Viscoelastic Material Properties Research Articles

Thermo-viscoelastic analysis of a composite disk under parabolic temperature distribution using the Rayleigh-Ritz Method with Trigonometric Ritz Functions

The study focuses on the thermo-viscoelastic behavior of a composite disk subjected to a parabolic temperature distribution. The analysis employs the Rayleigh-Ritz method, combined with trigonometric Ritz functions, to model the dynamic response of the disk. The key objective is to investigate how temperature variations and viscoelastic material properties influence the radial and tangential stresses and strains in the disk. The thermo-viscoelastic problem is formulated by considering the time-dependent evolution of stresses and strains, incorporating both thermal expansion and viscoelastic relaxation effects. The radial stress and tangential stress are expressed as functions of time, governed by the relaxation functions, respectively. These functions describe the material's viscoelastic behavior, while the thermal expansion coefficients account for temperature-induced strain variations. The parabolic temperature distribution introduces a spatially varying thermal load, which is integrated into the thermo-viscoelastic equations. The Rayleigh-Ritz method is used to discretize the problem, with trigonometric Ritz functions chosen to represent the spatial variation of stresses and strains. This approach allows for efficient computation of the disk's response while capturing the anisotropic and viscoelastic nature of the composite material. The results highlight the interplay between thermal effects and viscoelastic behavior in determining the stress and strain distributions. The parabolic temperature distribution leads to non-uniform thermal expansion, which interacts with the viscoelastic relaxation processes to produce complex stress patterns. The analysis provides insights into the time-dependent evolution of stresses and strains, offering a comprehensive understanding of the thermo-viscoelastic response of the composite disk under thermal loading.

Simplified Model for the Behaviour of Asphalt Mixtures Depending on the Time and the Frequency Domain.

Sigmoid functions are widely used for the description of viscoelastic material properties of asphalt mixtures. Unfortunately, there are still no known closed functions for describing connections among model parameters in the time and the frequency domains. In most cases, complicated interconversion methods are applied for the conversion of viscoelastic material properties. To solve this problem, an empirical material model with four parameters has been developed. Parameters of the model can be quickly determined in the frequency domain and can be used in an unchanged way for the description of the material behaviour of the asphalt mixture in the time domain. The new model starts from the mathematical formula of the Ramberg-Osgood material model (short form RAMBO) and its main advantage is that its parameters are totally independent. Model calculations have been performed for the determination of factors necessary for the interconversion in the time and the frequency domains, applying the approximate procedure of Ninomiya and Ferry. The analysis of data has indicated that the interconversion factors in the time and the frequency domains depend only on the slope of the new empirical model function. Consequently, there is no need for further calculations, since the RAMBO model parameters determined in the frequency domain provide an excellent characterisation of the analysed mixture in the time domain as well. The developed new empirical material model has been verified using laboratory data and exact numerical calculations.

Analysis of nonlinear behavior of viscoelastic damping in musical membranes using physics-informed self-organizing maps

This research offers a new analytical tool that unravels the nonlinear relation between the parameters of Viscoelastic Damping (VD) and the resulting frequency spectrum in musical membranes. Understanding how variations in VD parameters influence the resulting sounds is crucial for developing new tools for artistic expression and for designing musical instruments with distinct sound qualities. In the case of membranophones, the external damping is well understood, while the internal damping due to viscoelastic properties of materials remains unclear. In previous research, VD in musical membranes has been modeled using a Finite-Difference Time-Domain (FDTD) model. Nonetheless, analyzing the complex relationships between the large parameter space of the model and the nonlinear behavior of VD is a challenging task. This study addresses this analysis through physics-based machine learning. We employed a FDTD model of a viscoelastically damped membrane to create a physics-informed dataset, which we subsequently analyzed using Self-Organizing Maps (SOMs). Our findings reveal that the damping coefficient is the primary criterion when clustering the data. Furthermore, we found the internal structure of the cluster to depend on the rate of decay of the memory effect, i.e., the rate at which the energy introduced back into the system decreases. The study also demonstrates the benefits of using principal component analysis for the SOM initialization.

Sensitivity of Lamb waves in viscoelastic polymer plates to surface contamination.

