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In the context of soft matter and cellular mechanics, microrheology - the use of micron-sized particles to probe the frequency-dependent viscoelastic response of materials – is widely used to shed light onto the mechanics and dynamics of molecular structures. Here we present the implementation of active microrheology in an Acoustic Force Spectroscopy setup (AFMR), which combines multiplexing with the possibility of probing a wide range of forces (~ pN to ~nN) and frequencies (0.01–100 Hz). To demonstrate the potential of this approach, we perform active microrheology on biological samples of increasing complexity and stiffness: collagen gels, red blood cells (RBCs), and human fibroblasts, spanning a viscoelastic modulus range of five orders of magnitude. We show that AFMR can successfully quantify viscoelastic properties by probing many beads with high single-particle precision and reproducibility. Finally, we demonstrate that AFMR to map local sample heterogeneities as well as detect cellular responses to drugs. An in-depth characterization of single-particle active microrheology via Acoustic Force Spectroscopy shows potential to measure viscoelastic moduli spanning five orders of magnitude and local heterogeneity in collagen gels and cells. [ABSTRACT FROM AUTHOR]

Viscoelastic materials (VEMs) have gained increasing popularity for their ability to dampen vibrations in various structural applications in recent years. The mechanical characteristics of VEMs can be effectively described using constitutive models featuring both integer and fractional derivatives. This study examines the mechanical behavior of VEMs using fractional Zener models with four, five, and six parameters, as well as the generalized Maxwell model with 16 parameters, which relies on integer derivatives. To accomplish this, the study formulates an optimization problem with the aim of minimizing an error function defined by the quadratic relative distance between theoretical model responses and experimental data. Solving the optimization problem involves the use of a hybrid optimization technique, which combines genetic algorithms and non-linear programming. After obtaining optimal designs for each viscoelastic model, qualitative assessments demonstrate that all analytical models provide satisfactory fits to the experimental data. Subsequently, a statistical analysis employing Akaike's Information Criterion is conducted to identify the models that best describe the mechanical behavior of the analyzed VEMs. In this quantitative evaluation encompassing all viscoelastic models, it is noted that the generalized Maxwell model with 16 terms produces a lower relative error and statistically outperforms the fractional Zener models only in a global analysis. However, in a temperature-by-temperature analysis, the GMM16 proves to be inferior to all fractional models. Furthermore, when focusing solely on the fractional models, the five-parameter Fractional Zener Model exhibits the best statistical fit to the experimental data. [ABSTRACT FROM AUTHOR]

The response of a body described by a quasi-linear viscoelastic constitutive relation, whose material moduli depend on the mechanical pressure (that is one-third the trace of stress) is studied. The constitutive relation stems from a class of implicit relations between the histories of the stress and the relative deformation gradient. A-priori thresholding is enforced through the pressure that ensures that the displacement gradient remains small. The resulting mixed variational problem consists of an evolutionary equation with the Volterra convolution operator; this equation is studied for well-posedness within the theory of maximal monotone graphs. For isotropic extension or compression, a semi-analytic solution of the quasi-linear viscoelastic problem is constructed under stress control. The equations are studied numerically with respect to monotone loading both with and without thresholding. In the example, the thresholding procedure ensures that the solution does not blow-up in finite time. [ABSTRACT FROM AUTHOR]

A serious problem in computer simulation of a stress state of polymer structures is to validate the mathematical description of the mechanical properties of materials. The structural model of a viscoelastic material has a number of advantages in describing both the rheology of a material and strain curves of it. In this model, a material is described as a structure consisting of several elements with relatively simple rheological properties. Reproduction of a complex behavior of a material under alternating non-isothermal loading is provided through the interaction of these simple elements. A technique developed in this work for modeling a viscoelastic material is intended for strength calculations of structures made of materials operating under conditions of a long-term repetitive thermomechanical impact using the finite element method. The application of the developed procedure to a polymeric material, polymethyl methacrylate (PMMA), is considered. The results of testing this material under uniaxial compression at a constant temperature are presented. The methodology and results of identification of the developed structural model using a specialized software code are described. Formulas are obtained for the approximation of the deformation characteristics of the material at a constant strain rate and for the time dependence of the deformation of the material during its holding at a constant stress level. Approximation is an important stage in the validation of the material model, which facilitates the systematization of the initial experimental data and their further mathematical processing. The best approximation of the deformation characteristics of a viscoelastic material is provided by a hyperbolic tangent function, whereas a logarithmic function provides the best results for the deformation upon holding. Further construction of the structural model was performed by selecting sequential parameters of bilinear rheological functions of the separate elements of the model and by iterative refinement of these parameters. The simulation results are compared with the experiments performed at different strain rates and with holding at different stress levels. In this work, the results of the initial stage of the performed experimental and theoretical studies are presented. [ABSTRACT FROM AUTHOR]

A unified approach to the analysis of the nonstationary vibrations of piezoelectric ceramic plane layers, cylinders, and spheres taking into account the functional inhomogeneity and viscoelasticity of the material is proposed. The standard model of vibration damping and the Kelvin–Voigt viscoelastic model are considered. The proposed approach makes it possible to study the transition of the transducer to a static state or to a steady-state vibration mode under nonstationary perturbations. The effect of functional inhomogeneity on the nonstationary vibrations of a piezoelectric element is analyzed. The damping of the vibrations and viscoelastic axisymmetric vibrations of a radially polarized cylinder under electrical and mechanical perturbation using the Heaviside function is calculated. The dynamics of damping is analyzed, and the obtained results are compared with the static solution to validate the results. The generation of voltage by a piezoceramic cylinder under mechanical axisymmetric loading is also studied taking into account the viscoelastic properties of the material. It was found that the time to reach the steady-state mode for mechanical and electrical loads is almost the same. [ABSTRACT FROM AUTHOR]

The salient viscoelastic properties of aramid textile materials and methods of their study are described. Preliminary information about the viscoelasticity of the studied materials can be obtained from experimental tensile diagrams and, for a more detailed study of viscoelastic properties, mathematical modeling of relaxation or deformation processes is necessary. [ABSTRACT FROM AUTHOR]

