Viscoelastic Deformation Research Articles

Friction in soft biological systems and surface self-organization: the role of viscoelasticity

AbstractFriction is a critical factor in the proper functioning of human organs as well as in the potential development of disease. It is also important for the design of diagnostic and interventional medical devices. Nanoscale surface roughness, viscoelastic or plastic deformations, wear, and lubrication all influence the functions of individual cells. The effects of friction in soft matter systems are quantified using different types of frictional coefficients, including the dynamic friction coefficient, friction-skin drag, and pressure drag. These coefficients are determined by the viscoelastic properties of the two systems in contact and their relative velocity. In this review, several biological systems are considered, including (i) epithelial tissues in contact with soft hydrogel-like implants, (ii) the collective migration of epithelial monolayers on substrate matrices, (iii) blood flow through blood vessels, and (iv) the movement of cancer cells past epithelial clusters along with the migration of epithelial cells within the cluster.

A PROBLEM IN FRACTIONAL ORDER THERMO-VISCOELASTICITY THEORY FOR A POLYMER MICRO-ROD WITH AND WITHOUT ENERGY DISSIPATION

A new study has been developed that considers the size-dependent interaction between viscoelastic deformation and thermal fields, incorporating the fractional heat conduction law with and without energy dissipation. The model is used for a particular one-dimensional problem involving a polymer micro-rod of arbitrary length experiencing three different types of thermal loading without the presence of any heat source. The study uses Laplace transforms and numerical inversion to examine how fractional order, nonlocal elasticity, and nonlocal thermal conduction impact thermal dispersion and thermo-viscoelastic response. Comparative numbers demonstrate the effects of various parameters. Findings demonstrate that nonlocal thermal and viscoelastic characteristics have a significant impact on all recorded field values, offering possible suggestions for the creation and assessment of thermal-mechanical attributes in nanoscale devices.

Interseismic Locking of the Xiaojiang Fault May Be Controlled by Pore Fluid Pressure

AbstractAlthough fault locking state has been widely acquired with space geodetic observations, the mechanisms controlling fault locking are poorly known. Here, we infer the locking state of the Xiaojiang fault with a viscoelastic deformation model and integrated GNSS data, based on which we probe the mechanism that may control the locking pattern of the fault. Our results reveal four highly locked asperities along the Xiaojiang fault, which are separated by weak locking zones. Relying on the inferred locking degree and spring water temperature along the fault, we construct a model to connect the fault hydraulic conductivity with the cooling process of upwelling water. Model results suggest that high spring water temperature correlates with high hydraulic conductivity. Further, we use an experimental law to infer that the obtained high hydraulic conductivity may associate with high pore fluid pressure, which in turn weakens the fault frictional strength and leads to weak locking.

Rutting and fatigue behavior of neat and nanomodified asphalt mixture with SiO2 and TiO2

Modern asphalt technology has adopted nanomaterials as an alternative option to assert that asphalt pavement can survive harsh climates and repeated heavy axle loading during service life and prolong pavement life. This work aims to elucidate the behavior of the modified asphalt mixture fracture model and assess the fatigue and Rutting performance of Hot Mix Asphalt (HMA) mixes using the outcomes of indirect Tensile Strength (IDT), Semicircular bend (SCB) and rutting resistance; for this, a single PG (64−16) nanomodified asphalt binder with 5 % SiO2 and TiO2 have been investigated through a series of laboratory tests, including: Resilient modulus, Creep compliance, and tensile strength, SCB, and Flow Number (FN) to study their potential role of these nanomaterials to improve the rutting characteristics and fatigue life of wearing asphalt mixture at different temperatures. The outcome of this study revealed the positive role of these materials in enhancing mixture IDT characteristics, fracture energy, and viscoelastic deformation component of crack propagation; on the other hand, at higher temperatures, the modified mixture exhibited a superior performance in reducing the permanent deformation of asphalt mixture with SiO2 followed by TiO2 as compared to neat asphalt mixture.

