Viscoelastic Hysteresis Research Articles

High‐precision numerical simulation method for thermal–mechanical coupling in rubbers

AbstractImproving the precision of numerical simulations in thermal–mechanical coupling for amorphous polymer materials is crucial for their effective utilization. To enhance the precision of rubber numerical simulations, this study proposed a method considering the temperature and strain rate to establish tensile testing conditions based on the principle of time–temperature equivalence. Additionally, to obtain more precise parameters for hyperelastic constitutive equations, stress relaxation experiments were conducted to determine a set of stress values under complete rubber stress relaxation, which were used to fit the hyperelastic components of the hyper‐viscoelastic algorithm. A finite element model of rubber rebound was established, and a hyperelastic model based on loss factor and a hyperelastic model based on Prony series (hyper‐viscoelastic) were used to calculate the temperature changes caused by rubber rebound coefficient and energy dissipation during the rebound process at 110, 120, and 130°C. We compared the calculation results of these two algorithms with experimental data to verify their accuracy. The research results show that the average error of the rebound coefficient of the hyperelastic algorithm at three temperatures is 3.63%, and the average error of the rebound coefficient of the hyper‐viscoelastic algorithm at these three temperatures is 0.93%. The comparison with the rebound test results shows that the hyper‐viscoelastic method is more accurate and better captures the viscoelastic hysteresis of rubber, but the model calculation time is longer. In addition, at the moment of rebound sample impact, the maximum temperature rise amplitude of the hyperelastic algorithm sample impact position is 2.60, 1.75, and 0.91°C, which are 110, 120, and 130°C, respectively; The maximum heating amplitudes of the hyper‐viscoelastic algorithm are 2.05, 1.35, and 0.61°C. The hyper‐viscoelastic algorithm is closer to the actual test results.Highlights Applied the principle of time–temperature equivalence. Determination of material parameters using the hyper‐viscoelastic algorithm. Calculated the temperature change during the rubber rebound process.

Study on the dynamic evolution of friction and wear of polyurethane material for pipeline inspection gauge

The dynamic evolution in friction and wear can lead to interface failure and induce vibrations in pipeline inspection gauge. The friction behavior between polyurethane and X70 steel was evaluated with annular face contact under 0.042 to 0.07 MPa. The temperature increase was recorded using infrared cameras. Dynamic simulations of frictional heat and stress-strain were conducted using Abaqus software. The results indicate that in the initial stages, abrasive wear, stress (1.5 MPa), and frictional temperature rise (65 °C) of PU were observed in the inner-ring region at 0.056 MPa. The surface roughness (3.394 μm) of the PU became comparable to that of the steel ring (3.768 μm) due to abrasive wear. In the later stages, a higher frictional temperature (80 °C) and increased stress (3.8 MPa) were observed in the outer ring. Concurrently, Schallamach waves and ridge-like stripes indicative of stick-slip behavior emerged in the outer ring. The viscoelastic hysteresis effect is the fundamental cause of the dynamic evolution of the friction coefficient and wear. Frictional heat exacerbates the evolution of stick-slip behavior and increases fluctuations in the friction coefficient. The findings of this research can be utilized to analyze the causes of interface failure and vibration in pipeline inspection gauge.

Viscoelasticity and rheological hysteresis

Rheological characterization of complex fluids subjected to cyclic shear-rate sweep often exhibits hysteresis. Since both viscoelastic and thixotropic materials show hysteresis loops, it is important to understand distinguishing features (if any) in the same shown by either. Lately, there has been substantial work that attempts to relate the area enclosed by the hysteresis loop with the manner in which shear rate is varied in the cycle, in order to infer thixotropic parameters of a material. In this work, we use the nonlinear Giesekus model to study its response to the application of cyclic shear-rate sweep. We find that this model produces each type of qualitatively similar hysteresis loop that has hitherto been ascribed to thixotropic materials. We also show that the area of the hysteresis loop for a viscoelastic material as a function of sweep rate shows bell-shaped/bi-modal curves as has been observed for thixotropic materials. This study illustrates that caution needs to be exercised while attributing hysteresis loops and associated features observed in a material exclusively to thixotropy. Another feature related to the hysteresis loop is the occurrence of shear banding instability. We find that viscoelastic hysteresis may not have any connection to shear banding instability.