Detecting surface contamination on thin thermoformed polymer plates is a critical issue for various industrial applications. Lamb waves offer a promising solution, though their effectiveness is challenged by the strong attenuation and anisotropy of the polymer plates. This issue is addressed in the context of a calcium carbonate (CaCO3) layer deposited on a polypropylene (PP) plate. First, the viscoelastic properties of the PP material are determined using a genetic algorithm inversion of data measured with a scanning laser vibrometer. Second, using a bi-layer plate model, the elastic properties and thickness of the CaCO3 layer are estimated. Based on the model, the sensitivity analysis is performed, demonstrating considerable effectiveness of the A1 Lamb mode in detecting thin layers of CaCO3 compared to Lamb modes A0 and S0. Finally, a direct application of this work is illustrated through in-situ monitoring of CaCO3 contaminants using a straightforward inter-transducer measurement.

Fractional Order Kelvin-Voigt Constitutive Model and Dynamic Damping Characteristics of Viscoelastic Materials

Viscoelastic damping materials are often under complex service conditions. To precisely characterize its dynamic damping properties, based on fractional calculus and viscoelastic theory, considering the periodic characteristics of viscoelastic materials, the distributed fractional order Kelvin-Voigt constitutive model (DFKV) was constructed. The model accuracy was validated by quasi-static experiments. The dynamic modulus expressions were derived, and the model parametric feature analysis was carried out. Dynamic Mechanical Analysis (DMA) and Separate Hopkinson Pressure Bar (SHPB) experiments were performed with silicone rubber as the subject. The results show that the silicone rubber has an obvious temperature and frequency dependence, and it has a strong strain rate correlation considering that the strain rate effect indexes that are under high strain is 29.331. At the same time, clearly the viscoelastic dynamic constitutive behavior has phased characteristics that are in line with the scientific assumption of the distribution order. The fitting accuracy of DFKV model is higher than the existing contrast models, which reflects DFKV model and favorably represents the dynamic mechanical properties of viscoelastic materials under wide temperature, frequency and strain rate. The model is highly accurate, has fewer parameters, and the physical meaning of its parameters is clearer. It can provide a theoretical reference for the research and design of viscoelastic damping materials.

Organic-Inorganic Hybrid Ladder-like Polysilsesquioxanes as Compatibilized Nanofiller for Nanocomposite Materials.

Nanocomposite materials composed of an organic matrix and an inorganic nanofiller have been the subject of intense research in recent years. Indeed, the synergy between these two phases confers improved properties thanks to an increased surface-volume ratio, which reinforces the interactions between the particles and the polymer matrix. These interactions depend on many factors such as the shape, size and dispersion of the nanoobjects. Polysilsesquioxanes (PSQs) are a silicon polymer family that offers different sizes, shapes and structures and possesses ceramics properties (i.e., high thermal and/or oxidative resistance and high chain rigidity), thanks to the siloxane backbone. In this article, we propose to incorporate polymer-grafted ladder polysilsesquioxanes (LPSQs) as nanofillers in thermoplastic matrices. Chloride-functionalized LPSQs were synthesized from two different precursors and thoroughly characterized by 1H, 13C and 29Si NMR, as well as by SEC and WAXS. The well-defined LPSQ was then converted into an azide analog. The resulting hybrid material was functionalized with poly(ethylene glycol) (PEG) chains and incorporated into poly(ethylene oxide) or poly(methyl methacrylate) matrices. We found that the viscoelastic properties of the nanocomposite materials were impacted by plasticizing or the reinforcement effect depending on the grafted PEG chain length.

Response Analysis and Vibration Suppression of Fractional Viscoelastic Shape Memory Alloy Spring Oscillator Under Harmonic Excitation

This study investigates the dynamic behavior and vibration mitigation of a fractional single-degree-of-freedom (SDOF) viscoelastic shape memory alloy spring oscillator system subjected to harmonic external forces. A fractional derivative approach is employed to characterize the viscoelastic properties of shape memory alloy materials, leading to the development of a novel fractional viscoelastic model. The model is then theoretically examined using the averaging method, with its effectiveness being confirmed through numerical simulations. Furthermore, the impact of various parameters on the system’s low- and high-amplitude vibrations is explored through a visual response analysis. These findings offer valuable insights for applying fractional sliding mode control (SMC) theory to address the system’s vibration control challenges. Despite the high-amplitude vibrations induced by the fractional order, SMC effectively suppresses these vibrations in the shape memory alloy spring system, thereby minimizing the risk of catastrophic events.

