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Background: Modifying the mechanical properties of the solid phase of a porous material, in this study calcium-silicate-hydrate, is frequently possible by changing synthesis conditions, but changes in these conditions can also influence porosity, which in turn may affect the mechanical properties of the porous material. Experimental methods to decouple porosity from the viscoelastic properties of the porous material will aid in optimization of the structure of the solid phase to achieve the desired mechanical properties. Objective: Explore different nanoindentation techniques in order to determine the viscoelastic properties of the solid phase (without the affect of porosity) of a stiff porous material via experimental methods alone. Methods: Compacted pellets of calcium-silicate-hydrate were prepared with different porosity and subjected to three nanoindentation techniques to determine viscoelastic behavior and the influence of porosity: dynamic, stress relaxation, and creep. Results of the porosity and of the viscoelastic behavior measurements were analyzed with a reverse-micromechanics model to determine viscoelastic properties of the solid phase, which has not been achieved previously for calcium-silicate-hydrate. These methods can be used in development and refinement of materials to determine how changes in the solid phase (e.g. molecular structure) influence viscoelastic behavior while considering the effect of porosity. Results: Dynamic nanoindentation was found to be unreliable for the stiff material studied in this work. Normalized stress relaxation and creep data were found to be independent of porosity. Reverse micro-mechanics modeling allowed for characterization of the creep modulus that is consistent with other studies that used computational or synchrotron x-ray methods to characterize mechanical properties of the solid calcium-silicate-hydrate phase. Conclusion: Creep experiments provide more reliable data than dynamic or stress relaxation experiments. When the porosity is known, reverse-micromechanics modeling can be used determine the creep modulus of the solid phase and thus be used to predict creep modulus of a composite with an arbitrary porosity. If the porosity is not known, the viscoelastic properties of the solid phase can still be compared to each other using a normalized creep modulus that is independent of porosity. [ABSTRACT FROM AUTHOR]

Mechanical stress governs the dynamics of viscoelastic polymer systems and supercooled glass-forming fluids. It was recently established that liquids with long terminal relaxation times are characterized by transiently frozen stress fields, which, moreover, exhibit long-range correlations contributing to the dynamically heterogeneous nature of such systems. Recent studies show that stress correlations and relaxation elastic moduli are intimately related in isotropic viscoelastic systems. However, the origin of these relations (involving spatially resolved material relaxation functions) is non-trivial: some relations are based on the fluctuation-dissipation theorem (FDT), while others involve approximations. Generalizing our recent results on 2D systems, we here rigorously derive three exact FDT relations (already established in our recent investigations and, partially, in classical studies) between spatio-temporal stress correlations and generalized relaxation moduli, and a couple of new exact relations. We also derive several new approximate relations valid in the hydrodynamic regime, taking into account the effects of thermal conductivity and composition fluctuations for arbitrary space dimension. One approximate relation was heuristically obtained in our previous studies and verified using our extended simulation data on two-dimensional (2D) glass-forming systems. As a result, we provide the means to obtain, in any spatial dimension, all stress-correlation functions in terms of relaxation moduli and vice versa. The new approximate relations are tested using simulation data on 2D systems of polydisperse Lennard–Jones particles. [ABSTRACT FROM AUTHOR]

At present, structural analysis of polymer composite materials is a highly relevant issue. The complexity of taking into account the viscoelastic stress–strain dependence and the time-dependent distribution of stress–strain state parameters over the volume occupied by a solid is a limiting factor. The relevance and demand for new efficient methods of mathematical modeling of creep and relaxation processes in viscoelastic structures are obvious. The aim of this work is to verify and validate the method for solving boundary value problems of a linear viscoelastic solid. The proposed approach is based on the formulation of the generalized principle of correspondence between elastic and viscoelastic problems, according to which a viscoelastic solution can be obtained by replacing elastic constants by some time functions, which are hereinafter called time-effective moduli. The results derived from the theoretical validation and the solution of several problems suggest that the proposed method can be used for solving problems on the stress–strain state of viscoelastic structures. [ABSTRACT FROM AUTHOR]

In this study, the viscoelastic properties of porcine kidney in the upper, middle and lower poles were investigated using oscillatory shear tests. The viscoelastic properties were extracted in the form of the storage modulus and loss modulus in the frequency and time domain. Measurements were taken as a function of frequency from 0.1 Hz to 6.5 Hz at a shear strain amplitude of 0.01 and as function of strain amplitude from 0.001 to 0.1 at a frequency of 1 Hz. Measurements were also taken in the time domain in response to a step shear strain. Both the frequency and time domain data were fitted to a conventional Standard Linear Solid (SLS) model and a semi-fractional Kelvin–Voigt (SFKV) model with a comparable number of parameters. The SFKV model fitted the frequency and time domain data with a correlation coefficient of 0.99. Although the SLS model well fitted the time domain data and the storage modulus data in the frequency domain, it was not able to capture the variation in loss modulus with frequency with a correlation coefficient of 0.53. A five parameter Maxwell–Wiechert model was able to capture the frequency dependence in storage modulus and loss modulus better than the SLS model with a correlation of 0.85. [ABSTRACT FROM AUTHOR]

This paper analyzes the effect of crosslinking reactions on a thermoset polymer's viscoelastic properties. In particular, a numerical model to predict the evolution of epoxy's mechanical properties during the curing process is proposed and implemented in an Ansys APDL environment. A linear viscoelastic behavior is assumed, and the scaling of viscoelastic properties in terms of the temperature and degree of conversion is modeled using a modified version of the TNM (Tool–Narayanaswamy–Mohynian) model. The effects of the degree of conversion and structural relaxation on epoxy's relaxation times are simultaneously examined for the first time. This formulation is based on the thermo-rheological and chemo-rheological simplicities hypothesis and can predict the evolution of epoxy's relaxation phenomena. The thermal–kinetic reactions of curing are implemented in a homemade routine written in APDL language, and the structural module of Ansys is used to predict the polymer's creep and stress relaxation curves at different temperatures and degrees of conversion. [ABSTRACT FROM AUTHOR]

The viscoelasticity of mechanically sensitive tissues such as periodontal ligaments (PDLs) is key in maintaining mechanical homeostasis. Unfortunately, PDLs easily lose viscoelasticity (e.g., stress relaxation) during periodontitis or dental trauma, which disrupt cell–extracellular matrix (ECM) interactions and accelerates tissue damage. Here, Pluronic F127 diacrylate (F127DA) hydrogels with PDL‐matched stress relaxation rates and high elastic moduli are developed. The hydrogel viscoelasticity is modulated without chemical cross‐linking by controlling precursor concentrations. Under cytomechanical loading, F127DA hydrogels with fast relaxation rates significantly improved the fibrogenic differentiation potential of PDL stem cells (PDLSCs), while cells cultured on F127DA hydrogels with various stress relaxation rates exhibited similar fibrogenic differentiation potentials with limited cell spreading and traction forces under static conditions. Mechanically, faster‐relaxing F127DA hydrogels leveraged cytomechanical loading to activate PDLSC mechanotransduction by upregulating integrin–focal adhesion kinase pathway and thus cytoskeletal rearrangement, reinforcing cell–ECM interactions. In vivo experiments confirm that faster‐relaxing F127DA hydrogels significantly promoted PDL repair and reduced abnormal healing (e.g., root resorption and ankyloses) in delayed replantation of avulsed teeth. This study firstly investigated how matrix nonlinear viscoelasticity influences the fibrogenesis of PDLSCs under mechanical stimuli, and it reveals the underlying mechanobiology, which suggests novel strategies for PDL regeneration. [ABSTRACT FROM AUTHOR]