There is a growing need to develop accurate nonlinear viscoelastic material models and tools that could describe the complex nonlinear behavior of being developed composite material systems at their simulations at high loads and temperatures or to move the industry towards more sustainable bio-based alternatives. Developing such models in 3D formulation for materials with changing material state due to physical aging, change of crystallinity or degree of cure is also imperative since the loading is mostly multiaxial in real-live applications and manufacturing processes. The present paper contains the derivation of two material models with varying complexity and accuracy. The incremental procedure for implementation of the nonlinear viscoelastic material model within the numerical analysis was presented. Two relatively simple simulations with the incremental methodology developed were performed, namely triaxial mechanical loading and thermal stress development during the manufacturing process. The results obtained showed significant differences between stresses calculated using 1D and 3D simulations. Significantly higher stresses obtained in 3D simulations demonstrated the necessity of 3D models. [ABSTRACT FROM AUTHOR]

In this paper, shaped fibers which are especially useful for radiative cooling have been firstly deposited by Electrohydrodynamic direct-writing based on Micro-Weissenberg effect (MWE). At first, The process of pumping viscoelastic fluids (polyethylene oxide) in micro-tube (non-circle nozzle) based on Micro-Weissenberg effect has been studied to reveal the mechanism of Micro-Weissenberg effect. We have found that the pumping based on MWE have obvious periodic fluctuation when the flow rate is small. Then the process of steel pins without small diameter pipes pumping viscoelastic fluid which is a continuous, less wall and controllable pumping manner have been studied in detail. It is found that the pumping based on MWE mainly stem from an interesting capillarity between two pins and the viscoelasticity of fluid. So compare with the traditional Electrohydrodynamic direct-writing, the shaped fibers have been more easily deposited by Electrohydrodynamic direct-writing based on MWE due to the capillarity and the shear thinning in Micro-Weissenberg effect. [ABSTRACT FROM AUTHOR]

Issues with evaluation of the degree of reliability of the mathematical modeling and prediction of viscoelastic and plastic processes of polymeric textile materials based on integral adequacy criteria of mathematical modeling of the viscoelasticity of these materials are examined. The criteria were an evaluation of deviations of integral convolutions of polymeric textile relaxation and creep nuclei from the theoretically based unit value. The less the integral convolutions differed from the unit value, the greater the adequacy of the developed mathematical models of relaxation and creep were, meaning that the numerical prediction of the viscoelastic and plastic processes of the studied polymeric textiles were more accurate. [ABSTRACT FROM AUTHOR]

Polymers are often used for enhanced oil recovery (EOR) and in situ site remediation. Polymers with high specific surface area and porosity can be used to remove contaminants from water for water remediation. The additional viscosity improves mobility control as compared to water. Polymers are also non-Newtonian (having shear-dependent viscosity) and might be viscoelastic. However, the effects of non-Newtonian rheology on fracture opening and fluid leakoff morphology is largely unexplored as compared to Newtonian fluids. In this study, we inject Newtonian, shear thinning and viscoelastic fluids into a sand-filled Hele–Shaw cell to study fluid invasion and fracturing patterns of sand and injected fluids. The experimental results demonstrate complex fracture patterns depending on injection velocity, fluid viscosity, boundary conditions, and fluid rheology. We use digital image correlation to demonstrate that the fracturing mechanism in sand is associated with shear dilation at the tip of fracture and fracture offshoots. The presence of stress-free boundaries causes the fracture opening to be nearly perpendicular to the minimum principal stress, and the peak injection pressure to increase as compared to the fixed–displacement boundaries. We observe two fluid flow regimes: capillary-dominated flow and viscous drag-dominated flow. When compared with Newtonian fluids, shear-thinning fluids cause thinner fracture openings and more leakoff. Injecting viscoelastic fluid into sand creates a more irregular leakoff pattern, with fluid sometimes leaking mostly at the fracture tip for high injection rates. Finally, we propose a dimensionless parameter to quantify fluid invasion and fracturing patterns of sand and injected fluids and show that the ratio of fracture to leakoff area increases with the parameter for inelastic fluids. However, we observe the opposite behavior for viscoelastic fluids, which we attribute to shear-thickening behavior flowing through variable pore throats. Highlights: There is a lack of research on the injection of viscoelastic polymer into sand. This paper studies the injection of non-Newtonian polymers into sand. Polymer injectivity is sometimes higher than expected due to polymer-driven fractures. This paper quantifies the fracture and leakoff of power–law non-Newtonian polymers. This study shows for first time shear thickening of viscoelastic polymers in a fractured porous medium and demonstrate the leakoff morphology of viscoelastic fluids. [ABSTRACT FROM AUTHOR]

Background: Mechanical characterization of materials that solely relies on global responses may overlook important local behavior that significantly affects the characterization of material properties. Field displacements such as from digital image correlation (DIC) can provide high-fidelity experimental data, which combined with finite element method (FEM) can form DIC-FEM inverse method that can better account for complex mechanical properties of materials. Despite its capability, the DIC-FEM inverse method has been mainly applied to an elastic-dominant regime even though inelastic deformation is important in many engineering materials. Specifically, the DIC-FEM inverse method has not been fully extended to viscoelastic materials due to the complex representation of the time-dependent modulus. Objective: This study aimed at establishing a DIC-FEM inverse framework to identify constitutive properties of homogeneous elastic and viscoelastic materials. Methods: Two example materials (i.e., polyetheretherketone (PEEK) and a viscoelastic fine aggregate matrix (FAM) with a bituminous binder) were selected for the elastic and viscoelastic investigation, respectively. Both were experimentally tested using three-point bending incorporated with DIC. FEM simulated the experiment and the Nelder-Mead nonlinear optimization algorithm was implemented to solve the inverse problem. Results: The DIC-FEM inverse method successfully identified Young's modulus of an example linear elastic PEEK and the linear viscoelastic relaxation modulus of FAM. Conclusions: The resulting DIC-FEM inverse method is applicable to various materials with inelastic deformation and can be extended to localized behavior induced by microstructure heterogeneity and fracture. [ABSTRACT FROM AUTHOR]