Comparison of active and passive vibration control techniques for electric drive power electronic subsystem: Experimental validation

Reducing vibration and noise from power electronics components is vital for enhancing the performance and acceptance of electric vehicles, emphasizing the need for effective mitigation strategies in sustainable transportation. This paper compares passive and active vibration techniques, with a specific focus on utilizing particle damping for passive vibration control. The method achieves vibration reduction through viscoelastic deformation and friction resulting from the movement and collisions of granular material within the cavity. This contribution outlines diverse design strategies for integrating particle dampers into power electronic components. The active control approach, operating typically in the 50 Hz to 1200 Hz frequency range, can concurrently support passive noise treatments. Piezoelectric ceramics serve as both actuators and sensors in active noise reduction. Following the identification of dominant mode shapes, appropriate actuator and sensor positions are chosen. The control problem of the smart system is then addressed, opting for a velocity feedback control algorithm in a real collocated design. This algorithm computes input signals for actuators bonded to the outer surface, achieving significant active damping effects. Lab-tested techniques are validated in real-world conditions with a full-scale electric-drive toolkit, affirming their efficacy in reducing vibration and noise and underscoring their potential for implementation in electric vehicles.

A theoretical framework for multi-physics modeling of poro-visco-hyperelasticity-induced time-dependent fracture of blood clots

Fracture resistance of blood clots plays a crucial role in physiological hemostasis and pathological thromboembolism. Although recent experimental and computational studies uncovered the poro-viscoelastic property of blood clots and its connection to the time-dependent deformation behavior, the effect of these physical processes on clot fracture and the underlying fracture mechanisms are not well understood. This work aims to formulate a thermodynamically consistent, multi-physics theoretical framework for describing the time-dependent deformation and fracture of blood clots. This theory concurrently couples fluid transport through porous fibrin networks, non-linear visco-hyperelastic deformation of the solid skeleton, solid-fluid interactions, mechanical degradation of tissues, gradient enhancement of energy, and protein unfolding of fibrin molecules. The constitutive relations of tissue constituents and the governing equation of fluid transport are derived within the framework of porous media theory by extending non-linear continuum thermodynamics at large strains. A physics-based, compressible network model is developed for the fibrin network of blood clots to describe its mechanical response. The kinetic equations of the internal variables, introduced for describing the non-linear viscoelastic deformation, non-local damage driving force and protein unfolding, are formulated according to the thermodynamics principles by incorporating a non-equilibrium energy of fibrin networks, a gradient-enhanced energy, and a stretch-induced energy of fibrin molecules, respectively, into the total free energy density function. An energy-based damage model is developed to predict the damage and fracture of blood clots, and an evolving regularization parameter is proposed to limit the damage zone bandwidth. The proposed model is implemented into finite element code by writing subroutines and is experimentally validated using single-edge cracked clot specimens with different constituents. The fracture of blood clots subject to different loading conditions is simulated, and the mechanisms of clot fracture are systematically analyzed. Computational results show that this model can accurately capture the experimentally measured deformation and fracture. The viscoelasticity and fluid transport play essential roles in the fracture of blood clots under physiological loading.

A perspective on the time‐dependent structure and properties of amorphous polymer

AbstractA molecular mechanism of viscoelastic deformation is presented. Amorphous polymers are characterized as a heterogeneous network of nanoscale cells. A “cell” is a homogeneous region within the network. Each cell phase fluctuates between the glassy and elastomer states with a period τ. The values of τ vary from cell to cell over several orders of magnitude and are strong functions of temperature. Whether a given cell responds as glassy or elastomeric depends on the ratio between its period of phase fluctuation (τj) and the period of observation (1/f), where f is the test frequency. We express this ratio, the Deborah number, as (τj × f), and present equations for modulus and energy loss as functions of (τj × f). The condition (τj × f) = 1 defines the glass transition of a cell, which arises cell‐by‐cell over a range of temperature, or over a range of time under stress. Viscoelastic deformation occurs if a cell changes phase while under stress. Energy stored during glassy state deformation is lost if the cell fluctuates to the elastomeric state. Stress is out of phase with strain, because strain rate controls the level of stress in glassy cells between phase fluctuations.Highlights A molecular mechanism of viscoelasticity is presented that does not involve viscous flow. Amorphous polymer is a heterogeneous network of nanoscale cells. Cells fluctuate in phase between glassy and elastomeric states due to their size. Time‐dependent properties are caused by time‐dependent structure. Energy is lost when glass phase cells under stress fluctuate to the elastomer phase.

