composite with an initial velocity of 4.0 m s −1 [121]; (c) 2D CT scans and 3D renderings of PEG and STF filled panels subjected to high-velocity shock, (c1) PEG core, (c2) STF core [122]; (d) Dynamic stress and strain curves of hollow, waterfilled and STF-filled sandwich plates in pyramid lattice truss cores [123].