A new forecasting method for failure time of creep landslide based on nonlinear creep behavior and new pre-warning criterion

The forecast of failure time of unstable slope and the definition of early warning threshold are very important for preventing landslide disaster and reducing its losses. Based on the monitoring curve of unstable slope deformation varying with time, the mathematical models are used to accurately describe the nonlinear creep behavior in the initial creep stage and the unstable creep stage of unstable slope and a forecasting method for creep landslide is proposed. In addition, this study examines an improved tangential angle criterion obtained by a new forecasting method. The results show that the initial creep stage of unstable slope can not be neglected for forecasting the failure time. The initial creep velocity v0 and the viscoelastic hysteresis coefficientξof the slope are determined at initial creep stage, which together control the creep process of the unstable slope. Moreover, in the secondary creep stage, there is an inverse relationship between the velocity and the critical tangential angle. According to the average velocity of the secondary creep stage, the early warning criterion of the landslide tangential angle is proposed. Combined with the forecast parameters of the unstable slope, comparative analysis of the critical tangential angle warning criterion and an improved tangential angle criterion, the early warning and forecasting system of landslide with creep characteristic is established. This system is applied to the early warning and forecasting analysis of reported soil and rock landslides cases with creep characteristics. The forecasting effect and applicability of the new method are studied in order to make it a better supplement to the early warning strategy of landslide.

Fracture toughness determination of porcine muscle tissue based on AQLV model derived viscous dissipated energy

The ability of soft collagenous tissue (SCT) to withstand propagation of a defect in the presence of a macroscopic crack is termed the ’fracture toughness parameter’. In soft tissues not undergoing significant plastic deformation, it is purported that a considerable amount of additional energy is dissipated during failure processes, due to viscoelasticity. Hence the total work, measured experimentally during failure, is the sum of fracture and viscoelastic energies. Previous authors have aimed to apply constitutive modeling to describe viscoelastic hysteresis for fracture toughness determination with a tendency of models to either over or underestimate the viscous energy. In this study, the fracture toughness of porcine muscle tissue is determined using two strategies. Firstly, it was determined experimentally by calculation of the difference in dissipated energy of notched and unnotched tissue specimens undergoing cyclic ’triangular wave’ excitation with increasing strain levels in uniaxial tension. The second strategy involved the extension and use of the adaptive quasi-linear viscoelastic model (AQLV) to model cyclic loading (model parameters were obtained from a previous study) and sequentially the dissipated energy was calculated. The mean value of the dissipated energy based on the AQLV approach was then subtracted from the total dissipated energy of notched porcine muscle tissue samples to determine the fracture toughness. The mean experimental viscous dissipated energy ratio was 0.24 ± 0.04 in the experimental approach, compared to 0.28 ± 0.03 for the AQLV model. Fracture toughness determined experimentally yielded 0.84 ± 0.80 kJ/m2, and 0.71 ± 0.76 kJ/m2 for the AQLV model, without a significant difference (p = 0.87). Hence, the AQLV model enables a reasonable estimation of viscous dissipated energy in porcine muscle tissue with the advantage to perform tests only on notched specimens, instead of testing additional unnotched samples. Moreover, the AQLV model will help to better understand the constitutive viscoelastic behaviour of SCTs and might also serve as a basis for future fracture toughness determination with constitutive model simulations.

The dissipative dynamic performances of dielectric elastomer actuator with viscoelastic effects