A new thermo-optical system with a fractional Caputo operator for a rotating spherical semiconductor medium immersed in a magnetic field

PurposeUnderstanding the mechanical and thermal behavior of materials is the goal of the branch of study known as fractional thermoelasticity, which blends fractional calculus with thermoelasticity. It accounts for the fact that heat transfer and deformation are non-local processes that depend on long-term memory. The sphere is free of external stresses and rotates around one of its radial axes at a constant rate. The coupled system equations are solved using the Laplace transform. The outcomes showed that the viscoelastic deformation and thermal stresses increased with the value of the fractional order coefficients.Design/methodology/approachThe results obtained are considered good because they indicate that the approach or model under examination shows robust performance and produces accurate or reliable results that are consistent with the corresponding literature.FindingsThis study introduces a proposed viscoelastic photoelastic heat transfer model based on the Moore-Gibson-Thompson framework, accompanied by the incorporation of a new fractional derivative operator. In deriving this model, the recently proposed Caputo proportional fractional derivative was considered. This work also sheds light on how thermoelastic materials transfer light energy and how plasmas interact with viscoelasticity. The derived model was used to consider the behavior of a solid semiconductor sphere immersed in a magnetic field and subjected to a sudden change in temperature.Originality/valueThis study introduces a proposed viscoelastic photoelastic heat transfer model based on the Moore-Gibson-Thompson framework, accompanied by the incorporation of a new fractional derivative operator. In deriving this model, the recently proposed Caputo proportional fractional derivative was considered. This work also sheds light on how thermoelastic materials transfer light energy and how plasmas interact with viscoelasticity. The derived model was used to consider the behavior of a solid semiconductor sphere immersed in a magnetic field and subjected to a sudden change in temperature.

Three-dimensional numerical simulations and experimental studies on the viscoelastic rheological and deformation behavior of polymer catheter in gas-assisted extrusion processing

Gas-assisted extrusion is an effective method for improving the deformation behavior of polymer catheters during extrusion. However, the underlying mechanisms that dictate how geometrical and constitutive models influence the complex rheological behavior of the melt are not yet fully understood, which hinders further utilization and optimization. In this study, the three-dimensional (3D) gas–liquid–gas model for catheter gas-assisted extrusion was constructed. Subsequently, the Bird–Carreau model and the Phan–Thien–Tanner (PTT) model were employed in finite element numerical simulations to analyze the complex behavior. For comparative analysis, simplified two-dimensional (2D) model numerical simulations were also conducted. Additionally, experiments on catheter gas-assisted extrusion and parameterization studies of key constitutive model parameters were performed. The findings indicate that the 3D model, when integrated with the PTT constitutive model, demonstrates superior predictability and aligns more closely with experimental results. Furthermore, as the flow rate increases, discrepancies among different models diminish, and the distance required for the melt and gas to achieve motion equilibrium decreases. The internal mechanisms behind these phenomena are elucidated through the analysis of velocity and stress field distributions. This research enhances our understanding of the complex rheological behavior in polymer catheter gas-assisted extrusion, providing valuable insights for both academic research and industrial production in this field.

The effects of spinal flexion exposure on lumbar muscle shear modulus and posture.

Spinal flexion exposure (SFE) leads to alterations in neuromuscular and mechanical properties of the trunk. While several studies reported changes in intrinsic trunk stiffness following SFE, there is a lack of studies evaluating the effects on lumbar muscle shear modulus (SM). Therefore, the aim of our study was to investigate the effects of SFE on lumbar muscle SM and posture. Sixteen young volunteers were included in this clinical study. Passive lumbar muscle SM, lumbar lordosis, lumbar flexion range of motion and sitting height were measured prior to and following a 60-min SFE protocol. For SM, our results did not show a significant muscle × time interaction effect (p = 0.40). However, we found increased SM (from 6.75 to 15.43%-all p < 0.02) and maximal lumbar flexion (15.91 ± 10.88%; p < 0.01), whereas lumbar lordosis ( - 7.67 ± 13.97%; p = 0.03) and sitting height ( - 0.57 ± 0.32%; p < 0.01) decreased following SFE. Our results showed no significant correlations between the changes in the included outcome measures (p = 0.10-0.83). We hypothesized that increased lumbar muscle SM following SFE might be a compensation for decreased passive stability due to viscoelastic deformations of connective tissues, which are indicated by increased maximal lumbar flexion and decreased sitting height. However, there were no significant correlations between the changes of the included outcome measures, which implies that increased muscle SM and reduced lumbar lordosis are more likely an independent consequence of SFE.

