Viscoelastic Deformation Research Articles

Effects of UHMWPE viscoelasticity on the squeeze‐film lubrication of hip replacements

AbstractMany studies have been performed to analyse the lubrication of artificial joints since the pioneer work by the late Professor Duncan Dowson. However, the viscoelastic deformation of one of the most widely used bearing materials, ultra‐high‐molecular‐weight polyethylene (UHMWPE), has only been considered recently. The described study attempted to investigate the effect of UHMWPE viscoelasticity on the elastohydrodynamic lubrication of such a soft artificial hip replacement under squeeze‐film motion. A transient viscoelastic squeeze‐film lubrication model of a typical hip implant was developed and solved to obtain the film thickness and pressure distributions. A boundary film thickness was adopted to consider the direct and indirect lubricant contact conditions. The results showed that the viscoelasticity had marked effects on the squeeze‐film lubrication performance of UHMWPE artificial hip joints. The minimum film thickness in the viscoelastic model was smaller than that of the elastic model, causing an earlier direct contact. However, the film thickness within the central contact region in the viscoelastic model was greater than that of the elastic model due to the restricted flow of the lubricant, therefore enhancing the lubricating effect and particularly with a short relaxation time and mechanical loss factor.

Experimental and modeling investigation on the viscoelastic-viscoplastic deformation of polyamide 12 printed by Multi Jet Fusion

The viscoelastic-viscoplastic deformation of Multi Jet Fusion-printed polyamide 12 (MJF PA12) was investigated with experimental and numerical approaches. Multi-loading–unloading–recovery tests were conducted to distinguish between the viscoelastic and viscoplastic deformations. The influence of the void defects on deformation of PA12 was investigated through the micro-computed tomography (μCT) and field emission scanning electron microscope. A finite-strain viscoelastic-viscoplastic constitutive model based on the logarithmic stress rate for the matrix of MJF PA12 was developed within the thermodynamic framework as well as an introduction of the accumulated plastic deformation–induced damage into the proposed model. A representative volume element was modeled based on the μCT results of MJF PA12. The simulated results, such as stress–strain and strain–time curves, agreed with the experimental results. Moreover, the model revealed the mechanism that the low tensile ductility of MJF PA12 is caused by the increase in strain localization and narrowing of the shear band.

In-situ measurement of mechanical properties and dimensional changes of preceramic thermosets during their pyrolysis conversion to ceramics using thermomechanical analysis

The study deals with the thermomechanical analysis of the pyrolysis process of four structurally different types of cross-linked preceramic polymers: methylsiloxane, methyl-phenyl-siloxane, hydrosilylation cured methyl-phenyl-siloxane and phenol-formaldehyde resins. During the transformation of polymer to ceramics by pyrolysis, the investigated polymeric materials undergo significant softening and subsequent hardening, which are accompanied by considerable dimensional changes, but crosslinking of the thermoset microstructure greatly limits stress relaxation by plastic deformation. The parallel action of these processes leads to a high risk of cracking at certain temperatures, which is the biggest problem of preceramic polymer technology. To analyse these processes in detail an in-situ thermomechanical experiment using cyclic indentation method was chosen, where a flat-ended cylinder was used as an indenter. To characterize the rheological behaviour development during pyrolysis, a cyclic loading with a trapezoidal pulse with a period of 120 s was applied. Due to the risk of cracking, the experiments were performed at very low applied loads and heating rates. These experiments made it possible to obtain simultaneous temperature characteristics of elastic, viscoelastic and residual deformations as well as overall pyrolysis shrinkage. The acquired results thus provide a comprehensive insight into the gradual changes in mechanical behaviour and volume changes during the thermal transformation of thermosets. A model of the thermomechanical and rheological response on the indentation during pyrolysis was developed to analyse deeply obtained TMA data.