With large deformability and high energy density, Dielectric elastomers (DEs) deserve interest in soft robotics. Many challenges remain in the real-world applications, for the dynamic performance of dielectric elastomer actuator and their energy efficiency are affected by the dissipation mechanisms in the actuators. Concerning the viscoelasticity of DEs, we present a modeling approach to describe the dissipation mechanism to predict how the dissipative process affects the dynamic behavior. The validity and generalization of the model have been extensively verified under various excitation voltages (different peak voltages, frequencies, pre-stretching, and signal waveforms). For harmonic voltages at different frequencies (0.05, 0.1, 0.2, 0.5, 1 Hz), the root mean square error is less than 5.99%. The phase difference was adopted to quantify the viscoelastic hysteresis dissipative behavior of DEs. The results show that the viscoelastic hysteresis is sensitive to frequency and waveform. In addition, we found that the viscoelastic hysteresis of the DEs under harmonic excitation can be improved by inserting a small amount of saw-tooth excitation loads. This finding is particularly useful for the actuation of soft actuators and soft robots, which use alternating loads as the dominant excitation signal. For future applications, this model presents a method to describe the dissipative behaviors in dynamic actuation quantitatively and paves the way to high-performance actuation control and manipulations for soft robots.

Role of blend phase ratio in controlling morphology, compressive, and recovery behavior of low‐density polyethylene/ethylene‐vinyl acetate foams

AbstractThis work presents a detailed study on the influence of blend phase ratio upon the morphology, crystallinity, mechanical and viscoelastic properties of cross‐linked foams based on blends of low‐density polyethylene (LDPE) and ethylene‐vinyl acetate copolymer (EVA). Non‐isothermal foaming is carried out via melt compression molding using dicumyl peroxide and azodicarbonamide as crosslinking and foaming agents, respectively. Rheo‐mechanical spectrometer characterization reveals faster crosslinking for EVA, leading to higher rate of melt viscosity increase for EVA‐rich blends during heating. This results in the formation of foams with higher cell density and gel content than LDPE‐rich foams. Compressive stress–strain behavior and viscoelastic hysteresis of the LDPE‐rich foams are governed by the degree of crystallinity and cell density, whereas for the EVA‐rich foams cell density and gel content are dominant. Increasing the crosslink density results in enhanced compressive behavior with excellent recovery of stress to 60% strain during four compression cycles.

Crooks Fluctuation Theorem for Single Polymer Dynamics in Time-Dependent Flows: Understanding Viscoelastic Hysteresis.

Nonequilibrium work relations have fundamentally advanced our understanding of molecular processes. In recent years, fluctuation theorems have been extensively applied to understand transitions between equilibrium steady-states, commonly described by simple control parameters such as molecular extension of a protein or polymer chain stretched by an external force in a quiescent fluid. Despite recent progress, far less is understood regarding the application of fluctuation theorems to processes involving nonequilibrium steady-states such as those described by polymer stretching dynamics in nonequilibrium fluid flows. In this work, we apply the Crooks fluctuation theorem to understand the nonequilibrium thermodynamics of dilute polymer solutions in flow. We directly determine the nonequilibrium free energy for single polymer molecules in flow using a combination of single molecule experiments and Brownian dynamics simulations. We further develop a time-dependent extensional flow protocol that allows for probing viscoelastic hysteresis over a wide range of flow strengths. Using this framework, we define quantities that uniquely characterize the coil-stretch transition for polymer chains in flow. Overall, generalized fluctuation theorems provide a powerful framework to understand polymer dynamics under far-from-equilibrium conditions.

Ascending aortic aneurysm haemodynamics are associated with aortic wall biomechanical properties.

The effect of aortic haemodynamics on arterial wall properties in ascending thoracic aortic aneurysms (ATAAs) is not well understood. We aim to delineate the relationship between shear forces along the aortic wall and loco-regional biomechanical properties associated with the risk of aortic dissection. Five patients with ATAA underwent preoperative magnetic resonance angiogram and four-dimensional magnetic resonance imaging. From these scans, haemodynamic models were constructed to estimate maximum wall shear stress (WSS), maximum time-averaged WSS, average oscillating shear index and average relative residence time. Fourteen resected aortic samples from these patients underwent bi-axial tensile testing to determine energy loss (ΔUL) and elastic modulus (E10) in the longitudinal (ΔULlong,E10long) and circumferential (ΔULcirc,E10circ)directions and the anisotropic index (AI)for each parameter. Nine resected aortic samples underwent peel testing to determine the delamination strength (Sd). Haemodynamic indices were then correlated to the biomechanical properties. A positive correlation was found between maximum WSS and ΔULlongrs=0.75,P=0.002 and AIΔUL (rs=0.68,P=0.01). Increasing maximum time-averaged WSS was found to be associated with increasing ΔULlong (rs=0.73,P=0.003) and AIΔUL (rs=0.62,P=0.02).Average oscillating shear index positively correlated with Sd (rs=0.73,P=0.04). No significant relationship was found between any haemodynamic index and E10, or between relative residence time and any biomechanical property. Shear forces at the wall of ATAAs are associated with local degradation of arterial wall viscoelastic hysteresis (ΔUL) and delamination strength, a surrogate for aortic dissection. Haemodynamic indices may provide insights into aortic wall integrity, ultimately leading to novel metrics for assessing risks associated with ATAAs.