Developing a viscoelastic model for the cyclic thermomechanical loading of thermosetting polymers is the main goal of this study. The model includes memory for residual thermal stresses and can consider stress accumulation across many loading cycles. By considering stress accumulation, we can improve predictions and understand how thermosetting polymers' stress–strain state changes under cyclic thermomechanical loading. This approach was validated through experimental verification to ensure its applicability in practical engineering scenarios. The experiment showed that the thermosetting polymer can accumulate stress during cycles of heating and mechanical loading during use. The results of the modeling and experiment are compared. The results have led to corrections in the way this model is applied to thermosetting polymers like the epoxy resin in this study. The corrected results matched well with the experimental measurements of stress under cyclic thermomechanical load, with a difference of only 1 to 6%. [ABSTRACT FROM AUTHOR]

We propose an anisotropic and nonlinear generalization of the Kelvin–Voigt viscoelastic model obtained considering the additive splitting of the Cauchy stress tensor in an elastic and a dissipative part. The former one corresponds to a fiber-reinforced hyperelastic material while the dissipative effect is described by the most general linear transverse-isotropic tensorial function of symmetric part of the velocity gradient. In a such a way we characterize the dissipative contribution via three viscoelastic moduli. We then show, by a detailed analysis of the simple shear quasistatic motion and the corresponding creep phenomena, that this motion may be used to determine experimentally the viscoelastic parameters. [ABSTRACT FROM AUTHOR]

Understanding the time-dependent mechanical behavior of tough and viscoelastic hydrogels under complex external loading is crucial. In this study, we utilized tough and viscoelastic hydrogels synthesized through the copolymerization of methacrylic acid and methacrylamide as a model system to investigate their mechanical behavior under multiaxial stretching across a wide range of strain rates. Three stretching modes examined were uniaxial, pure shear, and equal biaxial stretching. Our findings show that under equal biaxial stretching, the hydrogels exhibit higher mechanical properties and energy dissipation compared to uniaxial and pure shear stretching, owing to the greater contribution of hydrogen bonds to energy dissipation in the former stretching mode. Additionally, employing the time-elongation separability method during the stretching process, we observed that the relaxation of dynamic hydrogen bonds in the hydrogels only depends on stretching time, independent of the elongation ratio and stretching modes. We anticipate that this study will yield valuable contributions to the design of durable load-bearing soft materials, particularly in dealing with complex deformation and strain rate responses. [ABSTRACT FROM AUTHOR]

• The variable-order fractional viscoelastic models are developed considering three typical viscoelastic behaviors. • The linear form of the order function is chosen to reflect the evolution of mechanical properties in materials. • The sensitivity of the viscoelastic behaviors to the parameters in the order function is analyzed in detail. In variable-order fractional calculus, the order is allowed to be in a functional form, which provides a novel way to describe the time-dependent physical processes. In this work, the performance of variable-order fractional viscoelastic models to the order function parameters is comprehensively investigated. Firstly, the variable-order fractional constitutive model is deduced from the theory of constant-order fractional viscoelasticity. The effect of order function is studied which shows that the linear order function can effectively describe the viscoelastic properties. Then the variable-order fractional viscoelastic models are developed considering three kinds of viscoelastic behaviors, including stress-strain relationship, creep, and stress relaxation. The sensitivity of the viscoelastic behaviors to the parameters in the linear order function is analyzed in detail. Finally, the effectiveness of the proposed models is validated by comparing them to the existing experimental data of typical viscoelastic behaviors, and the laws of the order function for each case are discussed based on the fractional viscoelastic theories. It is proved that the variable-order fractional models can give an accurate description of the viscoelastic behaviors under various loading conditions, and the change of the fractional order can visualize the evolution of the mechanical properties of the material. [ABSTRACT FROM AUTHOR]

This study constructs a model to represent the strain–stress field surrounding a splay fault and demonstrates the accumulation processes of both strain and stress around the splay fault. We consider the case of multiple fault dislocations, construct the model as a function of the effective viscosity in the media, and investigate the influence of the effective viscosity on the strain and stress accumulation patterns. The results show that the strain and stress tend to accumulate in the splay fault and the subducting oceanic crust, and the rate of accumulation varies with the effective viscosity. The accumulation and relaxation of strain and stress are simultaneous, and the slower the effective viscosity, the slower the accumulation rate. We discuss the relationship between the splay faults, fluid, and intraslab earthquakes. Finally, the possibility that effective viscosity may contribute to the mode of occurrence of intraslab earthquakes at the Hikurangi subduction margin is discussed. Plain Language Summary: We construct a simple model to explain the evolution of strain and stress over time in a subduction margin. The model constructed in this study is the case where a fault branches from a plate boundary. We investigate the influence of the effective viscosity of its constituents on the temporal evolution of strain and stress. The results show that the rate of strain and stress accumulation varies with the effective viscosity. Our result may suggests the influence of the effective viscosity on the source distribution of the microearthquakes observed at the Hikurangi subduction margin. Key Points: Temporal evolution of strain and stress caused by the dislocation of tri‐materials with different effective viscosities is calculatedStrain and stress accumulation rate depends on the effective viscosityStrain and stress accumulated at the multiple fault edge strongly influence the stress perturbations in the subducting oceanic crust [ABSTRACT FROM AUTHOR]

In recent years, there has been a growing interest in changes in dynamic mechanical properties of mixed rubber during dynamic shear, yet the influence of vulcanized characteristics on the dynamic shear behavior of vulcanized rubber, particularly the effect of cross-linking density, has received little attention. This study focuses on styrene–butadiene rubber (SBR) and aims to investigate the impact of different cross-linking densities (Dc) on dynamic shear behavior using molecular dynamics (MD) simulations. The results reveal a remarkable Payne effect, where the storage modulus experiences a significant drop when the strain amplitude (γ0) exceeds 0.1, which can be attributed to the fracture of the polymer bond and the decrease in the molecular chain's flexibility. The influence of various Dc values mainly resides at the level of molecular aggregation in the system, where higher Dc values impede molecular chain motion and lead to an increase in the storage modulus of SBR. The MD simulation results are verified through comparisons with existing literature. [ABSTRACT FROM AUTHOR]

Purpose: Abnormal iris mechanical properties have been considered to be an important cause of pupillary-block and angle-closure glaucoma. In this research, viscoelasticity, anisotropy and location-dependence of mechanical properties of rabbit iris were investigated using uniaxial tensile test. Methods: Iris strips were taken along three directions: inner-circumferential direction (ICD), outer-circumferential direction (OCD) and radial direction (RD), respectively. Quasi-static tensile tests and stress-relaxation tests were applied on the iris strips. Then, the stress-stretch data was fitted with third order Ogden model; the stress-relaxation data was fitted with the third order Prony series model. Through comparing the tangent modulus and relaxation limit of the strips from different directions and locations, the viscoelasticity, anisotropy and location-dependence of mechanical properties of rabbit iris were explored. Results: The tangent moduli of iris at the stretch of 1.05 along ICD, OCD, and RD were 3.2 ± 1.4 kPa, 4.2 ± 2.6 kPa, 1.5 ± 0.8 kPa, respectively. Iris strips in ICD and OCD were found to have almost the same stress-relaxation behavior, and both relaxed slower than iris strips in RD. Conclusions: The mechanical properties of the iris were typically nonlinear, viscoelastic, anisotropic and location-dependent. The stress growth rate of the circumferential direction iris strip is significantly lower than that of RD and the stress-relaxation rate is significantly higher than that of the RD. That is, the iris is more prone to deformation in RD and the stress-retention ability after deformation in RD is weak, which is consistent with the fact that the iris bombe more likely happens in RD in vivo. The results of this study may also help us to establish a more accurate finite element model to simulate the flow field of humor aqueous and find the key factor of pupillary-block. [ABSTRACT FROM AUTHOR]