Three-dimensional modeling of pendulum waves propagation under dynamic loading of underground excavation surface

The propagation of surface pendulum waves under nonstationary loading on the free surface of a cavity located in a block half-space is studied numerically. A mathematical model of transient viscoelastic deformation of the block medium is proposed. This model is based on the idea that dynamic behavior of the block medium can be approximately described as the movement of rigid blocks due to the compliance of interlayers between them. To describe the viscoelastic behavior of the interlayers, an internal friction model is used with the merit factor of the material as the determining parameter. The medium is modeled by a three-dimensional lattice of masses connected by elastic springs and viscous dampers in axial and diagonal directions. The influence of the merit factor and the cavity depth on the amplitudes of block velocities on the surface of the half-space is investigated for the longitudinal and Rayleigh waves.

Effect of Viscoelastic Deformation for CA Mortar on Mechanical Responses of Track Structures

The viscoelastic deformation of cement emulsified asphalt mortar (CA mortar) can lead to gaps between the mortar and track slab, thereby adversely affecting the mechanical capability and deformation behavior of the track structures. According to the time hardening rate method, a solid model of the China Railway Track System I (CRTS-I) slab track was established to study the viscoelastic characteristics of mortar. What’s more, this paper also analyzed the influence of viscoelastic deformation of mortar on the mechanical responses of track structures. The results obtained indicate that the viscoelastic deformation of CA mortar under train loading occurs mainly in the area from the track slab end to the third fastener, which is about 1.5 m long. Its viscoelastic deformation can reach nearly 0.6 mm. The maximum mortar stresses under passenger train and freight train loads with considering the viscoelastic deformation of mortar 0.6 mm, are 0.382 MPa and 0.566 MPa, respectively, which are both 2 to 3 times greater than those under normal conditions (without CA mortar failure, namely none vertical deformation of mortar). Besides, the vertical accelerations of rail and track slab are also significantly larger than those under normal conditions when the viscoelastic deformation of CA mortar is taken into account. And these values under the freight train load are greater than those under the passenger train load. Therefore, we suggest that future research should take the adverse impact of viscoelastic deformation of CA mortar into account when studying the mechanical responses of track structures. Furthermore, for the shared passenger and freight railway lines, the passage of freight trains should be strictly controlled.

A Nonlinear Fractional Viscoelastic-Plastic Creep Model of Asphalt Mixture.

The mechanical behavior of asphalt mixture under high stresses presents nonlinear viscoelasticity and permanent deformation. In this paper, a nonlinear fractional viscoelastic plastic (NFVEP) creep model for asphalt mixture is proposed based on the Nishihara model, with a Koeller spring-pot replacing the Newton dashpot. The NFVEP model considers the instantaneous elasticity, viscoelasticity with damage and time-hardening viscoplasticity with damage concurrently, and the viscoelastic response is modeled by fractional derivative viscoelasticity. To verify the model, uniaxial compressive creep tests under various stresses ranging from 0.4 MPa to 0.8 MPa were carried out at room temperature. The NFVEP model predictions are in good agreement with the experiments. The comparison with the modified Nishihara model and the Burgers model reveals the advantages of the NFVEP model. The results show that the NFVEP model, with the same set of parameters, can not only describe the primary and steady-state creep stages of asphalt mixture under low stress levels but also the whole creep process, including the tertiary creep stage, of asphalt mixture under high stress levels.

Reaction synthesis of gradient coatings by annealing of three-layer Ti–Ni–Ti nanolaminate magnetron sputtered on the TiNi substrate