Bending analysis of viscoelastic plates according to the Reissner’s theory using meshless local Petrov–Galerkin method and hereditary integral formulation

Purpose The purpose of this study is to apply the Meshless Local Petrov–Galerkin (MLPG) method to solve the bending problems of linear viscoelastic plates, considering Reissner’s theory.Design/methodology/approachThe weak formulation for the set of equations that govern Reissner’s plate theory is implemented in conjunction with the integral formulation applied to viscoelastic constitutive expressions. A meshless method based on the Moving Least Squares (MLS) approximation is considered in the numerical implementation. The final equation system is assembled by adopting simple and efficient schemes for numerical integration, considering a simplified formulation through centralization of the local interpolation domains and Gaussian quadrature at the same field point. The results obtained are compared with available solutions to demonstrate the efficiency of the proposed formulation.FindingsThe hereditary integral approach proved to be the most general way to analyze the viscoelastic problem, especially when applied together with the modified scheme for numerical integration. In addition, the variable changing technique is demonstrated to be an efficient formulation for solving shear-locking effects in thin plate problems.Originality/valueThe differential of the present study is related to the manner in which the properties of linear viscoelastic materials are considered in the formulation. Although most authors consider this point through the application of the correspondence principle, the present study works with a hereditary integral formulation. In addition, the variable changing technique is applied to solve the shear-locking effects, and an alternative approximation technique is considered to speed up the numerical integration process.

Design of a non-oxidative adhesive dopamine-grafted hyaluronic acid/NOCC hydrogel for enhanced cell spheroid formation and soft tissue regeneration

Tissue adhesive hydrogels from dopamine represent a compelling material with diverse applications across engineering and medical fields. Although numerous designed adhesive hydrogels have been developed, significant limitations have arisen from the reliance on hydrogen peroxide as an activating agent for crosslinking hydrogels. To address this, our study investigates an innovative approach to create an adhesive and biocompatible hydrogel from dopamine conjugated-hyaluronic acid (Da-HA) and N, O-Carboxymethyl Chitosan (NOCC) without the need for oxidative agent treatment for use in biomedical engineering application. The reactions were performed under mild alkaline conditions, vigorous stirring, and curing, resulting in DHC hydrogels. Proper modification and reactions in the hydrogel matrix were confirmed by NMR spectroscopy and Fourier transform infrared spectroscopy (FTIR). The gelling and tissue adhesive properties of the produced DHC hydrogel are proportional to the Da-HA content in the hydrogel. Scanning electron microscopy revealed changes in pore walls among samples and pore diameters ranging from 100 to 300 nm. Rheological analysis demonstrated a high visco-elastic material and self-healing properties. Importantly, the growth of L929 cell spheroids was noted upon their cultivation atop the designed hydrogel. The material holds significant promise for 3D printing and cell encapsulation therapies, as well as in situ tissue repair, particularly for mechanically dynamic tissues like the dermis.

Description of nonlinear viscous and viscoelastic properties of polyacrylamide solution under loading