The 3D nonaxisymmetric local stability loss problem is studied for a hollow cylinder, made of a viscoelastic composite material, under the axial compression. The criterion of an infinitesimal initial imperfection is employed, and the evolution of this imperfection is investigated by 3D geometrically nonlinear exact equations of viscoelasticity theory. The corresponding nonlinear problem is solved by the boundary perturbation method. The material of the cylinder is modeled as a viscoelastic transversely isotropic medium. Numerical results for the critical time and critical compressive forces are presented, discussed, and compared with those obtained by approximate shell theories. [ABSTRACT FROM AUTHOR]

In this work, the geometry-constraint-based non-ordinary state-based peridynamic (GC-NOSBPD) model is further generalized to study the mechanical responses and rate-dependent fracture behaviors of viscoelastic materials. The viscoelasticity is generated by directly incorporating the classical viscoelastic constitutive relation in the form of the Generalized Maxwell Model, which is expressed as Prony-series type expansion, into the GC-NOSBPD framework. A strain-based scalar damage variable only driven by elastic energy, whose evolution follows a rate-independent law, is proposed to describe the progressive growth of the mode-I crack. Combining the rate-independent damage variable and viscoelasticity results in a rate-dependent damage model in the hypothesis that the fracture of viscoelastic material is driven by both elastic and viscous components of the energy. The fidelity of this model is established in the absence of damage by comparison with the benchmark solution for the viscoelastic response of a 3D bar subjected to various load histories. Further, the proposed model is employed to simulate two quasi-static fracture tests under various loading rates: a three-point bend fracture test for concrete and a double-cantilever-beam delamination test for rubber interface. These numerical results agree well with experimental tests, showing that the proposed model can effectively capture rate-dependent crack propagation. [ABSTRACT FROM AUTHOR]

Rutting resistance is an important consideration for paving asphalt mixes. The cause of rutting is a shear strain in the asphalt pavement structure. Here, the rutting behavior of asphalt pavements was evaluated through laboratory simulations using the Hamburg Wheel-Tracking Test (HWTT), UK Wheel-Tracking Test (UKWTT), and Scaled Accelerated Load Simulator (SALS) test. The correlation between the three simulation tests was analyzed to determine the conversion factor (CF). Two parameters of temperature and speed of simulation testing were evaluated in this study. Subsequently, the representative frequency and dynamic modulus were calculated with consideration of viscoelasticity and time-temperature superposition. Using logical analysis, CF between the three simulation tests was validated. The results showed that the full-scale test yielded the highest stiffness modulus of 4,015 MPa, and the UKWTT yielded the lowest stiffness modulus of 1,857 MPa at 60 °C. From the HWTT results, it was found that the impact of moisture damage at 40 °C is not substantial compared to that at 50 °C. The conversion factor of HWTT at 40 °C, HWTT at 50 °C and UKWTT at 60 °C to SALS were 0.92, 0.74, and 0.63, respectively. Furthermore, the similar rutting performance among SALS, HWTT at 40 °C in dry and wet conditions, and HWTT at 50 °C in dry condition can be observed when the CF is applied. Lastly, the effectiveness of the conversion factor is diminished with increasing rutting damage. [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]

Viscoelasticity is a natural property of biological tissue that is often used as a diagnostic parameter of cancer diagnosis. Recently, it was discovered that the fractional calculus accurately describes the experimental effects of viscoelastic materials. In this work, the model of the thermo-viscoelasticity theory of fractional dual-phase-lag heat conduction law with rheological properties of the volume is constructed to investigate one-dimensional bioheat transfer and heat-induced mechanical response in human skin tissue. The model is applied to the one-dimensional problem of the skin tissue layer with an arbitrary thickness. The bounding plane of the skin tissue is subjected to three different types of thermal loading. The method of transforming Laplace was used and the reversal was measured using the Tzuo process. The influences of fractional dual-phase-lag relaxation parameters and rheological properties of the volume on the distributions of temperature, displacement and stress are obtained and illustrated graphically. [ABSTRACT FROM AUTHOR]

To gain a complete view on the unique spatial attenuation phenomenon arising from the periodicity and the material viscoelasticity of the two-dimensional phononic crystals with finite out-of-plane extension, this paper presents a theoretical study of the viscoelastic phononic crystal slabs to investigate the wave transmission characteristics in terms of the dispersion relations for the propagating, evanescent, and complex modes. A numerical approach based on the theory of three-dimensional elasticity is proposed to eliminate the restrictions of plane analysis and to obtain the complex band diagrams using the wave expansion functions combined with the finite discretization technique. This formulation allows one to perform the simulations associated with the nonlinear frequency-dependent viscoelastic property which is accurately described by a generalized Maxwell model in this work. Numerical results are presented to show the validity of the established model and to reveal the dissipation mechanisms inside and outside the band gaps as well as to investigate the effects induced by the material viscoelasticity on the attenuation diagrams. Furthermore, the influences of the out-of-plane extension, the geometrical size and the shape of the etcfhed holes are detailed discussed to obtain thorough understandings of such a finite solid viscoelastic periodic lattice which is indispensable to practical applications. [ABSTRACT FROM AUTHOR]

The mechanism of adhesive friction between viscoelastic materials is a key question. In this study, the friction process of the adhesive interface between a friction lining and a wire rope is dynamically observed in real time to analyze the adhesion hysteresis friction intuitively and quantitatively. The adhesion is determined by the state of motion, while the relative displacement of the wire rope and lining is used to find the magnitude of the adhesive friction. The hysteresis friction is reflected by the internal deformation of the lining. The magnitude of the hysteresis friction is determined by the displacement difference (Δx) in the sliding direction of two marked points at different distances from the contact surface. The results show that the adhesion friction is proportional to the loss modulus and the hysteresis friction is proportional to the ratio of the loss modulus to the square of the storage modulus (E″/(E′2)). The frictional vibration first decreases and then increases with the increase in pressure. The K25 lining has the highest adhesion hysteresis friction and minimal frictional vibration. The result provides a simple and intuitive method for research into the friction transmission and vibration of viscoelastic materials. [ABSTRACT FROM AUTHOR]