In this work, Ti-Ni-Ti nanolaminate was deposited on a TiNi substrate by magnetron sputtering. Subsequent synthesis in Ar at temperatures of 500, 700 and 900 °C was carried out. To investigate the effect of the reaction synthesis temperature for obtaining a dense thin intermetallic biofunctional coating, a comparative analysis of the morphology, structure, phase composition, mechanical properties and wettability of the coatings was carried out. It was found that crystallization processes have a different impact on the amorphous Ti and Ni layers depending on temperature. In all cases, multilayer gradient crystalline coatings were formed that bound to the substrate by the diffusion zone. The reaction synthesis temperatures of 500 and 700 °C are insufficient for reaction completion and complete transformation; therefore, the obtained thin loose layers are unstable under stresses caused by the substrate. Reaction synthesis in Ti – Ni – Ti nanolaminate at 900 °С formed a dense two-layer gradient coating 2 µm thick, which reliably protects the matrix from further diffusion of interstitial impurities and segregation of Ni atoms onto the surface. An analysis of the nano-indentation deformation diagrams showed that the coatings do not prevent the viscoelastic deformation of the TiNi substrate.

Time-space characteristics of viscoelastic post-seismic deformations corresponding to different rheology models

On a long time (> 1 a) scale, the viscoelastic properties of mantle media significantly affect post-seismic deformation. The stress field disturbance in viscoelastic medium caused by fault slip gradually relax, and the relaxation process and its temporal-spatial characteristics are determined by the viscoelastic model. In this paper, we assume that the mantle media are types of common linear rheological models, i.e., the Burgers body, the standard linear solid, and the Maxell body, and we calculate the dislocation Love number and Green function for a spherically symmetric, non-rotating, viscoelastic, and isotropic (SNRVEI) Earth model. The characteristics of the post-seismic relaxation deformations corresponding to the different models are compared. Our results show that for a short time period, the Burgers body and standard linear solid are similar; while for the long time period, the Burgers body and Maxwell body are similar. This suggests that the observations of post-seismic deformation on the surface have a great potential for the inversion of underground viscoelastic structures. However, the potential of using surface displacement to distinguish different rheological models is limited when the observation period is not long enough.

Seismic Moment Accumulation Response to Lateral Crustal Variations of the San Andreas Fault System

AbstractRheologic variations in the Earth's crust (like elastic plate thickness [EPT] or crustal rigidity) modulate the rate at which seismic moment accumulates for potentially hazardous faults of the San Andreas Fault System (SAFS). To quantify rates of seismic moment accumulation, Global Navigation Satellite Systems, and Interferometric Synthetic Aperture Radar data were used to constrain surface deformation rates of a four‐dimensional viscoelastic deformation model that incorporates rheological variations spanning a 900 km section of the SAFS. Lateral variations in EPT, estimated from surface heat flow and seismic depth to the lithosphere‐asthenosphere boundary, were converted to lateral variations in rigidity and then used to solve for seismic moment accumulation rates on 32 fault segments. We find a cluster of elevated seismic moment rates (11–20 × 1015 Nm year−1 km−1) along the main SAFS trace spanning the historical Mw 7.9 1857 Fort Tejon earthquake rupture length; present‐day seismic moment magnitude on these segments ranges from Mw 7.2–7.6. We also find that the average plate thickness in the Salton Trough is reduced to only 60% of the regional average, which results in a ∼60% decrease in moment accumulation rate along the Imperial fault. Likewise, a 30% increase of average plate thickness results in at least a ∼30% increase in moment rate and even larger increases are identified in regions of complex plate heterogeneity. These results emphasize the importance of considering rheological variations when estimating seismic hazard, suggesting that meaningful changes in seismic moment accumulation are revealed when considering spatial variations in crustal rheology.

Macroscopic viscoelastic deformation at room temperature in mechanically rejuvenated Zr-based metallic glass

By employing mechanical rejuvenation, we demonstrated that the viscoelastic deformation become visible in macroscopic tensile test. The clear tensile strain rate dependence of yield stress was observed only in the rejuvenated sample, showing that the macroscopic elongation is governed by the thermally activated process. Activation volumes estimated from the mechanical responses during the macroscopic tensile test and microscopic nanoindentation test showed consistent values. The rejuvenated sample having tensile ductility showed larger STZ volume comparing with the relaxed samples. These results indicate that the fraction and connectivity of liquid-like regions in BMG can be controlled by appropriate use of mechanical rejuvenation.