Phase field modeling of fracture mechanics for ion-exchanged glass considering large viscoelastic deformation, mechanic–electrochemical coupling

A phase field model is proposed to investigate the fracture mechanics of ion-exchanged glass, which involves significant viscoelastic deformation and stress-diffusion interaction. Based on this theoretical model, the fracture behavior of both double-sided and single-sided ion exchange processes was studied. The results indicate that, compared to single-sided ion exchange, the double-sided process is more likely to induce crack initiation and propagation, ultimately resulting in a notable reduction in glass strength. For both cases, increasing the glass thickness and interfacial energy density will significantly improve the fracture resistance of the glass. Notably, when the glass thickness or interfacial energy density is large enough, the crack can be completely closed, ensuring the integrity of the glass during the ion exchange process. Furthermore, the study conducted a preliminary investigation of two industrially relevant conditions: edging and impurities. The impacts of edging parameters, glass interfacial energy density, and covering radius on glass stress evolution, mechanical deformation, crack initiation, and crack propagation during chemical strengthening were summarized. These findings offer valuable theoretical support and a reference for optimizing chemical strengthening process parameters and enhancing the strength of glass products.

Vertical Crustal Deformation Due To Viscoelastic Earthquake Cycles at Subduction Zones: Implications for Nankai and Cascadia

AbstractDespite significant progress in studying subduction earthquake cycles, the vertical deformation is still not well understood. Here, we use a generic viscoelastic earthquake‐cycle model that has recently been validated by horizontal observations to explore the dynamics of vertical earthquake‐cycle deformation. Conditioned on two dimensionless parameters (i.e., the ratio of earthquake recurrence interval T to mantle Maxwell relaxation time tM (T/tM) and the ratio of downdip seismogenic depth D to elastic upper‐plate thickness Hc (D/Hc)), the modeled viscoelastic deformation exhibits significant spatiotemporal deviations from the simple time‐independent elastic solution. Caution thus should be exercised in interpreting fault kinematics with vertical observations if ignoring Earth's viscoelasticity. By systematically exploring these two parameters, we further investigate three metrics that characterize the predicted vertical deformation: the coastal pivot line (CPL), the uplift zone (UZ) landward above the downdip seismogenic extent, and the secondary subsidence zone (SSZ) in the back‐arc region. We find that these metrics can all be time‐dependent, subject to D/Hc and T/tM. The CPL location and the UZ width are mainly controlled by D/Hc and T/tM, respectively. The presence of the SSZ is prevalent during the interseismic phase due to viscous mantle flow driven by ongoing plate convergence. Contemporary vertical deformation in Nankai and Cascadia is largely consistent with the model predictions and features differences mainly related to contrasting D/Hc values in the two margins. These findings suggest that vertical crustal deformation bears fruitful information about subduction‐zone dynamics and is potentially useful for inversions of key subduction‐zone parameters, deserving properly designed monitoring.

Creep behavior of epoxy adhesives subjected to different hygrothermal aging conditions—nanoindentation creep tests and theoretical study

Epoxy adhesives have been extensively used in the aerospace, marine, and automotive industries to join different components. A major concern with the use of epoxy adhesives is their viscoelastic behavior in aggressive service conditions such as hygrothermal ageing. Surveying the creep behavior of adhesives is of paramount importance to increase long-term durability. In this work, nanoindentation creep tests were performed on an epoxy adhesive exposed to distilled water and seawater at 55 °C for various ageing durations (0, 14, 38, 160, 251, 383, 582, and 800 h). The hardness, modulus, creep displacement, and creep rate sensitivity were quantitatively investigated to elucidate the effect of hygrothermal ageing. All the mechanical properties were found to decrease with the ageing time. The adhesive subjected to distilled water showed lower creep resistance due to higher absorption of moisture. In addition, linear relationships were observed between different mechanical properties and moisture contents irrespective of ageing conditions. Subsequently, the generalized Kelvin model was applied to investigate the creep compliance and the dependence of different deformation types (elastic, viscoelastic, and viscous deformation) on the ageing time and ageing conditions. The motion of molecular structures was also discussed. Finally, a modified creep model was proposed based on the generalized Kelvin model and continuum damage theories, which established the relationship between the dry and aged adhesive via the moisture-dependent degradation factors. The predicted creep displacements coincided well with the experimental results for the case, demonstrating the reliability of the creep model.