Polyamide exhibits hygroscopic nature and can absorb up to 10% of moisture relative to its dry weight. The absorbed moisture increases the mobility of the molecular chains and causes a reduction in the glass transition temperature. Thus, depending on the moisture distribution, a polyamide component can show different stiffness and relaxation times. Moreover, the moisture distribution also depends on the mechanical loading of the material as the volumetric deformation results in a change of the available free volume for the moisture. Thus, a strongly coupled model is required to describe the material behaviour. In this work, a thermodynamically consistent coupled model within the framework of mixture theory is developed. The mechanical deformation of polyamide 6 (PA6) is based on a linear viscoelastic material model, and the moisture transport is based on a nonlinear diffusion model. The stiffness and the relaxation time of the viscoelastic model change with the moisture concentration. Furthermore, the moisture transport is affected by the pressure gradient generated by the mechanical loading of the material. This strongly coupled model has been implemented using the finite element method, and simulation results are presented for a three-point bending experiment. [ABSTRACT FROM AUTHOR]

The phase-field approach has proven to be a powerful tool for the prediction of crack phenomena. When it is applied to inelastic materials, it is crucial to adequately account for the coupling between dissipative mechanisms present in the bulk and fracture. In this contribution, we propose a unified phase-field model for fracture of viscoelastic materials. The formulation is characterized by the pseudo-energy functional which consists of free energy and dissipation due to fracture. The free energy includes a contribution which is related to viscous dissipation that plays an essential role in coupling the phase-field and the viscous internal variables. The governing equations for the phase-field and the viscous internal variables are deduced in a consistent thermodynamic manner from the pseudo-energy functional. The resulting model establishes a two-way coupling between crack phase-field and relaxation mechanisms, i.e. viscous internal variables explicitly enter the evolution of phase-field and vice versa. Depending on the specific choice of the model parameters, it has flexibility in capturing the possible coupled responses, and the approaches of recently published formulations are obtained as limiting cases. By means of a numerical study of monotonically increasing load, creep and relaxation phenomena, rate-dependency of failure in viscoelastic materials is analysed and modelling assumptions of the present formulation are discussed. [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]

Passive particle manipulation using inertial and elasto-inertial microfluidics have received substantial interest in recent years and have found various applications in high throughput particle sorting and separation. For separation applications, elasto-inertial microfluidics has thus far been applied at substantial lower flow rates as compared to inertial microfluidics. In this work, we explore viscoelastic particle focusing and separation in spiral channels at two orders of magnitude higher Reynolds numbers than previously reported. We show that the balance between dominant inertial lift force, dean drag force and elastic force enables stable 3D particle focusing at dynamically high Reynolds numbers. Using a two-turn spiral, we show that particles, initially pinched towards the inner wall using an elasticity enhancer, PEO (polyethylene oxide), as sheath migrate towards the outer wall strictly based on size and can be effectively separated with high precision. As a proof of principle for high resolution particle separation, 15 µm particles were effectively separated from 10 µm particles. A separation efficiency of 98% for the 10 µm and 97% for the 15 µm particles was achieved. Furthermore, we demonstrate sheath-less, high throughput, separation using a novel integrated two-spiral device and achieved a separation efficiency of 89% for the 10 µm and 99% for the 15 µm particles at a sample flow rate of 1 mL/min—a throughput previously only reported for inertial microfluidics. We anticipate the ability to precisely control particles in 3D at extremely high flow rates will open up several applications, including the development of ultra-high throughput microflow cytometers and high-resolution separation of rare cells for point of care diagnostics. [ABSTRACT FROM AUTHOR]

Pavement analysis encompasses the use of different assumptions for material assessment that can in turn induce variations in the predicted pavement critical strains and affect the outcome of pavement evaluation. This research deals with the incorporation of mechanistic principles into asphalt pavements structural assessment, considering variable mechanical behavior (elastic and viscoelastic) for the Asphalt Concrete (AC) materials. A field experiment along a new asphalt pavement structure was performed including Non-Destructive Testing (NDT) and coring. The study focused on the tensile strains within the AC layers that usually trigger rehabilitation actions. For strain calculations, the standard practice of Multi-Layered Elastic Theory (MLET) and the rheological Huet-Sayegh model were both implemented into the analysis. Results indicated statistically significant discrepancies between elastic and viscoelastic calculations that may become considerable in terms of decision-making. Thus, pavement engineers should not proceed with the decision-making process based solely on a unique approach. In addition, the issue of performing a new pavement's evaluation based on the design assumptions was discussed. A substantial material differentiation pinpointed the need to extract cores in order to perform viscoelastic material characterization. Moving forward with a regression analysis, a practical approach was developed for viscoelastic strains prediction from NDT data in order to avoid extensive coring. Overall, the implementation of the framework at a new structure is grounded on that the methodology followed for pavement evaluation throughout its service life can predefine the way of decision-making in terms of consistently interpreting the analysis output and assessing future maintenance needs. [ABSTRACT FROM AUTHOR]

Reliable accelerated testing routines involving tests at enhanced temperatures are of paramount importance in developing viscoelastic models for polymers. The theoretical basis, the time-temperature superposition (TTS) principle, is used to construct master curves and temperature-dependent shift factor, which is the necessary information to simulate the material response in arbitrary temperature and strain regimes. The Dynamic Mechanical and Thermal Analysis (DMTA) TTS mode, being one of the most promising approaches in terms of time efficiency and maturity of the software, is compared in this paper with macrotests at enhanced temperatures in their ability to give reliable master curves. It is shown, comparing simulations with test data for a chosen epoxy polymer, that none of the three DMTA TTS mode-based attempts used (at different temperature steps during frequency scanning) was successful in predicting the epoxy behavior in tests. On the contrary, using one-hour macrotests at enhanced temperatures gives a viscoelastic model with a very good predicting accuracy. Simulations were performed using an incremental formulation of the previously published VisCoR model for linear viscoelastic materials. [ABSTRACT FROM AUTHOR]

We apply a quasistatic nonlinear model for nonsimple viscoelastic materials at a finite-strain setting in Kelvin's-Voigt's rheology to derive a viscoelastic plate model of von Kármán type. We start from time-discrete solutions to a model of three-dimensional viscoelasticity considered in Friedrich and Kružík (SIAM J Math Anal 50:4426–4456, 2018) where the viscosity stress tensor complies with the principle of time-continuous frame-indifference. Combining the derivation of nonlinear plate theory by Friesecke, James and Müller (Commun Pure Appl Math 55:1461–1506, 2002; Arch Ration Mech Anal 180:183–236, 2006), and the abstract theory of gradient flows in metric spaces by Sandier and Serfaty (Commun Pure Appl Math 57:1627–1672, 2004), we perform a dimension-reduction from three dimensions to two dimensions and identify weak solutions of viscoelastic form of von Kármán plates. [ABSTRACT FROM AUTHOR]