Background. Currently, the solution of the problem of describing the rheological behavior of viscoelastic and nonlinear viscous properties of liquid and solid-like materials is far from perfect. For successful application of polymer systems to enhance oil recovery and for preparation of fracturing fluids and drilling fluids, knowledge of their rheological properties is necessary. Objective. To determine the nonlinear viscous and viscoelastic properties of polyacrylamide solution. Material and methods. We made an attempt to describe the rheological behavior of a polyacrylamide solution depending on the shear rate and on the loading time. A binomial rheological model was used to describe steady-state stresses at different shear rates, which showed a high degree of accuracy. To describe the stress from time, we proposed to use a numerical solution of a system of two differential equations representing the well-known Maxwell and Kelvin–Voigt equations. To describe the initial section of the curves for times less than 0.05 s, a model with a variable modulus of elasticity was used. Results. A high degree of correspondence of experimental and design stresses with a time of more than 0.05 s was achieved. The overall solution was achieved by combining two solutions based on shear rate and shear stress. Relationships with high correlation coefficients were found between the elastic modulus, viscosities of Maxwell and Kelvin and the shear stress and shear rate. Conclusions. We show that in addition to the “ordinary” shear rate determined by the rotation of the viscometer cylinder, it is necessary to consider an additional shear rate due to stress changes in time. Due to this approach, a description of the stress maximum and its displacement from the shear rate can be made. We note that the additional shear rate occurred immediately after the start of loading, rather than at the time of stress drop, as commonly believed.

Propagation of eigenwaves in plane three-layer media

The paper considers the problem of propagation of natural stress waves in a strip that is in contact with an unbounded isotropic viscoelastic medium made of another material. It is assumed that there are no external influences during the propagation of natural waves. In some cases, the physical properties of viscoelastic materials are described by linear hereditary Boltzmann–Voltaire relations with integral differences of heredity kernels. Some of the layers can be elastic. In this case, the heredity kernels describing the rheological properties of the layers are identically zero. A system in which the rheological properties of the layers are identical (the nuclei of heredity of elements are equal to each other) will be called dissipatively homogeneous. In the particular case, when there are no external influences, the propagation of damped waves of the system is considered; — in the presence of external influences — forced. The main problem is the study of the dissipative (damping) properties of the system as a whole, as well as its stress-strain state.

Experimental & numerical investigations of ultra-high-speed dynamics of optically induced droplet cavitation in soft materials

Perfluorocarbon (PFC) droplets represent a novel class of phase-shift contrast agent with promise in applications in biomedical and bioengineering fields. PFC droplets undergo a fast liquid-gas transition upon exposure to acoustic or optical triggering, offering a potential adaptable and versatile tool as contrast agent in diagnostic imaging and localized drug delivery vehicles in therapeutics systems. In this paper, we utilize advanced imaging techniques to investigate ultra-high-speed inertial dynamics and rectified quasi-static (low-speed) diffusion evolution of optically induced PFC droplet vaporization within three different hydrogels, each of different concentrations, examining effects such as droplet size and PFC core on bubble dynamics and material viscoelastic properties. Gelatin hydrogels reveal concentration-dependent impacts on bubble expansion and material elasticity. Embedding PFC droplets in gelatin increases internal pressure, resulting in higher equilibrium radius and continuous bubble growth during quasi-static evolution. Similar trends are observed in fibrin and polyacrylamide matrices, with differences in bubble behavior attributed to matrix properties and droplet presence. Interestingly, droplet size exhibits minimal impact on bubble expansion during inertial dynamics but influences quasi-static evolution, with larger droplets leading to continuous growth beyond 60 s. Furthermore, the core composition of PFC droplets significantly affects bubble behavior, with higher boiling point droplets exhibiting higher maximum expansion and faster quasi-static dissolution rates. Overall, the study sheds light on the intricate interplay between droplet characteristics, matrix properties, and multi-timescale bubble dynamics, offering valuable insights into their behavior within biomimetic hydrogels.

All-polymer syntactic foams: Linking large strain cyclic experiments to Quasilinear Viscoelastic modelling for materials characterisation

The time-dependent behaviour of polymeric composites is critical in a broad range of applications, including those in marine, aerospace, and automotive environments. In the present study, we assess the validity of the quasi-linear viscoelastic (QLV) model to fit the stress–strain behaviour of all-polymer syntactic foams under large cyclic compressional strain in a novel experimental configuration. These syntactic foams were manufactured by adding hollow polymer microspheres of various sizes and wall thicknesses into a polyurethane matrix. These materials are known for their relatively large initial stiffness, and strong recoverability after large strains. In the QLV model, several strain energy functions (SEFs) were employed, including neo-Hookean, Ogden type I, and type II. The bulk and shear moduli are presented in the form of a Prony series. By estimating these experimental data using optimisation, the natural viscoelastic material properties and coefficients associated with the SEF were determined. The influence of the microsphere filling fraction was also explored. We show that at the strain rate considered here of 0.013 s−1, the compressible QLV model coupled with the Ogden-I SEF is capable of providing an excellent fit to experimental data. Critically, this fit can be achieved over a range of cycles via model optimisation to the first cyclic response only.