Viscoelastic fibre prestressing (VFP) is a promising technique to counterbalance the potential thermal residual stress within a polymeric composite, offering superior mechanical benefits for structural engineering applications. It has been demonstrated that the time required for a desirable creep strain can be significantly reduced by implementing higher creep stress, while its long-term stability is still unknown. Here, we developed the prestress equivalence principle and investigated the durability of viscoelastic fibre prestressing within a composite in order to further enrich the prestress mechanisms. The effectiveness of the prestress equivalence principle was refined through Charpy impact testing of prestressed samples with various pre-strain levels. The durability was investigated by subjecting samples to both natural aging (up to 0.5 years) and accelerated aging (by using the time-temperature superposition principle). It is found that the prestress equivalence principle offers flexibility for viscoelastically prestressed polymeric matrix composite (VPPMC) technology; the impact benefits offered by VFP are still active after being accelerated aged to an equivalent of 20,000 years at 20 °C, inferring long-term reliability of VFP-generated fibre recovery within a polymeric composite. These findings demonstrated that both materials and energy consumption could be conserved for advanced composites. Therefore, they promote further steps of VPPMC technology toward potential industrial applications, especially for impact protection. [ABSTRACT FROM AUTHOR]

To illuminate brittle and ductile fracturing of magma, we investigated bubble expansion and fracturing in two contrasting fluids: a Maxwell‐type viscoelastic fluid and a Bingham‐type yield‐strength fluid. Measurements of the complex shear modulus, G′ + iG″ (i is the imaginary unit), under small‐strain oscillation showed that both fluids are elastic (G′ > G″) with similar rigidity. Viscous behavior (G′ < G″) appeared at lower frequency in the Maxwell fluid but at larger strain in the Bingham fluid. When we injected air into the Maxwell fluid, bubbles expanded viscously at low flux, fractured in a brittle manner at high flux, and behaved transitionally at intermediate flux. In contrast, we observed no fracturing in the Bingham fluid. This demonstrates that the G′ > G″ condition is insufficient to infer that brittle fracturing can occur. Brittle fracturing of the Maxwell fluid occurred not at a critical strain rate but under decreasing strain rate and increasing stress. Plain Language Summary: The flow‐to‐fracture transition of magma is an essential process controlling eruption explosivity. This transition has been explained based on the linear Maxwell viscoelastic model: magma can flow slowly but breaks in a brittle manner under rapid deformation. The Bingham model represents another type of fluid‐solid transition: a material flows under a sufficiently large force but behaves elastically below this force. The present study investigates bubble growth and fracture by air injection in Maxwell‐type and Bingham‐type fluids, both having similar elasticity. We demonstrate that brittle fracture occurs in the Maxwell fluid at high air flux but never in the Bingham fluid. Detailed observations of the deformation until brittle fracture reveals a stress increase and strain rate decrease. The fracture onset is not determined by the critical strain rate, contrary to conventional brittle fragmentation criteria widely used in volcanology. These results will help improve brittle‐ductile transition models for complex fluids in volcanic eruptions. Key Points: Rapid air injection generated brittle fracture in a Maxwell fluid but not in a Bingham fluid, although they have similar elasticityThe observation of elasticity in small‐amplitude oscillation tests is not sufficient to infer that the fluid can fractureThe strain rate around a bubble decreased toward fracture, contrary to the conventional critical strain‐rate fracture criterion [ABSTRACT FROM AUTHOR]

To improve the production yield rate, reliability is one of the important indicators of electronic packaging products. In past research, however, the influence of the fabrication process was rarely taken into consideration. In this thesis, mold flow analysis software Moldex3D is used to develop a series analysis procedure for IC package products. The effects of many factors, including process, structure, and materials were being taken into account. Especially for epoxy molding compound, namely EMC, is studied on its properties during the molding and post-mold cure (PMC) processes. This paper adopted P–V-T-C equations, which consider both volume shrinkage due to thermal mismatch and chemical shrinkage to predict the amount of warpage and residual stresses after the mold filling process. Next, dual shift factor model for viscoelastic analysis was used to model the PMC process and predict the amount of warpage and residual stresses after PMC. And the influence of different PMC process conditions and loading conditions on the warpage results is discussed. The residual stresses after PMC simulation are set as the initial conditions for reliability analysis and then the stress distribution after two thermal cycles is analyzed. It is observed that the deformed shape of the simulation and experiment results after PMC were consistent. Both are concave downwards. In comparison with experiment results, the error of warpage simulation results was between 10% and 50%. The biggest error was found in the short direction. During two thermal cycles, it is can be found that the maximum stress of the lead frame is 505.7 MPa and the location of the possible failure is at the top left of the die. In addition, when considering or not considering the process-induced residual stress in the thermal cycle analysis, the stress states are very different. [ABSTRACT FROM AUTHOR]

This study investigates the size-dependent wave propagation behaviors under the thermoelectric loads of porous functionally graded piezoelectric (FGP) nanoplates deposited in a viscoelastic foundation. It is assumed that (i) the material parameters of the nanoplates obey a power-law variation in thickness and (ii) the uniform porosity exists in the nanoplates. The combined effects of viscoelasticity and shear deformation are considered by using the Kelvin-Voigt viscoelastic model and the refined higher-order shear deformation theory. The scale effects of the nanoplates are captured by employing nonlocal strain gradient theory (NSGT). The motion equations are calculated in accordance with Hamilton's principle. Finally, the dispersion characteristics of the nanoplates are numerically determined by using a harmonic solution. The results indicate that the nonlocal parameters (NLPs) and length scale parameters (LSPs) have exactly the opposite effects on the wave frequency. In addition, it is found that the effect of porosity volume fractions (PVFs) on the wave frequency depends on the gradient indices and damping coefficients. When these two values are small, the wave frequency increases with the volume fraction. By contrast, at larger gradient index and damping coefficient values, the wave frequency decreases as the volume fraction increases. [ABSTRACT FROM AUTHOR]

A methodology is presented for the back-analysis of convergence measurements in deep tunnels to determine the constitutive parameters of the surrounding rock mass. Since increasing deformations and stresses with time are due to both the face advance and the time-dependent behavior of the ground, the two effects must be considered during the excavations. To that end, an analytical solution assuming an unlined circular tunnel excavated in a homogeneous isotropic ground under an initial isotropic stress field and assuming a fractional viscoelastic plastic behavior is developed. A second closed-form solution is also derived assuming an instantaneous excavation. Additionally, combining the developed analytical solution that takes into account the progressive face advance and an empirical approach, convergences are back-analyzed based on a least-squares optimization method to calibrate the constitutive parameters of the ground. The presented methodology aims to characterize the long-term behavior of tunnels and offers the advantage of being directly applicable during the excavation phase as soon as convergence measurements are available. Finally, the method is illustrated by two case studies related to the Fréjus road tunnel and the Saint-Martin-la-Porte access gallery (SMP2). • New analytical solutions for deep tunnels in viscoelastic plastic rocks are derived. • Both the face advance and the viscosity of the ground are considered simultaneously. • The time-dependent behavior is modeled using a fractional viscoelastic law. • Convergences are back-analyzed to determine the constitutive parameters of the rock. • The proposed methodology is applied to two different case studies. [ABSTRACT FROM AUTHOR]