Here we consider a string composed by three different materials: thermo elastic, viscoelastic and elastic. Our main result is that the exponential stability depends on the position of each material. That is, we prove that the model is exponentially stable if and only if the viscoelastic material is not in the center of the string. Otherwise, there is not exponential stability and the corresponding semigroup also goes to zero, but now polynomially. [ABSTRACT FROM AUTHOR]

Viscoelastic polymer composites are widely used for vibration control in different fields of engineering like aerospace, mechanical, and structural engineering. The viscoelastic properties of these materials are strain rate-dependent and are highly related to frequency. Yet to date, less attention has been paid to quantifying the effects of these parameters and their interactions on damping properties and providing an approximation method for further applications. In the present research, a series of experimental tests was conducted on a viscoelastic material and the experimental data were numerically analyzed in detail. Sensitivity analyses are usually applied to quantify uncertainty using sampling techniques. However, in this study a method was proposed to derive a closed-form solution using the response surface function and a derivative-based global sensitivity analysis to evaluate the output contribution of each parameter. These effects were quantified and several approximation statistics were provided for future engineering implementations. The computational evaluation conducted in this study gives a detailed insight into the mechanical behavior of viscoelastic materials. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to characterisation of asphalt mixtures constitutive models, with application to pavement structures. It is well-known fact that temperature, frequency and time of loading have a great influence on the mechanical properties of bituminous mixtures. For this reason, the properties are usually presented in the frequency domain as complex numbers having real and imaginary parts. This convenient representation in terms of complex modulus and phase angle leads to the dynamic modulus master curve. The effective use of the theory of linear viscoelasticity to characterise constitutive model of asphaltic material is shown in this paper. Viscoelastic constitutive model is represented by a combination of rheological schemes, and its identification is based on both laboratory tests results and mixture composition. The temperature–frequency or temperature–time superposition principle being applied in order to produce master curves of mechanical properties is illustrated with real experimental data. Further, the process of identification of Huet–Sayegh parameters is carried out using best-fitting methods implemented in MATLAB. Fractional rheological model is used as it needs only a small number of elements to fully characterise the response of asphalt materials. [ABSTRACT FROM AUTHOR]

In this work, the capacity of the generalized fractional Maxwell (GFMM) and Kelvin-Voigt (GFKM) models for the interconversion of dynamic to static (creep and relaxation) functions, with regard to appropriate experimental data of various polymeric structures, is examined. The analysis is executed within the frame of linear viscoelasticity. Furthermore, a comparative study with the results produced by the implementation of the fractional Zener model has been performed. A good approximation of the generated viscoelastic functions by GFKM and GFMM model was postulated. Concerning the fractional Zener model, it can be extracted that its effectiveness to the interconversion of the viscoelastic functions is dependent on the specific material's viscoelastic response, and the wideness of the time/frequency region examined. It was found that the incorporation of a correction factor in the calculation procedure of the creep compliance function can result in significantly better results, regardless of the model used. Graphical abstract [ABSTRACT FROM AUTHOR]

This research study presents analytical solutions for the stresses and displacements around deeply buried non-circular tunnels, taking into account the viscoelasticity of the ground, and the sequential excavation of the tunnels' cross-sections. General initial far-field stress states are assumed, and the time-dependent pressures exerted at the internal tunnel boundaries are found to account for the support effects or water pressures of the hydraulic tunnels. Then, solutions are derived for tunnels with a time-varying sizes and/or shape, by assuming the time-dependent functions specified by the designers. The analytical solutions for the stresses and displacements around elliptical and square tunnels are specifically presented for linearly viscoelastic models using a Muskhelishvili complex variable method and Laplace transform techniques. For validation purposes, numerical analyses are performed for the excavations of elliptical and square tunnels in rock which are simulated by Poynting-Thomson or generalized Kelvin viscoelastic models. Good agreements are observed between the analytical and numerical results of this study. Then, parametric analyses are carried out in order to investigate the effects of the far-field shear stress, along with the distribution forms of the internal pressures, on the ground displacements and stresses. The proposed analytical solutions can be employed to accurately predict the stress concentrations, as well as the time-dependent displacements around deeply buried elliptical or square-shaped tunnels. Furthermore, it is confirmed that this study's described methodology may be potentially applied to obtain analytical solutions for other arbitrary shaped tunnels sequentially excavated in viscoelastic rock. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop a novel numerical modeling optimization technique and implement it with the boundary element method (BEM) based on convolution quadrature method for studying optimization of anisotropic viscoelastic porous permeable structures. After applying the quadrature rule to the discretized boundary integral equation, a time stepping procedure based on the use of the linear multistep method is obtained. To obtain anisotropic fundamental solutions, the calculation of a double integral should be performed, but it increases the total computation time in the BEM. In order to overcome this problem and improve the computational efficiency of the formulation, our new proposed BEM technique is implemented. The method of implicit differentiation with respect to design variables has been implemented to calculate the displacements and pore pressure design sensitivities, and the effects of viscosity on these sensitivities are discussed. The resulting topology optimization problem has been solved using the method of moving asymptotes algorithm with adjoint variable method to optimize material distribution and find the influence of viscosity on the optimal design. The validity, efficiency and accuracy of the proposed BEM technique were confirmed by comparing obtained results for elliptical sandwich structure and multi-well reservoir with the corresponding results of finite difference method, lattice Boltzmann method and finite element method, which are special cases of our general and complex problem. [ABSTRACT FROM AUTHOR]