Generalised viscoelastic fibre at small strain

A straight elastic fibre is usually perceived as a one-dimensional structural component, and its similarity with a cylindrical rod makes its concept analogous, if not equivalent with the concept of an elastic spring. This analogy enables this communication to match the one-dimensional response of a relevant viscoelastic fibre with that of a viscoelastic spring and, hence, to describe its one-dimensional behaviour in the light of a new, generalised viscoelastic spring model. The model shares simultaneously properties of an elastic spring and an inelastic damper (dashpot) and this communication is interested on its applicability at small strain only. However, the form of its constitutive equation, which is based on the combined action of an internal energy function and a viscous flow potential, is non-linear as well as differential and, also, implicit in the stress. The model enables a posteriori determination of (i) the manner that the elastic and the inelastic parts of the fibre strain are assembled and form the observed total deformation, (ii) the part of stress that creates recoverable work and the part of stress wasted in energy dissipation, and (iii) the amount of work stored in the material as well as the amount of energy dissipation during the fibre deformation. A detailed analysis is presented for the case that small-strain, steady viscoelastic deformation takes place in a spatially homogeneous manner. This includes a complete relevant solution of the problem of interest and is accompanied by an adequate set of corresponding qualitative numerical results.

Mechanical and viscoelastic properties of wrinkled graphene reinforced polymer nanocomposites – Effect of interlayer sliding within graphene sheets

Multilayer graphene sheets (MLGSs) are promising nano-reinforcements that can effectively enhance the mechanical properties of polymer matrices. Despite many studies on MLGSs-reinforced polymer nanocomposites, the effect of wrinkles formed in MLGSs on the reinforcement effect and the viscoelastic properties of polymer nanocomposites has remained largely unknown. In this study, building upon previously developed coarse-grained models of MLGSs and poly(methyl methacrylate) coupled with molecular dynamics simulations, we have systematically investigated nanocomposites with different numbers of graphene layers and various wrinkle configurations. We find that with decreasing degree of waviness and increasing numbers of layers, the elastic modulus of the nanocomposites increases. Interestingly, we observe a sudden stress drop during shear deformation of certain wrinkled MLGSs-reinforced nanocomposites. We further conduct small amplitude oscillatory shear simulations on these nanocomposites and find that the nanocomposites with these specific wrinkle configurations also show peculiarly large loss tangents, indicating an increasing capability of energy dissipation. These behaviors are attributed to the activation of the interlayer sliding among these wrinkled MLGSs, as their interlayer shear strengths are indeed lower than flat MLGSs measured by steered molecular dynamics technique. Our study demonstrates that the viscoelastic properties and deformation mechanisms of polymer nanocomposites can be tuned through MLGS wrinkle engineering.

Viscoelastic properties of the human A2 finger pulley.

Biomechanical evaluation of the viscoelastic properties tissue deformation, stiffness, and maximum breaking load of the human A2 pulley. We hypothesized that the A2 pulleys of index, middle, and ring fingers exhibit no difference regarding the aforementioned biomechanical parameters. Forty-one A2 pulleys of 14 upper extremities (8 body donors) were assessed. Cyclic and load-to-failure testing were performed. The biomechanical parameters tissue deformation during cyclic and load-to-failure testing, stiffness, and maximum breaking load were determined. No significant differences between the fingers could be detected regarding the biomechanical parameters. A significant negative correlation could be detected between stiffness and deformation of the pulley. Significant positive correlations could be identified between stiffness and maximum breaking load and between maximum breaking load and deformation of the pulleys. Assessment of the viscoelastic properties of the A2 finger pulley promotes precise diagnosis of pulley lesions and will help to optimize treatment.