The flexural wave propagation in a micro-beam mounted on viscoelastic foundation is considered in the present work. The mechanical behavior of the micro-beam is modeled by nonlocal strain gradient elasticity with the size-effects taken into account. The constraint is modeled by the Pasternak foundation with the rheology behavior modeled by fractional-order viscoelasticity. The main concerns are the dispersion and attenuation feature of five kinds of possible flexural waves derived from the governing equations of the presented micro-beam model. The influences of the nonlocal effects, strain gradient effects and the fractional-order viscoelastic effects are investigated by a parameter study in the numerical examples. This research is helpful for the design of micro-sensor, micro-actuator and energy-harvest devices in micro electric-mechanic system (MEMS). [ABSTRACT FROM AUTHOR]

Solid propellant is a composite material exhibiting classic nonlinear viscoelastic mechanical characteristic, which is due in a large part to a cumulative damage process caused by the formation and growth of microflaws inside. The standard relaxation tests and uniaxial tension tests under different velocities of hydroxyl-terminated polybutadiene (HTPB) propellant are carried out in this paper, where Digital Image Correlation (DIC) technique is applied to record deformation. The experimental results show that the material mechanical behavior is rate-dependent. It is also observed that the yield stress and failure stress are significantly rate-dependent on the tensile velocity. Based on these experimental results, it can be inferred that the stiffness degradation and damage evolution of HTPB propellant are a rate-dependent processes. Therefore, the damage accumulation of HTPB propellant is considered rate-dependent in this research. In order to describe the mechanical characteristic precisely, a nonlinear viscoelastic constitutive model with rate-dependent cumulative damage is developed. The damage model is developed based on the concept of pseudo strain, in which a Prony series representation of viscoelastic material functions is applied. Besides, a rate-dependent damage variable is introduced into the model through considering the rate-dependent characteristics of cumulative damage process. In addition, a new normalized failure criterion is derived on the basis of the proposed damage model, which is independent of strain-rate after normalization. Finally, it is implemented in commercial finite element software for stress analysis to verify the predictive capacities of the damage model. The accuracy of the constitutive model and failure criterion is validated under uniaxial tensile tests of various strain rates. [ABSTRACT FROM AUTHOR]

To investigate the effects of viscoelasticity on the stick-slip behaviour, a new model reproducing the partial slip of viscoelastic materials under fully coupled conditions is developed in this paper. The ratio of retardation time to relaxation time is employed to characterize the rheological property of a viscoelastic material. It is found that materials with higher ratios exhibit more fluid-like behaviours while those with lower ratios perform more like solid. As long as the contact input (load or displacement) is constant, the stick ratio (ratio of stick area to contacting area) is found to be insensitive to the viscoelasticity of materials. However, the separation pattern of the stick and slip regions varies with time when different contact phenomena (creep or stress relaxation) are encountered in the lateral and normal directions. The transition process from partial slip to gross sliding of viscoelastic materials, unlike the elastic response, tends to be abrupt when fully coupled conditions between shear tractions and pressure are introduced. When identical contact parameters are specified for different viscoelastic materials, the more fluid-like material always experiences a quicker transition from partial slip to gross sliding. [ABSTRACT FROM AUTHOR]

• The analytical integration Legendre polynomial method is developed to study the wave attenuation. • Functionally gradient viscoelastic microstructures sandwiched in two elastic half-spaces are studied. • The couple stress decreases the attenuation, while the inhomogeneity increases the attenuation. • The couple stress effect weakens the viscoelasticity, while the viscoelasticity strengthens the couple stress effect. Taking the viscoelasticity and size-dependent effect into account, the reflection and transmission of elastic waves through functionally graded viscoelastic plate sandwiched in two elastic half-spaces are investigated. The extended analytical integration Legendre polynomial method and Kelvin-Voigt viscoelastic model in the context of the modified couple stress theory are utilized to perform the derivation. The global matrix method is used to confirm the validity of the extended analytical integration Legendre polynomial method. Compared with the global matrix method, the extended analytical integration Legendre polynomial method provides an efficient numerical calculation method without layering and iterative root seeking. The influences of the couple stress, viscoelasticity and inhomogeneity of medium on elastic wave reflection and transmission are discussed. In addition, the attenuation caused by the viscoelasticity is analyzed. It is found that the couple stress effect weakens the influence of the viscoelasticity, while the viscoelasticity strengthens the couple stress effect. The couple stress effect decreases the attenuation, while the inhomogeneity increases the attenuation. [ABSTRACT FROM AUTHOR]

The relationship between pressure (P) and volume (V) in the human lung has been extensively studied. However, the combined effects of gravity and the mechanical properties of elastin and collagen on alveolar and lung P–V curves during breathing are not well understood. Here, we extended a previously established thick-walled spherical model of a single alveolus with wavy collagen fibers during positive pressure inflation. First, we updated the model for negative pressure-driven inflation that allowed incorporation of a gravity-induced pleural pressure gradient to predict how the static alveolar P–V relations vary spatially throughout an upright human lung. Second, by introducing dynamic surface tension and collagen viscoelasticity, we computed the hysteresis loop of the lung P–V curve. The model was tested by comparing its predicted regional ventilation to literature data, which offered insight into the effects of microgravity on ventilation. The model has also produced novel testable predictions for future experiments about the variation of mechanical stresses in the septal walls and the contribution of collagen and elastin fibers to the P–V curve and throughout the lung. The model may help us better understand how mechanical stresses arising from breathing and pleural pressure variations affect regional cellular mechanotransduction in the lung. [ABSTRACT FROM AUTHOR]

The viscoelastic properties of materials such as polymers can be quantitatively evaluated by measuring and analyzing the viscoelastic behaviors such as stress relaxation and creep. The standard linear solid model is a classical and commonly used mathematical model for analyzing stress relaxation and creep behaviors. Traditionally, the constitutive equations for analyzing stress relaxation and creep behaviors based on the standard linear solid model are derived using the assumption that the loading is a step function, implying that the loading rate used in the loading process of stress relaxation and creep tests is infinite. Using such constitutive equations may cause significant errors in analyses since the loading rate must be finite (no matter how fast it is) in a real stress relaxation or creep experiment. The purpose of this paper is to introduce the constitutive equations for analyzing stress relaxation and creep behaviors based on the standard linear solid model derived with a finite loading rate. The finite element computational simulation results demonstrate that the constitutive equations derived with a finite loading rate can produce accurate results in the evaluation of all viscoelastic parameters regardless of the loading rate in most cases. It is recommended that the constitutive equations derived with a finite loading rate should replace the traditional ones derived with an infinite loading rate to analyze stress relaxation and creep behaviors for quantitatively evaluating the viscoelastic properties of materials. [ABSTRACT FROM AUTHOR]

Flexible viscoelastic foams with relative density in the range of 5-50% are widely used to control interaction forces, notably in cushions for impact protection, shoes, mechanical grippers, etc. The design of new foams to improve performance is challenging, due to the lack of efficient models to connect cellular architecture, viscoelasticity of the base resin, and non-linear responses that stem from large deformation of open pores. This paper presents highly efficient solutions for the response of linearly viscoelastic, kinematically non-linear and shear-deformable struts that are loaded at an oblique angle to their axis. The models can be used to predict structure-property relationships for strut-based metamaterials, including non-linear stress-strain response and accompanying hysteresis. To illustrate this, the entire design space of a simple unit cell is mapped in terms of a broad range of strut angles and thicknesses; the unit cell is inspired by features in stochastic foams that dominate their response. An enormous range of stress-strain responses can be obtained from this single foam-like cell, including purely softening, purely stiffening, and non-monotonic stiffness with adjustable tangent moduli. The model is also used to illustrate connections between viscoelastic material parameters, loading rate, and hysteresis for two distinct classifications of non-linear stress-strain response. • Efficient model to quantify the coupling of non-linear stress-strain response and hysteresis in strut-based metamaterials. • Model uses linearly viscoelastic, kinematically non-linear and shear-deformable struts loaded obliquely. • The entire simple unit cell design space is mapped in terms of a broad range of strut angles and thicknesses. • Stress-strain responses include stiffening, plateau and sigmoidal shapes. • Connections between viscoelastic material parameters, loading rate, and hysteresis are shown. [ABSTRACT FROM AUTHOR]