Fractional derivative and WLF equation are effective in describing the dynamic behavior and time-temperature effect of viscoelastic damping materials, respectively. These approaches have essentially evolved from the viscoelastic constitutive behavior. Based on such intrinsic relation, a fractional time-temperature superposition principle model (FTTSPM) that integrates the fractional constitutive relation and WLF equation was proposed. The parameters of this model were determined by performing tensile and DMA tests, and the master curves at 5 °C constructed by FTTSPM and WLF equation were compared. The theoretical prediction over the extended frequency span as the master curves was made by using the fractional standard linear solid model (FSLSM) to validate FTTSPM. The numerical results show that FTTSPM conforms to the time-temperature superposition principle. The parameters α and B′ in this model denote the impact of the material and environment on the shifted factor, respectively. For the storage and loss modulus, the extended frequency obtained by FTTSPM is broader than that obtained by the WLF equation. Moreover, the evaluation of the storage and loss modulus by FTTSPM is much closer to the theoretical prediction compared with that by the WLF equation. Therefore, FTTSPM is a concise and experiment-based approach with a higher precision and greater frequency-extended capacity compared with the WLF equation. However, FTTSPM inevitably faces a vertical shift when non-thermo-rheologically simple materials are considered. The physical mechanism and practical application of FTTSPM will be examined in further research. [ABSTRACT FROM AUTHOR]

The dissipative characteristics of rubber-cord composites under the action of cyclic load considering the features of their self-heating have been experimentally investigated. Full-scale uniaxial tension experiments are performed on the plane specimens along the reinforcement fibers of the unidirectional rubber-cord composites. In compliance with the test results, stress-strain curves for the specimens are determined, which form the hysteresis loops under cyclic loading. The tensile testing of the specimens is performed under long-term cyclic loading using the experimental setup INSTRON ElectroPuls E3000 Test System. The process of significant self-heating of the specimens under their long-term cyclic deformation has been experimentally established and studied. Using the non-contact methods, the variation in the specimen temperature in time is measured. The mechanisms of their non-stationary heating are obtained, as well as the dependences of the stabilization temperature of the thermal state on the loading conditions. It has been determined that the area of hysteresis loops, which is formed when specimens undergo deformation in the temperature-stabilized state, depends nonlinearly on the amplitude of strains. The qualitative and quantitative dependences of the loss modulus, as well as the dissipation coefficients and relaxation times on the loading frequency, strain amplitude and temperature due to the material self-heating, are determined. The approximation dependences of the loss modulus of the composite on the loading frequency and self-heating temperature are constructed on the basis of the generalized three-parameter linear (Zener) model and the exponential temperature-dependent initial elastic modulus. [ABSTRACT FROM AUTHOR]

Impact of wall slip on the yield stress measurement is examined for capillary suspensions consisting of cocoa powder as the dispersed phase, vegetable oil as the continuous primary fluid, and water as the secondary fluid using smooth and serrated parallel plates. Using dynamic oscillatory measurements, we investigated the yielding behavior of this ternary solid-fluid-fluid system with varying particle volume fraction, ϕ, from 0.45 to 0.65 and varying water volume fraction, ϕw, from 0.02 to 0.08. Yield stress is defined as the maximum in the elastic stress (G′γ), which is obtained by plotting the product of elastic modulus (G′) and strain amplitude (γ) as a function of applied strain amplitude. With serrated plates, which offer minimal slippage, capillary suspensions with ϕ ≥ 0.45 and a fixed ϕw = 0.06 showed a two-step yielding behavior as indicated by two peaks in the plots of elastic stress as a function of strain amplitude. On the other hand with smooth plates, the capillary suspensions showed strong evidence of wall slip as evident by the presence of three distinct peaks and lowered first yield stresses for all ϕ and ϕw. These results can be interpreted based on the fact that a particle-depleted layer, which is known to be responsible for slip, is present in the vicinity of the smooth surfaces. The slip layer presents itself as an additional “pseudo-microstructure” (characteristic length scale) besides the two microstructures, aqueous bridges and solid particle agglomerates, that may occur in the system. With serrated plates, both the yield stresses (σ1σ2) and storage moduli plateau at lower strain (before the first yield point) and at higher strain (before the second yield point) (Gp1′, Gp2′) were found to increase with ϕ (at a fixed ϕw = 0.06) following power-law dependences. Similarly with increasing ϕw (0.02 - 0.08) at a fixed ϕ = 0.62, the system behaved as a solid-like material in a jammed state with particles strongly held together as manifested by rapidly increasing σ1 and σ2. The usage of smooth surfaces primarily affected σ1 which was reflected by an approximately 70-90% decrement in the measured σ1 for all values of ϕ. By contrast, σ2 and Gp2′ were found to be unaffected as shown by close agreement of values obtained using serrated geometry due to vanishing slip layers at higher strain amplitudes. [ABSTRACT FROM AUTHOR]

The opening of a mode I crack in a polymeric composite with viscoelastic properties subject to tensile loads is solved within the framework of nonlinear fracture mechanics. The modeling of the viscoelastic properties of the composite and crack is analyzed. Techniques for studying the deformation of a cracked composite and determining safe loads under which the crack is at rest are proposed. The efficiency of the techniques is evaluated by comparing the computed results with experimental data for polymeric composites used in modern aircraft. [ABSTRACT FROM AUTHOR]

In an elastic medium, it was proved that the stiffness tensor is symmetric with respect to the exchange of the first pair of indices and the second pair of indices, but the proof does not apply to a viscoelastic medium. In order to indicate which phenomena could be observed in the wave field if the stiffness matrix were non-symmetric, we propose the frequency-domain ray series for viscoelastic waves with a non-symmetric stiffness tensor in this paper. [ABSTRACT FROM AUTHOR]

A constitutive model based on the continuum mechanics theory has been developed which represents interlamellar cohesion, regional variation of collagen fibril density, 3D anisotropy and both age-related viscoelastic and hyperelastic stiffening behaviour of the human cornea. Experimental data gathered from a number of previous studies on 48 ex vivo human cornea (inflation and shear tests) enabled calibration of the constitutive model by numerical analysis. Wide-angle X-ray scattering and electron microscopy provided measured data which quantify microstructural arrangements associated with stiffness. The present study measures stiffness parallel to the lamellae of the cornea which approximately doubles with an increase in strain rate from 0.5 to 5%/min, while the underlying stromal matrix provides a stiffness 2–3 orders of magnitude lower than the lamellae. The model has been simultaneously calibrated to within 3% error across three age groups ranging from 50 to 95 years and three strain rates across the two loading scenarios. Age and strain-rate-dependent material coefficients allow numerical simulation under varying loading scenarios for an individual patient with material stiffness approximated by their age. This present study addresses a significant gap in numerical representation of the cornea and has great potential in daily clinical practice for the planning and optimisation of corrective procedures and in preclinical optimisation of diagnostic procedures. [ABSTRACT FROM AUTHOR]