Oscillating viscoelastic periodic contacts: A numerical approach

A new numerical Boundary Element methodology is developed to investigate viscoelastic periodic contacts under general kinematic conditions. The approach is based on an integral formulation, where periodicity is accounted for by introducing an ad hoc defined periodic Green’s function, and allows to study any motion law between viscoelastic bodies into contact. Results are shown for paradigmatic cases with a specific application interest and, specifically, for vertical, horizontal, and mixed oscillations. Outcomes in terms of pressure and displacement distributions, and, most crucially, of dissipated work provide key information and demonstrate the importance of taking into account viscoelasticity in the contact mechanics of soft materials. There are clear implications in all the engineering systems, where viscoelastic hysteresis is a variable to be controlled, including e.g. dampers, seals and pick-and-place devices.

Effect of modulation of interfacial properties on the tribological properties of viscoelastic epoxy resin damping coatings

The viscoelastic materials exhibit different tribological responses when compared to the stiff materials, due to the intermediate mechanical properties between viscous liquid and elastic solid. In this work, the effect of damping materials viscoelasticity on sliding friction under dry condition was investigated. However, it was difficult to change its damping properties only while other properties (strength or surface hardness) remain unchanged, since viscoelasticity was one of its intrinsic properties. Therefore, the attention of interactions between the material components was closely paid. To achieve this, the experimental groups of damping materials with various viscoelasticity were established by adding various fillers and adjusting their surface properties. Additionally, a viscoelastic property determined friction coefficient model was obtained and validated by the molecular dynamic method. The results show that the test model is in good agreement with the experimental results. Meanwhile, tribo-pairs with higher proportion of viscous character had greater oscillations in friction. They also exhibited higher friction coefficient due to the increased contribution of viscoelastic hysteresis losses to friction.

Predicting anisotropic crushable polymer foam behavior in sandwich structures

An anisotropic elastic-plastic, viscoelastic-damage model was developed to predict the multiaxial crushing behavior of polymer foams used in the core of sandwich structures. This model was based on pressure vessel experiments on Divinycell H100, whereby the post-yield response of the foam was characterized by anisotropic hardening during plastic flow, as well as damage and viscoelastic hysteresis. Post-yield properties from uniaxial compression/tension and simple shear material hysteresis experiments were used to develop three-dimensional material constitutive equations for the foam. Plastic flow was governed by the Tsai–Wu failure criterion, which was verified to accurately predict yielding of the foam in the triaxial pressure experiments. The solution methodology proved to be very effective in predicting the hysteresis response of the foam under triaxial compression, triaxial compression–tension, and triaxial compression–shear. Good agreement was found between theoretical predictions and experimental results.

Structural response of melt-spun poly(3-hydroxybutyrate) fibers to stress and temperature

We have investigated the structural response of melt-spun poly-3-hydroxybutyrate (P3HB) fibers to stress and temperature and its impact on the mechanical properties. Low-stress (≤1.6 MPa, 100–130 °C) annealed P3HB fibers showed a considerable viscoelastic behavior and remained ductile up to at least two months. Stress annealing with high weights (≥32 MPa), however, lead to fibers with a higher tensile strength (182 MPa) and with a lower elongation at break (22%). These significant differences in the tensile properties are closely related to structural changes, which we have studied with in-situ wide-angle x-ray diffraction (WAXD) and small-angle x-ray scattering (SAXS) experiments. A highly oriented non-crystalline mesophase (Pnc), which is located in-between orthorhombic α-crystals is growing during high-stress annealing but disappears during low-stress annealing. However, it is possible to restore the mesophase by post-drawing. The viscoelastic hysteresis behavior of low-stress annealed fibers is explained by a reversible transformation of α-crystals into mesophase and back.