• The strain gradient viscoelastic solutions of the Mode-I and Mode-II crack in an infinite quasi-brittle advanced material are proposed based on the strain gradient viscoelasticity theory using the Wiener-Hopf method and the correspondence principle in Maxwell's standard linear solid model. The strain gradient viscoelasticity theory are successfully used to explain the fracture of microscale and nanoscale materials with viscosity and size effect. • The stress near the crack tip is time-dependent and size-dependent. The stress near the crack tip is more significant than that based on gradient elasticity theory. Compared with the elastic strain gradient effect, the viscous gradient effect makes the stress field at the crack tip harden. • The location and the value of maximum stress change with time, which differs from the case in strain gradient elasticity theory. The time that the normalized stress takes to stabilize also changes with the distance from the crack tip. When the viscosity effect is neglected or time tends to infinity, the strain gradient viscoelasticity theory can be reduced to the classical strain gradient elasticity theory. The impacts of size and viscosity become distinctly evident when considering micro- and nano-scale phenomena for advanced materials with micro- and nanostructures. In this study, the mechanical behavior of the advanced material is characterized by using the strain gradient viscoelasticity theory, and a novel solution is presented for the mode-I and mode-II cracks, which is formulated based on the strain gradient viscoelasticity theory, employing the Wiener-Hopf method. Besides, the gradient-dependent viscoelastic crack solutions are directly derived by applying the correspondence principle that aligns strain gradient viscoelasticity with strain gradient elasticity within the Maxwell's standard linear solid model. Relative to the influence of elastic strain gradient effects, the involvement of viscous gradient effects instigates a reinforcement to the stress field around the crack tip, thereby offering a more reasonable representation of advanced materials crack behavior. When the viscosity effect is omitted or as time tends to infinity, the solutions based on strain gradient viscoelasticity theory converges to those on the classical strain gradient elasticity theory. [ABSTRACT FROM AUTHOR]

The thermodynamic consistency of linear viscoelastic models is investigated. First, the classical Boltzmann law of stress–strain is considered. The kernel (Boltzmann function) is shown to be consistent only if the half-range sine transform is negative definite. The existence of free-energy functionals is shown to place further restrictions. Next, the Boltzmann function is examined in the unbounded power law form. The consistency is found to hold if the stress functional involves the strain history, not the strain–rate history. The stress is next taken to be given by a fractional order derivative of the strain. In addition to the constitutive equations involving strain–rate histories, finding a free-energy functional, consistent with the second law, seems to be an open problem. [ABSTRACT FROM AUTHOR]

Recent work modeling the rheological behavior of human blood indicates that blood has all the hallmark features of a complex material, including shear-thinning, viscoelastic behavior, yield stress, and thixotropy. There is renewed interest in the modeling of human blood with thixo-elasto-visco-plastic rheological models. Previous work [Armstrong and Tussing, Phys. Fluids 32, 094111 (2020)] has led to the development of the enhanced thixotropic viscoelastic model for blood (ethixo-mHAWB; called here, after a minor modification, ETV) that incorporates viscoelasticity to a thixotropic model for the stress contributed by the rouleaux aggregates, in addition to describing using a nonlinear viscoelastic model the stress contributed by the individual red blood cells deforming under the action of the flow. This model has shown superior performance in fitting human blood steady state and transient rheological data from a strain-controlled rheometer [Horner et al., J. Rheol. 62, 577–591 (2018); 63, 799–813 (2019)] as compared to other alternate models. In the present work, we first develop another variant of the ETV model, the enhanced structural stress thixotropic-viscoelastic (ESSTV) model, and the modification patterned following an elastoviscoplastic model developed recently [Varchanis et al., J. Rheol. 63, 609–639 (2019)]. We develop full tensorial stress formulations of the rouleaux stresses for both the above-mentioned models, resulting in the t-ETV and t-ESSTV models. We use steady state and step-ups, and step-downs in shear rate data to independently fit the parameters of all before-mentioned models. We compare predictions against experimental data obtained on small, large, and unidirectional large amplitude oscillatory shear conditions. We find that the full tensor stress formulations t-ETV and t-ESSTV significantly improved the predictive capability of the earlier ETV model. [ABSTRACT FROM AUTHOR]

The problem of analysis of creep strains in thin-walled tubular elements made of linearly viscoelastic materials under uniaxial tension, pure torsion, and combined tension with torsion is solved and experimentally validated. The analysis is based on the use of viscoelasticity models in the form of proportionality of deviators. The creep kernels are represented by fractional-exponential functions. The longitudinal, transversal, shear, and volume creep strains are calculated. [ABSTRACT FROM AUTHOR]

In rheological experiments, the relationship between stress and strain is determined. In the transient regime, this relationship may depend on which of these properties is applied and which is measured. In general, data collected using one or the other as the control parameter are not necessarily equivalent. Moreover, the assumed steady state and the relaxation following this state might depend on whether stress or strain has been applied. We examined colloidal suspensions with concentrations around the glass transition and compared their response to stress and strain, in particular, their transient response after the start-up of shear, their steady state, and their relaxation after cessation of shear. After the start-up of shear, the transient behavior was found to significantly depend on whether the sample is exposed to a constant shear rate or a constant stress. Nevertheless, the transients lead to a rheological steady state that is independent of how it is reached, as long as yielding occurred and the corresponding shear rate or stress is applied. After cessation of shear, the relaxation under strain and stress control shows both similarities and differences. This is quantified based on, e.g., the hydrodynamic, Brownian, and residual stress as well as the recovered strain. In addition, the responses of the rheometers to the abrupt changes have been characterized. The corresponding technical data are presented and taken into account in the data interpretation. [ABSTRACT FROM AUTHOR]

Background: Reed has high lignin content, wide distribution and low cost. It is an ideal raw material for replacing wood in the paper industry. Reeds are rich in resources, but the density of reeds is low, leading to high transportation and storage costs. This paper aims to study the compression process of reeds and the creep behaviour of compressed reeds, and provide theoretical guidance for the reed compressor management, bundling equipment and the stability of compressed reed bales. Results: We have established a multi-layer perceptron network prediction model for the creep characteristics of reeds, and the prediction rate R2 of this model is greater than 0.997. The constitutive equation, constitutive coefficient and creep quaternary model of the reed creep process were established by using the prediction model. The creep behaviour of the reed bale is positively correlated with the initial maximum compressive stress (σ0). During the creep of the reed, the elastic power and the viscous resistance restrict each other. The results show that the proportion of elastic strain in the initial stage is the largest, and gradually decreases to 99.19% over time. The viscoelastic strain increases rapidly with time, then slowly increases, and finally stabilizes to 0.69%, while the plastic strain accounts for the proportion of the total strain. The specific gravity of the reed increases linearly with the increase of creep time, and finally accounts for 0.39%, indicating that as time increases, the damage of the reed's own structure gradually increases. Conclusions: We studied the relationship between the strain and time of the reed and the strain and creep behaviour of the reed bag under different holding forces under constant force. It is proved that the multi-layer perceptron network is better than the support vector machine regression in predicting the characteristics of reed materials. The three stages of elasticity, viscoelasticity and plasticity in the process of reed creep are analysed in detail. This article opens up a new way for using machine learning methods to predict the mechanical properties of materials. The proposed prediction model provides new ideas for the characterization of material characteristics. [ABSTRACT FROM AUTHOR]