In the present paper, a methodology for complete characterization of linear isotropic viscoelastic material with spherical instrumented indentation test is proposed. The developed method allows for measuring two independent viscoelastic functions, shear relaxation modulus and time-dependent Poisson’s ratio, from the indentation test data obtained at non-decreasing loading, but otherwise arbitrary. Finite element modelling (FEM) is relied upon for validating the proposed methodology and for quantifying the influence of experimental variables on the measurements accuracy. Spherical indentation experiments are performed on several viscoelastic materials: polyoxymethylene, bitumen and bitumen-filler mastics. The viscoelastic material functions obtained with the indentation tests are compared with the corresponding results from the standard mechanical tests. Numerical and experimental results presented indicate that the methodology proposed allows mitigating the machine compliance and loading rate effects on the accuracy of the viscoelastic indentation tests. [ABSTRACT FROM AUTHOR]

To explain the hygrothermal recovery (HTR) behavior of tension wood (TW) from the physical and chemical point of view in relation to the time, species and microfibril angle, a theoretical discussion using an analytical one-dimensional viscoelastic modeling was made. The chosen model includes an elastic element, a deformation mechanism and two viscoelastic elements called also as Kelvin-Voigt model. In this analysis, a top-down approach between the model and the experimental data was introduced to find the realistic parameters for the model. It enables us to fit the model to the HTR experimental data for three wood species: konara oak ( Quercus serrata Murray), urihada maple ( Acer rufinerve Siebold et Zucc.) and keyaki wood ( Zelkova serrata Makino). The fitted experimental data show that the two compliances of the two viscoelastic elements are the most important parameters that explain the evolution of TW longitudinal strain during the thermal treatment. [ABSTRACT FROM AUTHOR]

This article presents vibration characteristics of a piezoelectric viscoelastic nanoplate under various boundary conditions embedded in a visco-Pasternak's medium using nonlocal plate theory. The piezo-hygrothermal effects are all included. The hygrothermal piezoelectric nanoplate is made of orthotropic viscoelastic material. Also, the visco-Pasternak's medium is modeled according to a Kelvin-Voigt foundation. A Two-variable sinusoidal shear deformation plate theory is presented. The imaginary and real parts of the eigenfrequency of piezoelectric viscoelastic nanoplates which are associated with viscoelastic foundation, nonlocal parameter, as well as the viscoelastic structural damping coefficient, are obtained. The effects of other parameters such as aspect ratio, side-to-thickness ratio, temperature change, and moisture concentration are all investigated. The predicted results are compared with the corresponding ones in the literature to check their validation. Additional results are presented and suitable discussions are made. [ABSTRACT FROM AUTHOR]

The problem of a two-dimensional steady flow of a second-grade fluid in a converging porous channel is considered. It is assumed that the fluid is injected into the channel through one wall and sucked from the channel through the other wall at the same velocity, which is inversely proportional to the distance along the wall from the channel origin. The equations governing the flow are reduced to ordinary differential equations. The boundary-value problem described by the latter equations is solved by the homotopy perturbation method. The effects of the Reynolds and crossflow Reynolds number on the flow characteristics are examined. [ABSTRACT FROM AUTHOR]

The present paper is the second part of a twofold work, whose first part is reported in Artioli et al. (Comput Mech, 2017. doi:), concerning a newly developed Virtual element method (VEM) for 2D continuum problems. The first part of the work proposed a study for linear elastic problem. The aim of this part is to explore the features of the VEM formulation when material nonlinearity is considered, showing that the accuracy and easiness of implementation discovered in the analysis inherent to the first part of the work are still retained. Three different nonlinear constitutive laws are considered in the VEM formulation. In particular, the generalized viscoelastic model, the classical Mises plasticity with isotropic/kinematic hardening and a shape memory alloy constitutive law are implemented. The versatility with respect to all the considered nonlinear material constitutive laws is demonstrated through several numerical examples, also remarking that the proposed 2D VEM formulation can be straightforwardly implemented as in a standard nonlinear structural finite element method framework. [ABSTRACT FROM AUTHOR]

A viscoelastic model is developed for a dissipative Thin spherical dielectric elastomer actuator (TSDEA), with which the air-coupled effect and the ambient pressure effect are considered. The evolution equation is constructed by using the rheological model and is solved by employing the improved Euler method. The sealed air in the TSDEA is governed by the ideal gas state equation. Numerical results show that the air-coupled effect is helpful for evolving into the stable state. It also shows that the ambient pressure and the loading parameters play an important role on the temporal evolution behavior of the TSDEA. The TSDEA can evolve into a much larger size configuration in a low ambient pressure environment than that in a high ambient pressure environment. The model can be employed to analyze or predict the viscoelastic behaviors of a TSDEA. [ABSTRACT FROM AUTHOR]

Electrophoretically deposited (EPD) lithium ferrophosphate (LFP) electrodes (LiFePO) containing either soft Mg(OH) or rigid PVdF binders have been fabricated and tested in LiSO aqueous solution. The use of Electrochemical Quartz-Crystal Microbalance with dissipation monitoring (EQCM-D) was shown to be extremely advantageous to distinguish between the effectively viscoelastic and rigid states of LFP and LFP/PVdF electrodes, respectively, based already on the raw EQCM-D (i.e. recording resonant frequency and resonance width changes of the electrode on multiple overtone orders). The approach that we developed for testing composite battery and supercapacitor electrodes is quite general, and includes mechanical characterizations of the electrodes in air, in contact with liquids and electrolyte solutions, and most importantly, during combined electrochemical and mechanical characterization of battery electrodes subjected to Li-ions insertion/extraction. A new theory of hydrodynamic admittance of porous semispherical bumps has been developed and successfully applied for the characterization of rigid porous LFP/PVdF composite electrode in its both intercalated and deintercalated states. We show that the extended Voight-type viscoelastic model describes quantitatively the intercalated and deintercalated states of LFP electrode coating containing soft Mg(OH) binder. The approach based on non-gravimetric application of EQCM-D developed in this work is unique and quite promising for in-situ mechanical characterization of a large variety of battery and supercapacitor electrodes for energy-storage devices. [ABSTRACT FROM AUTHOR]