Detectability of low-viscosity zone along lithosphere–asthenosphere boundary beneath the Nankai Trough, Japan, based on high-fidelity viscoelastic simulation

After the 2011 Tohoku-oki earthquake, a seafloor observation system observed rapid landward deformation. These seafloor observation data are potentially explicable via modeling of a low-viscosity zone under the subducting plate, called the lithosphere–asthenosphere boundary (LAB). However, the effect of a low-viscosity LAB has not been empirically examined in past earthquakes because of the absence of seafloor observation data, which are expected to have high sensitivity in the detection of a low-viscosity LAB. The Nankai Trough, southwest Japan, is one location where seafloor geodetic stations are in operation that could detect a low-viscosity LAB after a future earthquake. Therefore, we quantitatively model how the low-viscosity of the LAB is expected to affect postseismic crustal deformation following an anticipated future large earthquake under the Nankai Trough. Calculating viscoelastic deformation using a model that takes into account the realistic crustal structure in the southwestern Japanese Archipelago, we examine the effects of LAB viscosity on surface deformation patterns. The results show for very low LAB viscosities (2.5×1017\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2.5 \ imes 10^{17}$$\\end{document} Pa s), rapid landward displacement as large as 38 cm/yr occurs in the offshore area, with uplift and subsidence patterns highly dependent on the viscosity structure. Especially in the first year after the earthquake, the difference in deformation between the cases with and without a low-viscosity LAB was much larger than the observational error level of the current seafloor observation system. For such low LAB viscosities, the probability of detection is therefore high. On the other hand, for moderately low LAB viscosities (2.5×1018\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2.5 \ imes 10^{18}$$\\end{document} Pa s), the deformation patterns in the cases with and without a low-viscosity LAB are similar. Indeed, the difference in displacement lies within the observational error level of the current observational network, so detection is expected to be difficult for a LAB of only moderately low-viscosity. However, such a LAB may be detected by improving observational accuracy in the Global Navigation Satellite System–acoustic observation technique by performing more frequent measurements. Additional detection potential lies in expected future accuracy improvements in vertical displacement estimates at the DONET stations.Graphical

A new effective phenomenological constitutive model for semi‐crystalline and amorphous polymers

AbstractA new phenomenological constitutive model is proposed for the prediction of the tensile and compressive behavior of semi‐crystalline and amorphous polymers. The new model modifies the phenomenological model previously proposed by Zhou and Mallick (ZM model) to correctly predict the complex behavior of thermoplastic materials including the linear viscoelastic deformation, the non‐linear viscoelastic deformation, the yielding, the post‐yield strain softening and the post‐yield strain hardening. A validation activity based on literature data has been carried out for polyether‐ether‐ketone (PEEK) and polycarbonate (PC) materials. The new model proved effective in fitting with high accuracy all the phases of the flow stress behavior for the considered materials, across a wide range of strain rates and temperature conditions. Finally, the comparison with Zhu et al., Duan et al., Nasraoui et al., Mulliken‐Boyce and Zhou‐Mallick models showed the better fitting performance of the proposed phenomenological model.Highlights Formulation of a new phenomenological model. Validation on mechanical test of semi‐crystalline and amorphous thermoplastics. Comparison with different phenomenological models present in the literature. Superior prediction results achieved compared to previously developed models.

Exploring the tidal responses of ocean worlds with PyALMA3

Observations of the tidal response of celestial bodies quantified by the Love numbers are highly relevant in planetary geophysical investigations because they provide unique insight into the interior structures. For example, the high sensitivity of tidal deformations to the properties of the oceans detected beneath the icy surfaces of some moons is of paramount importance for investigations of their habitability. We present here PyALMA3, a software framework developed in Python devoted to the computation of planetary Love numbers. PyALMA3 is based on ALMA3, a previous version developed in Fortran. Conversion to Python significantly improves the accessibility and portability of the software. We tested PyALMA3 by applying it to the exploration of the tidal responses of Europa and the other Galilean moons. We show that accurate modeling of effects such as the viscoelastic deformations of ice and the water density gradient in the ocean (variations of 2–3% on the real part of k2) will be important in the context of geophysical investigations that will be conducted by future missions targeting icy moons, such as Europa Clipper and JUICE.

Modeling of viscoelastic deformation and rate-dependent fracture damage in rat bone

Bone is a complex hierarchical structural material whose organ-level response is highly influenced by its constitutive behavior at the microstructural level, which can dictate the inelastic nonlinear deformation and fracture within the organ. In the current study, a combined experimental-computational approach was sought to first obtain the local constitutive properties. Later, a multiscale modeling framework utilizing a novel rate-dependent nonlinear viscoelastic cohesive zone (NVCZ) model was used to explore the fracture behavior at the microstructure of the bone and its influence on the global scale (organ-level) response. Toward this end, nanoindentation testing was conducted within the cross-section of a rat femur bone specimen. An inverse optimization process was used to identify the isotropic linear viscoelastic (LVE) properties of cortical bone by integrating the test results with a finite element model simulation of the nanoindentation testing. Model results using different numbers of spring-dashpot units in the generalized Maxwell model showed that four spring-dashpot units are sufficient to capture the LVE behavior, while solely LVE constitutive relation is limited to fully characterize the rat femur. The LVE constitutive properties were then used along with the rate-dependent NVCZ fracture within the representative volume element (RVE), which was two-way coupled to the global scale bone. A parametric study was conducted by varying the fracture properties of the NVCZ model. The model demonstrated the capability and features to represent inelastic deformation and nonlinear fracture that are linked between length scales. This further implies that the inelastic fracture model and the two-way coupled modeling can elucidate the complex multiscale deformation and fracture of bone, while model validation and further advancements with test results remain a follow-up study and are currently in progress.