Background: Subsurface mechanisms can greatly affect the mechanical behavior of biological materials, but observation of these mechanisms has remained elusive primarily due to unfavorable optical characteristics. Researchers attempt to overcome these limitations by performing experiments in biological mimics like hydrogels, but measurements are generally restricted due to the spatio-temporal limitations of current methods. Objective: Utilization of contemporary 3D printing techniques into soft, transparent, aqueous yield-stress materials have opened new avenues of approach to overcoming these roadblocks. By incorporating digital image correlation with such 3D printing techniques, a method is shown here that can acquire full-field deformation of a hydrogel subsurface in real-time. Methods: Briefly, the method replaces the solvent of a transparent and low polymer concentration yield-stress material with an aqueous hydrogel precursor solution, then a DIC speckle plane is 3D printed into it. This complex is then polymerized using photoinitiation thereby locking the speckle plane in place. Results: Full-field deformation measurements are made in real-time as the embedded speckle plane (ESP) responds with the bulk to the applied load. Example results of deformation and strain fields associated with indentation, relaxation, and sliding contact experiments are shown. Conclusions: This method has successfully observed the subsurface mechanical response in the bulk of a hydrogel and has the potential to answer fundamental questions regarding biological material mechanical behaviors. [ABSTRACT FROM AUTHOR]

Strain/stress-controlled loading, loading–unloading, loading-relaxation (or creep), and corresponding cyclic tests are essential for characterizing the viscoelastic materials' rate-dependent stress–strain relationship. A three-parameter model is proposed based on the basic definition of fractional derivative viscoelasticity and time-varying viscosity. This model is applied to many complex loading conditions. The solutions for three monocyclic loading conditions are given and then further generalized to arbitrary linear loading conditions, which are assumed to be first-order functions of time. The generalized solution for the arbitrary linear loading path is validated by modelling the mechanical response of cyclic loading–unloading and loading–relaxation (or creep) tests. Four sets of experimental data for polymer materials are employed to demonstrate the proposed fractional derivative model's efficiency. The results show that it can accurately model strain/ stress-controlled response under various loading conditions using only three parameters. The model is then implemented in numerical software to explore its capacity further, and the simulation results show that it also succeeds in simulating cyclic loading–unloading tests. [ABSTRACT FROM AUTHOR]

Elastomers, such as polyurethane, exhibit hyperelastic behaviour and distinct rate dependence under a wide range of strain rates. Herein, a methodology for developing a hyper-viscoelastic constitutive model for succinctly characterising the mechanical behaviour of polyurethane under large deformations and a wide range of strain rates is proposed. The model is constructed using a long-term hyperelastic formulation combined with a rate-dependent viscoelastic model. This model is based on internal state variables and a finite strain formulation. A polyurethane elastomer was used as a sample to develop this model, by way of testing wide strain-rate mechanical behaviour (0.001–5000s−1) and viscoelastic behaviour. The viscoelastic behaviour was obtained using the equivalent time–temperature superposition relation. A parameter-fitting algorithm was adopted to separate the long-term behaviour from the viscoelastic behaviour. The long-term behaviour was modelled using a Mooney–Rivlin hyperelastic model, and its parameters were identified using the least-squares method. The time-dependent viscous effect calculated using the Prony series-based model was approximately determined based on the continuous relaxation spectrum. The characterisation capacity was confirmed through a thorough comparison with experimental curves. This model can be extended to other elastomers, even under tension, without any specific limitations of the internal components. • A novel hyper-viscoelastic constitutive model is proposed to capture the nonlinear large deformation and rate-sensitivity of elastomer. • A hyper-viscoelastic model is achieved by incorporating viscoelasticity at a finite strain and internal state variables. • Viscoelastic behaviour is characterized with the time-temperature-superposition principle and relaxation spectrum. • The proposed model can efficiently predict the stress-strain response under wide strain rate range. [ABSTRACT FROM AUTHOR]

Some reports have confirmed that discretizing the mass, damping, and stiffness characteristics of a continuum can result in remarkable deviations from the experimental results; as all these properties are intertwined and coupled within a single material. The viscoelastic constitutive laws with fractional-order time derivatives can model this integrity much more accurately, due to their capability of using a set of an infinite number of orders. Here, an innovative constitutive model with a nonlinear hyperelastic memory element that treats simultaneously the fractional-order viscoelasticity and Mooney-Rivlin hyperelasticity of the continuum is proposed to track the suppression of the short-term dynamic stresses and displacements and the redistribution of the long-term creep stress and deformations of the suddenly pressurized thick cylinders. While the spatial variations of the quantities of the incompressible cylinder are treated by an exact analytical approach, the resulting time-dependent system of equations is converted by a novel numerical solution scheme to an integrodifferential system that contains integer-order partial derivatives and a time-growing number of integral terms. An enhancement to Caputo's singular-kernel integral definition of the fractional-order derivatives is proposed here to replace these derivatives with equivalent integrals whose integer derivatives are computed based on second-order Taylor's expansion. The integer-order and fractional-order time derivatives are then computed numerically using the second-order Runge-Kutta and accumulation-based trapezoidal techniques, respectively. Finally, comparisons are made among the dissipative pattern and time variations of the dynamic/vibration stresses and large-deformations of the hyperelastic and fractional-order visco-hyperelastic cylinders in addition to the assessment of the effects of the constitutive parameters of the fractional-order model. Results show that while the larger magnitudes of both the nonlinear viscosity coefficients and fractional-order time derivatives diminish the resulting deformations and stresses, they respectively lead to smaller and larger frequencies of oscillation. • A fractional-order model with higher viscohyperelastic integrity components is proposed. • Dynamic dissipation and creep stress and displacement redistributions are studied. • A novel model proposed for suddenly loaded thick visco-Mooney-Rivlin cylinders. • Exact solution is proposed for the spatial variations of the incompressible cylinder. • A second-order expansion and a hybrid discretization are used in the Caputo integral. [ABSTRACT FROM AUTHOR]

Cell-cell adhesions are often subjected to mechanical strains of different rates and magnitudes in normal tissue function. However, the rate-dependent mechanical behavior of individual cell-cell adhesions has not been fully characterized due to the lack of proper experimental techniques and therefore remains elusive. This is particularly true under large strain conditions, which may potentially lead to cell-cell adhesion dissociation and ultimately tissue fracture. In this study, we designed and fabricated a single-cell adhesion micro tensile tester (SCAµTT) using twophoton polymerization and performed displacement-controlled tensile tests of individual pairs of adherent epithelial cells with a mature cell-cell adhesion. Straining the cytoskeleton-cell adhesion complex system reveals a passive shear-thinning viscoelastic behavior and a rate-dependent active stress-relaxation mechanism mediated by cytoskeleton growth. Under low strain rates, stress relaxation mediated by the cytoskeleton can effectively relax junctional stress buildup and prevent adhesion bond rupture. Cadherin bond dissociation also exhibits rate-dependent strengthening, in which increased strain rate results in elevated stress levels at which cadherin bonds fail. This bond dissociation becomes a synchronized catastrophic event that leads to junction fracture at high strain rates. Even at high strain rates, a single cell-cell junction displays a remarkable tensile strength to sustain a strain as much as 200% before complete junction rupture. Collectively, the platform and the biophysical understandings in this study are expected to build a foundation for the mechanistic investigation of the adaptive viscoelasticity of the cell-cell junction. [ABSTRACT FROM AUTHOR]