A porohyperviscoelastic model for the shear wave elastography of the liver

Shear wave elastography (SWE) enables the probing of the mechanical properties of soft tissues in vivo and has been demonstrated to be a promising technique for the diagnosis of diseases such as staging liver fibrosis, evaluating artery stiffening, and detecting cancers. In this study, a porohyperviscoelastic model is presented to address the shear wave elastography of soft tissues with emphasis on the liver. Based on this constitutive model, an analytical solution has been derived to reveal the dependence of the wave velocity on the constitutive parameters and deformation of the solid matrix generated by the internal pressure. The model and solution not only help understand the dispersion of the shear waves in porohyperviscoelastic soft tissues such as the liver, but also reveal that both the hyperelastic and viscoelastic deformation behaviors of the solid matrix may play an important role in the pronounced effect of the internal pressure on the shear wave velocity, as observed in experiments. The analysis results are expected to advance our understanding of SWE and facilitate its use in clinics.

Phase‐field modeling of rate‐dependent fluid‐driven fracture initiation and propagation

AbstractThe rate‐dependent behavior associated with deformation and fracturing of materials, such as natural rocks, poses significant challenges for modeling. In addition to the complications of the viscoelastic response, the speed of fracture propagation reflects micromechanical mechanisms in the fracture process zone (FPZ). In order to represent these complicated behaviors, a thermodynamically consistent, rate‐dependent fracture model is required. Based on rigorous thermodynamic principles, we derive a rate‐dependent phase‐field mechanical model coupled with single‐phase fluid flow in both the matrix and the fracture. The model is guaranteed to satisfy energy conservation during fracture propagation. The system of equations is solved using the introduced solution procedure and a novel preconditioner that accounts for the complex fluid–structure interaction. The proposed phase‐field model is tested against several benchmark problems on solid‐fluid coupling, fluid‐driven fracture propagation and rate‐dependent viscoelastic deformation. The model serves as a strong basis for investigating rate‐dependent fracturing experiments and for making predictions of material behaviors under new conditions.

Elongation deformation of a red blood cell under shear flow as stretch testing

The elongation of a tank-treading red blood cell (RBC) under shear flow was numerically simulated to understand its mechanical characteristics. The boundary element method was used to couple the viscoelastic deformation of the cell membrane and viscous flow of the surrounding fluids. Accordingly, it was found that elongation deformation and inclination angle, which depend on the cell membrane's viscoelasticity, inner viscosity, and swelling ratio, were related to the fluid traction difference between the suspending and RBC inner fluids. When the viscosity of an RBC is compatible with the suspending fluid, the elongation index responding fluid shear stress is similar to the responding external loads in the optical tweezers stretch, with different elongation mechanics. By identifying the viscoelasticity of the cell membrane to reproduce published experimental data, the strain hardening elasticity of the cell membrane was identified by modifying the model developed by Skalak et al. (1973); the exponential form of Fung (1973) successfully expressed the stronger strain hardening behavior for the latter deformation regime. These results indicate the applicability of the shear flow experiments as a stretch testing method to measure the viscoelasticity of the cell membrane.

Postseismic geodetic signature of cold forearc mantle in subduction zones

A sharp thermal contrast between the cold forearc and the hot arc and backarc is considered fundamental to various subduction-zone processes. However, direct observational evidence for this contrast is rather limited. If this contrast is present, it must cause a rheological contrast in the mantle wedge: elastic in the forearc and viscoelastic in the arc and backarc for the timescale of earthquake cycles. Here we demonstrate that postseismic deformation following large subduction earthquakes provides independent evidence for the thermally controlled rheological contrast. Specifically, we show that seaward postseismic motion is deflected upward at the edge of the cold forearc mantle wedge, causing diagnostic uplift just seaward of the volcanic arc. From numerical simulations of postseismic deformation following the 2011 moment magnitude (Mw) 9 Tohoku-oki, 2010 Mw 8.8 Maule, 2007 Mw 8.4 Bengkulu and 1960 Mw 9.5 Chile earthquakes, together with a global synthesis of postseismic uplift measurements, we find that cold forearc mantle is present irrespective of the diversity in tectonic settings. Our findings also indicate that field surveys eight years after the 1960 Chile earthquake provided some of the earliest evidence for viscoelastic postseismic deformation. We suggest that the established link between long-term thermal processes and short-term earthquake cycle deformation is important to understanding subduction-zone dynamics. Deformation after large subduction earthquakes reflects the thermal contrast between the mantle wedge and its nose, according to numerical simulations and a synthesis of postseismic uplift data from subduction zones.