Supramolecular blends of C-alkylpyrogallol[4]arenes and polytetrahydrofurans

A small series of the amphiphilic macrocycles – C-alkylpyrogallol[4]arenes has been synthesized and examined by single crystal X-ray analysis which showed the formation of two supramolecular arrangements depending on solvent used for crystallization, i.e., multilayered motif and hexameric capsule. Those structural findings provided an insight into blends prepared from aforementioned macrocycles and various polytetrahydrofurans (polyTHFs). Thus, 1:1 wt ratio mixtures were obtained and investigated by combination of Fourier-transform infrared spectroscopy (FT-IR), differential scanning calorimetry (DSC), and thermogravimetric analysis (TGA). As it turned out, the viscosity of these blends was increased compared to starting materials, which imply that pyrogallol[4]arenes can be successfully utilized as supramolecular cross-linkers enhancing H-bonding between adjacent macromolecular chains. As the major difference between compounds synthesized is the length and geometry of their respective alkyl side chains attached directly to macrocyclic core, i.e., n-propyl- and cyclohexyl- vs. n-dodecyl-, it seemed likely that even insignificant increase in their hydrophobicity can induce high order aggregation of nanoparticles in the slurries, thus affecting their viscosity. Overall, material viscoelastic properties are tunable at macroscopic level by choosing particular pyrogallol[4]arene/solvent combination and adjusting the temperature, which may be advantageous for the design of hybrid materials.

Research of viscoelastic and hygroscopic properties of adhesive, textile materials and packages based on them

Materials with multifunctional properties are the future of modern clothing, and the creation of such materials is extremely urgent. When creating such materials, it is appropriate to use non-woven nano-modified materials as components of clothing details. At the same time, it is important to ensure the viscoelastic and hygroscopic properties of packages of materials for making clothes. This study presents the analysis of these important properties of tissue packages depending on the parameters of their duplication.

Rapid wideband characterization of viscoelastic material properties by Bessel function-based time harmonic ultrasound elastography (B-THE)

Elastography is an emerging diagnostic technique that uses conventional imaging modalities such as sonography or magnetic resonance imaging to quantify tissue stiffness. However, different elastography methods provide different stiffness values, which require calibration using well-characterized phantoms or tissue samples. A comprehensive, fast, and cost-effective elastography technique for phantoms or tissue samples is still lacking.Therefore, we propose ultrasound Bessel-fit-based time harmonic elastography (B-THE) as a novel tool to provide rapid feedback on stiffness-related shear wave speed (SWS) and viscosity-related wave penetration rate (PR) over a wide range of harmonic vibration frequencies. The method relies on external induction and B-mode capture of cylindrical shear waves that satisfy the Bessel wave equation for efficient fit-based parameter recovery. B-THE was demonstrated in polyacrylamide phantoms in the frequency range of 20–200 Hz and was cross-validated by magnetic resonance elastography (MRE) using clinical 3-T MRI and compact 0.5-T tabletop MRI scanners. Frequency-independent material parameters were derived from rheological models and validated by numerical simulations.B-THE quantified frequency-resolved SWS and PR 13 to 176 times faster than more expensive clinical MRE and tabletop MRE and have a good accuracy (relative deviation to reference: 6 %, 10 % and 4 % respectively). Simulations of liver-mimicking material phantoms showed that a simultaneous fit of SWS and PR based on the fractional Maxwell rheological model outperformed a fit on PR solely.B-THE provides a comprehensive and fast elastography technique for the quantitative characterization of the viscoelastic behavior of soft tissue mimicking materials.