Novel viscoelastic self-diverting acid (VDA) systems with and without cosurfactant (sodium dodecylbenzenesulfonate, SDBS) added to enhance reaction retardation and to improve the conventional VDA system are studied. The novel system viscosifies at a pH of ~0.6 and attains a viscosity of ~500 mPa·s. The system without added SDBS viscosifies at a pH of ~2.2 and reaches a final viscosity of 403 mPa·s. Studies of the limestone-acid reaction kinetics showed that the reaction rate fell from 1.37·10 mol/(cm·s) for 20 wt. % HCl solution to 13.2·10 and 6.5·10 mol/(cm·s) for VDA solutions without and with added SDBS, respectively. The reaction rate constants (k) for the negative sample control and VDA systems I and II were 1.0740·10 (mol/cm)·(cm/s), 5.5221·10 (mol/cm)·(cm/s), and 6.3154·10 (mol/cm)·(cm/s), respectively. A dual-core flow test showed that wormholes were produced in both cores for the VDA systems rather than a large single channel in a high-permeability core when 20 wt.% HCl solution is used. Thus, a smaller volume of SDBS is needed for flow formation when VDA solution is added. The studies revealed that the novel VDA system retards reaction considerably, improves acid diversion, and has tremendous potential for field applications. [ABSTRACT FROM AUTHOR]

This work studies the influence of synthesis variables on the lineal viscoelastic properties of elastomers filled with soft magnetic particles. Three matrices [natural rubber (NR), high-temperature vulcanising silicone rubber (HTV-SR), and room-temperature vulcanising (RTV-SR)] and three volumetric particle contents (0%, 15%, and 30%) were studied. Anisotropic samples were synthesised with a softer matrix to obtain a larger magnetorheological (MR) effect, and the variation of their properties under an external magnetic field was examined. All samples were characterised within the lineal viscoelastic (LVE) region using a rheometer, because the MR effect is larger within this region. The influence of the matrix, particle content, and pre-structure on the viscoelastic properties of the synthesised samples was studied. The storage and loss modulus increased with the frequency owing to the viscoelastic behaviour of an elastomer in the rubbery phase. Both moduli also increased with the filler content. The influence of the filler is dependent on the matrix, and the maximum variation was seen in the NR-based samples. However, the maximum MR effect was seen in the samples with a softer matrix, and the effect was enhanced in the anisotropic samples. In this work, the MR effect on the loss modulus was studied, and the tendencies were found to be similar to those of the storage modulus. The main contribution of this work is that all dynamic behaviour results were comparable because all synthesis variables and characterisation conditions were identical. Therefore, how the particle content, frequency, and magnetic field affects each matrix can be studied. [ABSTRACT FROM AUTHOR]

The present study aims to study the propagation of Rayleigh-type wave in a layer, composed of isotropic viscoelastic material of Voigt type, with the effect of yielding base and rigid base in two distinct cases. With the aid of an analytical treatment, closed-form expressions of phase velocity and damped velocity for both the cases are deduced. As a special case of the problem it is found that obtained results are in good agreement with the established standard results existing in the literature. It is established through the study that volume-viscoelastic and shear-viscoelastic material parameter and yielding parameter have significant effect on phase and damped velocities of Rayleigh-type wave in both the cases. Numerical calculations and graphical illustration have been carried out for both the considered cases in the presence and the absence of viscoelasticity. A comparative study has been performed to analyse the effect of layer with yielding base, traction-free base and rigid base on the phase and damped velocities of Rayleigh-type wave. [ABSTRACT FROM AUTHOR]

Experimental observations have shown that most of plant fibres are characterised by an intricate structure, morphology and organisation. This complex geometrical characteristics may affect the mechanical behaviour of this kind of natural fibres and contribute to the high variability of their mechanical properties. So, this study proposes a numerical investigation on the relationship between the cross-sectional shape of primary hemp bast fibres and their tensile behaviour. A 3D viscoelastic model based on finite element method is used for this study. Real and elliptical simplified cross-sectional shapes are considered. Results of the tensile test simulations clearly show the strong influence of the degree of ellipticity on the tensile response of the fibre, and more exactly on the shape of the nonlinearity of the response. Results also show that this morphologic effect is strongly related and coupled to structural parameters and physical mechanisms, such as the cellulose microfibrils angle and the viscoelastic behaviour of the material of the fibre wall. Geometric issues could then contribute to explain the different types of tensile behaviour experimentally observed and deserve to be taken into account in plant fibre models. [ABSTRACT FROM AUTHOR]

The paper deals with an axially moving viscoelastic structure modeled as an Euler-Bernoulli beam. The aim is to suppress the transversal displacement (transversal vibrations) that occur during the axial motion of the beam. It is assumed that the beam is moving with a constant axial speed and it is subject to a nonlinear force at the right boundary. We prove that when the axial speed of the beam is smaller than a critical value, the dissipation produced by the viscoelastic material is sufficient to suppress the transversal vibrations. It is shown that the rate of decay of the energy depends on the kernel which arise in the viscoelastic term. We consider a general kernel and notice that solutions cannot decay faster than the kernel. [ABSTRACT FROM AUTHOR]

The results of research into the viscoelastic properties and processes of mechanical relaxation of polyvinylchloride (PVC) containing Cu nanoparticles obtained by means of electroerosion crushing and electrohydraulic destruction of agglomerates of disperse Cu in the presence of an ultrasonic field are presented. It is shown that, in the case of longitudinal shear deformation at a frequency of 0.4 × 10 s over a wide range of temperatures and content of ingredients, viscoelastic phenomena depending on structural changes in the PVC system occur. An analysis of quantitative results of the elastic and viscoelastic deformation of a body is carried out taking into account the energy and entropy components of interaction of the polymer and filler at their interface. [ABSTRACT FROM AUTHOR]