Discrimination of adhesion and viscoelasticity from nanoscale maps of polymer surfaces using bimodal atomic force microscopy.

The simultaneous excitation and measurement of two eigenmodes in bimodal atomic force microscopy (AFM) during sub-micron scale surface imaging augments the number of observables at each pixel of the image compared to the normal tapping mode. However, a comprehensive connection between the bimodal AFM observables and the surface adhesive and viscoelastic properties of polymer samples remains elusive. To address this gap, we first propose an algorithm that systematically accommodates surface forces and linearly viscoelastic three-dimensional deformation computed via Attard's model into the bimodal AFM framework. The proposed algorithm simultaneously satisfies the amplitude reduction formulas for both resonant eigenmodes and enables the rigorous prediction and interpretation of bimodal AFM observables with a first-principles approach. We used the proposed algorithm to predict the dependence of bimodal AFM observables on local adhesion and standard linear solid (SLS) constitutive parameters as well as operating conditions. Secondly, we present an inverse method to quantitatively predict the local adhesion and SLS viscoelastic parameters from bimodal AFM data acquired on a heterogeneous sample. We demonstrate the method experimentally using bimodal AFM on polystyrene-low density polyethylene (PS-LDPE) polymer blend. This inverse method enables the quantitative discrimination of adhesion and viscoelastic properties from bimodal AFM maps of such samples and opens the door for advanced computational interaction models to be used to quantify local nanomechanical properties of adhesive, viscoelastic materials using bimodal AFM.

Mathematical Model of Rheological Behavior of Wood Plate Taking Into Account the Zone of Evaporation of Moisture

The subject of this paper is a mathematical model of heat-transfer in the process which takes place in capillary-porous materials during drying. The moving boundaries of phase transitions for media are also considering. The analytical-numerical method was developed for mathematical model. The difference schemes were constructed with consideration for the boundaries of the evaporation zone of heat exchange with the environment in the presence of a phase transition in the conditions. The numerical realization and software were developed for solving the Stefan problem. The fractal structures of the medium were taking into account for synthesization of mathematical models of viscoelastic deformation. Functional dependences of the temperature field and the motion of the phase transition boundary in media, depending on the value of fractional parameters, were received for modelling different technological processes of drying capillary-porous materials.

Finite Element Study of Mixed Fracture: Velocity-Dependent Insertion Of Pointed Blades Into Soft Material

This study concerns the effect of applied velocity on the energy state and stress state related to the puncture-cutting of soft material. A finite element modeling (FEM) of combined puncture and cutting of neoprene rubber by a pointed blade was established at 17 velocities (from 10[Formula: see text]mm/min to 1500[Formula: see text]mm/min). The proposed FEM takes into consideration, the nonlinear material behavior of the elastomeric substrate. First, puncture-cutting tests are conducted and the evolution of puncture-cutting force with increased velocity is investigated. Second, the commonly used puncture-cutting energy criterion, including the fracture toughness of material and the friction energy occurring between the material and the pointed blade, are summarized and analyzed. Finally, an analysis of the stress state in the fracture process zone is proposed. Results show that the puncture-cutting force increases significantly with increasing insertion velocity. A low velocity of the pointed blade is dominated by a uniaxial tension with a constant energy, while a medium velocity causes a dominant biaxial tension with increasing energy, which may be the source of the viscoelastic deformation involved around the crack tip. However, an increase of the velocity increases the shear stress up to a maximum value and, therefore, shows a toughening of material.