We found an anomalous nonlinear behavior under large amplitude oscillatory shears, where the amplitude stress deviates strongly from the linear dependence of strain, while the time dependence of stress remains sinusoidal. This phenomenon is usually accompanied with the Payne effect of filled rubbers. In order to understand the molecular details regarding this unusual behavior, we examined a series of polybutadiene/tetradecane solutions filled with carbon black. Our results show that there is a previously unrecognized transition in the system as the matrix polymer concentration ϕ approaches and passes through a characteristic polymer concentration ϕc. Below ϕc, the system typically shows the classic nonlinearity, where the storage modulus G′ decreases as the strain amplitude γ0 increases and the resulting stress waveforms are distorted from sinusoidal waves. Above ϕc, the system displays an anomalous nonlinearity, where the stress responses at any given strain remain surprisingly sinusoidal regardless of the drop in the storage modulus G′. The critical concentration ϕc is about an order of magnitude greater than the entanglement polymer concentration ϕe. The degree of entanglement in the matrix apparently determines the occurrence of this unusual rheological event and plays a key role here. Increasing the polymer molecular weight enhances this transition. [ABSTRACT FROM AUTHOR]

• A trans -scale dynamic shear-lag model was established for predicting the impact performance of the fiber-reinforced composites containing micro- or nano-scale building blocks. • Our model highlights the mechanism by which the strain gradient effect diminishes the matrix's energy dissipation capacity. • Numerical analyses based on our model demonstrate that classical and higher-order viscosities work synergistically to optimize energy dissipation. This study proposes a new trans -scale dynamic shear-lag model that integrates the strain gradient linear viscoelasticity theory to investigate the effects of size and viscous softening on the dynamic mechanical properties and energy absorption characteristics of fiber-reinforced composites with micro- and nano-structures. The proposed model clarifies how the strain gradient effect can decrease energy dissipation in the matrix. Our investigation suggests that both classical and higher-order viscosities of the submicron-scale matrix can synergistically optimize energy dissipation. Furthermore, parametric studies demonstrate that the attenuation efficiency of absorbed energy changes non-monotonically with microstructure and constituent properties, such as matrix thickness, strain gradient elasticity parameter, classical viscosity, and high-order viscosity. The trans -scale dynamic shear-lag model advances our understanding of the energy dissipation in the submicron-scale viscoelastic matrix of fiber-reinforced composites and provides valuable guidance for developing composites with micro- and nano-structures that display exceptional dynamic properties. [ABSTRACT FROM AUTHOR]

A recent strategy for controlling saturated fat intake consists on the design of vegetable oil-based emulsions. The aim was to characterize the linear and nonlinear viscoelastic properties of o/w emulsions formulated with two types of cellulose: MX (methylcellulose, MC) and F4M (hydroxypropyl methylcellulose, HPMC). The emulsions were characterized by steady flow curves and frequency sweeps in SAOS (Small Amplitude Oscillatory Shear) regime. In order to evaluate linear and non-linear response, strain sweeps were performed from 0.01 to 1000% strain amplitude at different frequencies (0.1, 1 and 5 Hz). Fourier Transform rheology and orthogonal stress decomposition were applied and LAOS (Large Amplitude Oscillatory Shear) parameters (G' M , G' L , η M ' , η L ' , S and T) were analysed. The type of cellulose ether significantly affected both flow behaviour and internal structure of the samples. MX emulsion presented greater consistency at rest and higher gel strength in SAOS regime with a lower frequency dependence than F4M emulsion. However, both emulsions presented similar properties at large deformations, showing shear thinning and strain stiffening behaviour. Nonlinear viscoelastic analysis allows to improve the textural characterization of emulsions, providing complementary useful information for establishing the most suitable formulation in experimental conditions closer to real applications and processes. • Consistency and internal structure of the emulsions depended on the cellulose type. • Similar viscosity at high rates resulted from the different shear thinning character. • Both emulsions showed a similar strain stiffening behaviour for large deformations. • Characteristics in nonlinear regime were not in accordance with linear behaviour. [ABSTRACT FROM AUTHOR]

We present a hybrid discontinuous Galerkin method for the velocity/stress formulation of Zener's model in dynamic viscoelasticity. Our approach utilizes a spatial discretization that enforces strongly the symmetry of the stress tensor, and that allows for efficient handling of heterogeneous materials comprising both purely elastic and viscoelastic components. We provide an h p error analysis of the semidiscrete scheme, which yields quasi-optimal error estimates for the stress tensor and sub-optimal error estimates for the velocity field in the L 2 -norm. Next, we apply the Crank–Nicolson rule as a time-stepping scheme and analyze its primary convergence properties. Finally, we present the results of numerical experiments to validate our approach and confirm the theoretical rates of convergence. • Development of a HDG method for the stress/velocity formulation of Zener's viscoelasticity model. • Novel HDG approach significantly reduces computational effort while preserving accuracy and stability. • Strong enforcement of stress symmetry and immunity to locking phenomena in the nearly incompressible case. • Ability to handle composite elastic-viscoelastic structures. • Method offers h p -adaptivity, arbitrary order approximations, and flexibility in mesh design. [ABSTRACT FROM AUTHOR]

Delayed capillary break-up of viscoelastic filaments presents scientific and technical challenges relevant for drop formation, dispensing, and adhesion in industrial and biological applications. The flow kinematics are primarily dictated by the viscoelastic stresses contributed by the polymers that are stretched and oriented in a strong extensional flow field resulting from the streamwise gradients created by the capillarity-driven squeeze flow. After an initial inertiocapillary (IC) or viscocapillary (VC) regime, where elastic effects seem to play no role, the interplay of capillarity and viscoelasticity can lead to an elastocapillary (EC) response characterized by exponentially-slow thinning of neck radius (extensional relaxation time is determined from the delay constant). Less frequently, a terminal visco-elastocapillary (TVEC) response with linear decay in radius can be observed and used for measuring terminal, steady extensional viscosity. However, both IC/VC-EC and EC-TVEC transitions are inaccessible in devices that create stretched necks by applying a step strain to a liquid bridge (e.g., capillary breakup extensional rheometer). In this study, we use dripping-onto-substrate rheometry to obtain radius evolution data for unentangled polymer solutions. We deduce that the plots of transient extensional viscosity vs. Hencky strain (scaled by the respective values at the EC-TVEC transition) emulate the functional form of the birefringence-macromolecular strain relationship based on Peterlin's theory. We quantify the duration and strain between the IC/VC-EC and the EC-TVEC transitions using measures we term elastocapillary span and elastocapillary strain increment and find both measures show values directly correlated with the corresponding variation in extensional relaxation time. [ABSTRACT FROM AUTHOR]

Abstract A computational model for simulations of fused filament fabrication (FFF) – often also called fused deposition modeling (FDM) – that includes viscoelastic stresses, is presented. The flow of a viscoelastic polymer filament from a nozzle, the deposition of the filament onto a substrata or previously deposited filaments, and the cooling and solidification of the filament, are captured using the one-fluid formulations, where a single set of equations is written for all the fluids and phases involved (polymer and air). The governing equations are solved on a regular stationary grid and the boundary between the polymer and the air is followed using connected marker points. The model is based on an earlier development where the polymer stresses were assumed to be Newtonian. The method is tested by simulating the extrusion of a polymer from a nozzle and the predicted swelling compared with results from the literature. The method is then used to simulate three filaments deposited on top of each other and the fabrication of an object consisting of a filament deposited perpendicularly on top of several filaments. The effect of including viscoelasticity on the extruded filament size and shape are discussed. Highlights • A front-tracking/finite volume method is introduced to model Fused Filament Fabrication. • Fluid flow, heat transfer, viscoelasticity and moving boundary are included. • A fully resolved simulation is presented with accuracy and convergence validations. • Effects of including viscoelastic stresses are presented and discussed. [ABSTRACT FROM AUTHOR]