Characterization and modeling of viscoelastic hysteresis in a dielectric elastomer actuator

This paper presents characterization and modeling for viscoelastic hysteresis exhibited by dielectric elastomer actuator (DEAs). Firstly, output–input characteristics in terms of hysteresis, asymmetry and output nonlinearity are quantitatively described by proposed indicators. Their variations with the excitation frequency are investigated, revealing significant asymmetric property and strong frequency-dependence. Next, the Hammerstein model with a cascaded structure is proposed for viscoelastic hysteresis description. A modified Prandtl–Ishlinskii model, representing the static nonlinear element, is employed to characterize the asymmetric property of static hysteresis, while a finite-impulse-response based adaptive filter as the linear part captures the dynamic effect. The hysteresis loops of DEAs under the input voltages with different frequencies, waveforms and amplitudes are experimentally measured and compared with those predicted results. The relative error in terms of root-mean-square value ranges from 1.92% to a maximum of 5.53% over a wide frequency range of 0.1–10 Hz, demonstrating the effectiveness of the proposed model of rate-dependent hysteresis in DEAs. This work can be useful to promote the applications of DEAs to soft robotics and haptics.

Crushable multiaxial behavior of sandwich foam cores: Pressure vessel experiments

The objective of this study was to characterize the multiaxial, elastic-plastic and hysteresis behavior of Divinycell PVC H100 foam using a novel pressure vessel experiment. Cyclic, elastic and post-yield behavior of the foam under uniaxial compression and tension, shear, biaxial compression and shear, triaxial compression, triaxial compression-tension and triaxial compression and shear were obtained in both out-of-plane and in-plane directions of the foam. In all the above-mentioned modes, the foam exhibited elastic-plastic response followed by damage and viscoelastic hysteresis. The Tsai–Wu failure criterion was found to be superior in predicting yielding under triaxial stress states among all the anisotropic yield criteria considered. Based on the experimental results, an elastic-plastic, viscoelastic damage model was developed and used to obtain transversely isotropic, plastic strain hardening behavior as well as viscoelastic and damage properties associated with post-yield hysteresis.

Viscoelastic tribopairs in dry and lubricated sliding friction.

Soft contacts present different tribological responses compared to stiff materials, especially when soft materials exhibit viscoelastic behaviour, as viscoelastic materials have intermediate mechanical properties between viscous liquids and elastic solids. In this work, we investigated the influence of viscoelasticity of soft materials on sliding friction in dry and lubricated conditions. To achieve this, soft tribopairs with varying viscoelasticity were obtained by tuning the weight ratios of polydimethylsiloxane (PDMS) base and curing agent. The real-time friction force and preload were observed over multiple conditions, with systematic control of lubricant viscosity, preload, and sliding velocity. Tribopairs with a higher proportion of viscous character had more oscilliations in the friction force. They also presented a higher friction coefficient due to the increased contribution of viscoelastic hysteresis losses on friction. Through regression analysis, the models of the friction coefficient were found, which are in good agreement with experimental results. From the models, we found that in both dry and lubricated conditions, viscoelasticity of tribopairs, indicated as the loss modulus or loss tangent, plays a key role in determining the friction coefficient. This influence is particularly significant for dry contacts due to the direct interactions between surfaces of tribopairs. This study provides empirical proof and a focused analysis on the role of viscoelasticity in tribological contacts.