The earthquake probabilities of the Liupanshan fault zone based on the Coulomb stress and friction constitutive law

As the forefront of the northeastern margin of the Tibetan Plateau, the Liupanshan area is subjected to significant Cenozoic deformation. Considering the background of historical earthquakes and the current seismic activity, the Liupanshan fault poses a risk of strong earthquakes. This paper analyzes the evolution of Coulomb stress induced by the coseismic and postseismic viscoelastic deformation of six historical strong earthquakes that occurred around the Liupanshan area since the twentieth century. Additionally, based on the disturbance in Coulomb stress and the background seismicity rate, the probability of earthquake occurrence is quantitatively evaluated using the frictional constitutive law. The results indicate that northern section of the Liupanshan fault has higher earthquake potential than the southern section, warranting close attention. These findings serve as a reference for medium- and long-term earthquake forecast and risk assessment in the vicinity of the Liupanshan fault.

Nonlinear dynamic meshing force analysis of PEEK-based polymer composite involute spline coupling system

The dynamic meshing force affects the stability and wear life of PEEK polymer composite involute spline couplings, but most of the dynamic meshing force is obtained by empirical formula, and there is no effective calculation method in practice. Aiming at the viscoelasticity and nonlinear behavior of PEEK material, this work established a nonlinear dynamic model of the drive system of PEEK-based polymer composite involute spline pair by using the concentrated mass method, taking into account time-varying meshing stiffness, tooth side gap, and comprehensive transmission error, and obtained a dimensionless dynamic matrix that eliminates rigid body displacement. Aiming at the thermal stability of PEEK material, the dynamic meshing stiffness and dynamic meshing force of the involute spline of PEEK-based polymer composite were calculated by considering the thermal effect of misalignment and meshing deformation. The influence of misalignment on the dynamic characteristics of the system under dynamic and static loads was studied. The results show that the dynamic meshing stiffness and dynamic meshing force of involute spline coupling of PEEK-based polymer composite materials under misalignment represent complex nonlinear characteristics; Vibration, load, and viscoelastic deformation have an impact on transmission accuracy and efficiency; And the optimal selection range for friction coefficient, Poisson's ratio, and Young's modulus were determined within the parameter range of involute spline coupling of PEEK-based polymer composite materials as the matrix. It provides a theoretical foundation for designing high-performance, high-precision, and highly reliable PEEK-based polymer composite components.

Surface loading on a self-gravitating, linear viscoelastic Earth: moving beyond Maxwell

SUMMARY Constitutive laws are a necessary ingredient in calculations of glacial isostatic adjustment (GIA) or other surface loading problems (e.g. loading by ocean tides). An idealized constitutive law governed by the Maxwell viscoelastic model is widely used but increasing attention is being directed towards more intricate constitutive laws that, in particular, include transient rheology. In this context, transient rheology collectively refers to dissipative mechanisms activated in addition to creep modelled by the Maxwell viscoelastic model. Consideration of such viscoelastic models in GIA is in its infancy and to encourage their wider use, we present constitutive laws for several experimentally derived transient rheologies and outline a flexible method in which to incorporate them into geophysical problems, such as the viscoelastic deformation of the Earth induced by surface loading. To further motivate this need, we demonstrate, via the Love number collocation method, how predictions of crustal displacement depart significantly between Earth models that adopt only Maxwell viscoelasticity and those with transient rheology. Throughout this paper, we highlight the differences in terminology and emphases between the rock mechanics, seismology and GIA communities, which have perhaps contributed towards the relative scarcity in integrating this broader and more realistic class of constitutive laws within GIA. We focus on transient rheology since the associated deformation has been demonstrated to operate on timescales that range from hours to decades. With ice mass loss enhanced at similar timescales as a consequence of anthropogenically caused climate change, the ability to model GIA with more accurate constitutive laws is an important tool to investigate such problems.