A general model covering a large variety of the so-called adhesive or cohesive, possibly also frictional, contact interfaces between visco-elastic bodies with inertia considered in a thermodynamical context is presented. A semi-implicit time discretisation which conserves energy, is numerically stable and convergent, and which advantageously decouples the system is devised. An extension to porous media with adhesive contact influenced by a diffusant concentration is devised, too. [ABSTRACT FROM AUTHOR]

Abstract Viscoelastic nature of polymers makes their properties strongly dependent on temperature and strain rate. Characterization of material properties over a wide range of strain rates and temperatures requires an expensive and time consuming experimental campaign. While viscoelastic properties of materials are widely tested using dynamic mechanical analysis (DMA) method, the frequency dependent component of the measured properties is underutilized due to a lack of correlation between frequency, temperature, and strain rate. The present work develops a method that can extract elastic modulus over a range of strain rates and temperatures from the DMA data for nanocomposites. Carbon nanofiber (CNF) reinforced high-density polyethylene (HDPE) matrix nanocomposites are taken as the study material. Four different compositions of CNF/HDPE nanocomposites are tested using DMA from 40 to 120 °C at 1–100 Hz frequency. First, time-temperature superposition (TTS) principle is used to develop an extrapolation for the results beyond the test parameter range. Then the TTS curve is transformed to a time domain relaxation function using integral relations of viscoelasticity. Finally, the strain rate sensitive elastic modulus is extracted and extrapolated to room temperature. The transform results are validated with tensile test results and the error found to be below 13.4% in the strain rate range 10−5 to 10−3 for all four nanocomposites. Since the materials are tested with the aim of finding a correlation among the test methods, the quality of the material is not a study parameter and the transform should yield accurate results for any material regardless of composition and quality. [ABSTRACT FROM AUTHOR]

Abstract This paper describes a novel technique and methodology to characterize the stress relaxation behavior of polymers. The shaft-hole coupling test (SHCT) characterizes the stress relaxation mechanics of polymers through measurements of the decrease in the stress between a metallic shaft and a drilled polymeric specimen over time. The main benefits of SHCT are the low implementation costs and reduced time for which the mechanical testing machine is in continuous use, by adopting a device that can be detached from the machine. The stress relaxation of polytetrafluoroethylene (PTFE) was identified by the SHCT over the course of several days, verifying the feasibility of the technique. In order to describe the viscoelastic behavior of the material, an optimization routine via the finite element method (FEM) was used to calibrate the parameters of the Parallel Rheological Framework (PRF) model. Furthermore, the FEM analysis was able to reproduce the mechanical behavior of the material successfully and the methodology was validated via comparison with a conventional stress relaxation test under uniaxial compression loading. Highlights • A new method of assessing the stress-relaxation behavior of polymers is reported. • The methodology allows the efficient use of laboratory equipment. • FEM analysis is implemented to determine the constitutive model of the material. • The validation of the methodology was done via a comparison with a conventional stress relaxation test. • The methodology could be applied to other thermoplastic polymers and composites. [ABSTRACT FROM AUTHOR]

Abstract We ran a series of creep tests on samples from Baltic Basin in Northern Poland and analyzed theoretically the viscoelastic properties. Both elastic and creep data are reported. Elasticity data acquired during loading and unloading show that the tested shales exhibit a significant VTI (vertical transverse isotropy) symmetry, with elastic parameters in the following ranges: E h from 37.4 to 60.0 GPa, E v from 21.4 to 26.9 GPa, ν hv from 0.29 to 0.39, ν vh from 0.19 to 0.23, and ν hh from 0.18 to 0.21, and E h / E v anisotropy ratio from 1.4 to 2, where subscripts v and h indicate the symmetry axis and the perpendicular directions, respectively. The creep data show significant time-dependent deformations even in the time-scale of engineering operations, and strain at constant load may achieve more than a half of the observed instantaneous elastic strain in only two weeks. The creep data have been analyzed using fractional Maxwell model, with a novel fitting approach which takes into account the finite loading time. Such fitting strategy allowed to fit precisely the entire dataset, both the initial and long-term creep regimes. The obtained creep parameters η α , which may be referred to as quasi-viscosity are in the range 2.63·102 to 1.40·104 GPa·s α , with α ranging from 0.10 to 0.36 for the tested shales. Lateral strain data showed that during axial differential stress loading after initial extension, strain reversal may occur, which suggests a complex deformational behavior leading to volumetric compaction. To quantify this phenomenon, time-dependent Poisson's ratio has been introduced. However, because of data limitations (number of samples and duration of experiments), only qualitative description of the time-dependent Poisson's ratio has been provided. [ABSTRACT FROM AUTHOR]

Abstract Viscoelastic treatment has traditionally been used in industrial applications to reduce structural noise and vibration by dissipating part of the strain energy. Constrained-layer damping (CLD) treatments usually dissipate more energy than free-layer damping treatment (FLD), but its design must be integrated in the design process of the structure to be damped. Parametric studies are then necessary to determine the optimal viscoelastic material forming the CLD treatment, and the optimal placement and thickness of the layer. For structures with complex geometry, 3D finite elements are required and a change in the thickness or the placement of the viscoelastic layer implies a complete remeshing of the structure, which represents a significant additional computational cost in the parametric study. The goal of this work is to present a new strategy to model efficiently thin constrained viscoelastic layers. Two interface finite elements, based on a surface representation of the damping layer, are proposed. The first one is a joint element using relative displacements at the interface, and the second one is an original zero-thickness element which makes use of a volumetric integration. These elements are validated by comparison with 3D finite elements. Results show that the proposed interface elements allow a good representation of the damping layer's behaviour, especially for thin layers. Moreover, this modelling approach can be efficiently used in the context of parametric optimisation. [ABSTRACT FROM AUTHOR]

[Display omitted] • The lattice model is extended to analyze early-age creep of 3D printed segments through a sequence of linear analyses; • This newly proposed method requires no approximation of the creep constitutive law and produces the exact solution with the analytical model; • This model can account for the stress history and simulate the creep behaviour of cementitious materials under various loading conditions (namely, loading, unloading, and constant load); • The structural analysis of 3D printed segments highlights the necessity of creep for the accurate prediction of viscoelasticity deformation for 3D printing concrete. We propose a new numerical method to analyze the early-age creep of 3D printed segments with the consideration of stress history. The integral creep strain evaluation formula is first expressed in a summation form using superposition principle. The experimentally derived creep compliance surface is then employed to calculate the creep strain in the lattice model with a combination of stored stress history. These strains are then converted into element forces and applied to the analyzed object. The entire numerical analysis consists of a sequence of linear analyses, and the viscosity is modelled using imposed local forces. The model is based on the incremental algorithm and one of the main advantages is the straightforward implementation of stress history consideration. The creep test with incremental compressive loading is utilized to validate this model. The modelling results are in good agreement with experimental data, demonstrating the feasibility of the lattice model in early-age creep analysis under incremental compressive loading. To understand the impact of early-age creep on structural viscoelastic deformation during the printing process, additional analyses of a printed segment are carried out. These simulation results highlight the need to consider creep for accurate prediction of viscoelastic deformation during the printing process. [ABSTRACT FROM AUTHOR]