Feedforward Control of the Rate-Dependent Viscoelastic Hysteresis Nonlinearity in Dielectric Elastomer Actuators

Dielectric elastomer actuators have shown promising applications in the field of soft robotics. However, due to their rate-dependent viscoelastic hysteresis nonlinearity, it is still challenging to achieve precision tracking control of dielectric elastomer actuators. In this letter, we propose a feedforward control approach that can compensate for the rate-dependent viscoelastic hysteresis nonlinearity with maximum tracking errors of 6.18% and root-mean-square errors of 2.96% when the frequency of the input voltage is between 0.05 Hz and 1.5 Hz. Our control approach consists of two feedforward compensators: 1) for the ease of the hysteresis compensation, a creep compensator is firstly developed to remove the viscoelastic creep nonlinearity; 2) based on a phenomenological mathematical model, an inverse hysteresis compensator is then developed to compensate for the rate-dependent viscoelastic hysteresis nonlinearity. Experimental results of tracking various periodic trajectories demonstrate that: the maximum tracking errors are reduced by 87.17% and the root-mean-square errors are decreased by 89.53%, by comparing the results without the viscoelastic compensation. It is the first time to successfully compensate for both the viscoelastic creep nonlinearity and rate-dependent hysteresis nonlinearity of dielectric elastomer actuators by a feedforward control approach, which may pave the way for further applications in dielectric-elastomer-actuators based soft robotics.

High-Precision Tracking Control of a Soft Dielectric Elastomer Actuator With Inverse Viscoelastic Hysteresis Compensation

In this paper, we present a new control approach for high-precision tracking control of a soft dielectric elastomer actuator (DEA) with inverse viscoelastic hysteresis compensation. To this end, we first investigate the viscoelastic response of the DEA and divide it into transition region and stable region. Then, the viscoelastic response is characterized by creep and hysteresis effects according to the different features of the two regions. Finally, a two-level tracking control approach is developed as follows: a direct inverse hysteresis compensation controller with a phenomenological hysteresis model is designed for the viscoelastic hysteresis description and compensation, and a conventional proportional-integral feedback controller is combined to compensate for the model uncertainty and creep effect. To verify the effectiveness of the developed tracking control approach, several experiments are conducted with various reference sinusoidal trajectories. Experimental results show that: when the frequency of the trajectory is within the range of 0.1 to 1 Hz, the maximum tracking error and the root-mean-square error decrease from 40.63% to 3.95% and 28.38% to 1.86%, respectively. This paper is the first attempt to achieve high-precision tracking control of soft DEAs by combining a phenomenological-model feedforward compensator and a feedback control law for the viscoelastic compensation, which may accelerate the practical applications of DEAs to soft robots.

Fatigue Damage Analysis of an Asphalt Mixture Based on Pseudostiffness

The fatigue damage characteristics of an asphalt mixture were analyzed, a new fatigue damage model was constructed based on the Schapery pseudovariable theory and continuum damage mechanics. According to the Schapery theory and the generalized elastic-viscoelastic correspondence principle, the experimental stress–strain curves of the asphalt mixture are transformed into the stress vs. pseudostrain curves. The relation between stress and pseudostrain is shown to be linear, which eliminates the viscoelastic hysteresis effect of the asphalt mixture and its time dependence. Pseudostiffness decreases gradually with the number of fatigue cycles. The damage variable is defined by the change in pseudostiffness. The parameters of the fatigue damage model are verified by fatigue tests up to 1000 cycles, and the fatigue damage for 2000 cycles is predicted and compared with the test results, which are in good agreement between themselves.

Investigation of dynamic heat generation and transfer behavior and energy dissipation for nonlinear synchronous belt transmission

Study on energy dissipation and temperature distribution of synchronous belt transmission is of great importance in industrial engineering field, which is highly related to transmission efficiency estimation, thermal fatigue life prediction, and product design. However, the complex behaviors of viscoelastic hysteresis and meshing friction make it much more difficult to investigate heat generation and transfer mechanism of synchronous belt than other products. To accurately predict temperature and energy dissipation, a thermo-mechanical coupling model was developed through combining experiment and finite element analysis method, in which material nonlinearity of rubber hyper-viscoelasticity, and contact nonlinearity of meshing interference were comprehensively considered. Meanwhile, the friction heat flux partition coefficient and convective heat transfer coefficient were theoretically computed and corrected. As a result, the temperature distribution, hysteresis and friction energy dissipation of synchronous belt could be computed accurately, the transmission efficiency was estimated as well. The simulation temperatures of various operating conditions were confirmed by testing results. The presented methodology can completely predict energy dissipation and temperature distribution of synchronous belt transmission, which has far-reaching consequences in the engineering application filed.