Superdiffusion and heterogeneous dynamics in liquid crystals by microrheology

Microrheology (MR) has emerged as a powerful tool for unraveling the intricate local viscoelastic properties of various soft materials. By tracking the free (passive MR) or forced (active MR) diffusion of a tracer, valuable insights into the mechanical characteristics of the host system can be obtained. In this study, we investigate the forced diffusion of a spherical tracer within isotropic and smectic liquid crystal phases of hard rod-like particles. Our findings reveal superdiffusive behaviour induced by external forces, particularly pronounced when these are aligned parallel to the nematic director. Analysis of the dynamical susceptibility unveils heterogeneities strongly correlated with the magnitude and orientation of applied forces, highlighting the system's critical dependence on structural ordering. Intriguingly, we observe that tracer superdiffusion, driven by external forces and evident across all relevant system directions, does not demonstrate a strong correlation with resulting dynamical heterogeneities.

A study of soft and hard impact effects in single-particle impact dampers

Single-particle impact dampers (SPIDs) are simple, yet impactful devices that mitigate vibrations in various applications such as high-rise structures, machinery, and satellites. However, the high-intensity impact forces transmitted to the host structure pose a risk to older and vulnerable structures. Therefore, this study investigates the performance of SPIDs with soft impacts, employing viscoelastic materials to minimize the impact forces and noise levels without degrading the damping performance. Four different materials (rubber, ethylene-vinyl acetate, acrylic and poly-urethane foams) exhibiting different viscoelastic properties are studied and compared with hard impact. An approximate Voigt model for the stiffness and damping coefficient of viscoelastic material is used to conduct numerical simulations and to evaluate the damping performance of SPIDs. Dynamic mechanical analyser (DMA) tests are conducted to determine the dynamic properties of viscoelastic materials. An experimental rig which includes a single-degree-of-freedom host structure, and a prototype SPID is designed and manufactured. Experiments are conducted to determine the damping performance, impact force, and noise level with soft impacts and the results are compared with hard impacts. The results reveal a 40% reduction in vibration amplitude at resonance frequency, an impressive 96% reduction in impact force at resonance, an 11.55 dB reduction in the noise level using poly-urethane foam (softest impact) compared to steel (hard impact). Although viscoelastic materials may not be suitable in harsh environmental conditions, this study demonstrates that introducing a viscoelastic material in SPID can resolve its major drawbacks such as impact forces and noise leading to a simple, cost-effective, and safe SPID.

Condensate interfacial forces reposition DNA loci and probe chromatin viscoelasticity

Biomolecular condensates assemble in living cells through phase separation and related phase transitions. An underappreciated feature of these dynamic molecular assemblies is that they form interfaces with other cellular structures, including membranes, cytoskeleton, DNA and RNA, and other membraneless compartments. These interfaces are expected to give rise to capillary forces, but there are few ways of quantifying and harnessing these forces in living cells. Here, we introduce viscoelastic chromatin tethering and organization (VECTOR), which uses light-inducible biomolecular condensates to generate capillary forces at targeted DNA loci. VECTOR can be utilized to programmably reposition genomic loci on a timescale of seconds to minutes, quantitatively revealing local heterogeneity in the viscoelastic material properties of chromatin. These synthetic condensates are built from components that naturally form liquid-like structures in living cells, highlighting the potential role for native condensates to generate forces and do work to reorganize the genome and impact chromatin architecture.

Accessing activity and viscoelastic properties of artificial and living systems from passive measurement.

Living systems are complex dynamic entities that operate far from thermodynamic equilibrium. Their active, non-equilibrium behaviour requires energy to drive cellular organization and dynamics. Unfortunately, most statistical mechanics approaches are not valid in non-equilibrium situations, forcing researchers to use intricate and often invasive methods to study living processes. Here we experimentally demonstrate that an observable termed mean back relaxation quantifies the active mechanics of living cells from passively observed particle trajectories. The mean back relaxation represents the average trajectory of a particle after a recent motion and is calculated from three-point probabilities. We show that this parameter allows the detection of broken detailed balance in confined systems. We experimentally observe that it provides access to the non-equilibrium generating energy and viscoelastic properties of artificial bulk materials and living cells. These findings suggest that the mean back relaxation can function as a marker of non-equilibrium dynamics and is a non-invasive avenue to determine viscoelastic material properties from passive measurements.