Linear Viscoelastic Model Research Articles

Dynamic Behavior of Rubber Fiber-Reinforced Expansive Soil under Repeated Freeze–Thaw Cycles

Large volumes of waste tires are generated due to the rapid growth of the transportation industry. An effective method of recycling waste tires is needed. Using rubber from tires to improve problematic soils has become a research topic. In this paper, the dynamic response of rubber fiber-reinforced expansive soil under freeze–thaw cycles is investigated. Dynamic triaxial tests were carried out on rubber fiber-reinforced expansive soil subjected to freeze–thaw cycles. The results showed that with the increase in the number of freeze–thaw cycles, the dynamic stress amplitude and dynamic elastic modulus of rubber fiber-reinforced expansive soils first decrease and then increase, and the damping ratio first increases and then decreases, all of which reach the turning point at the 6th freeze–thaw cycle. The dynamic stress amplitude and dynamic elastic modulus decreased by 59.4% and 52.2%, respectively, while the damping ratio increased by 99.8% at the 6th freeze–thaw cycle. The linear visco-elastic model was employed to describe the hysteretic curve of rubber fiber-reinforced expansive soil. The elastic modulus of the linear elastic element and the viscosity coefficient of the linear viscous element first decrease and then increase with the increase in the number of freeze–thaw cycles; all reach the minimum value at the 6th freeze–thaw cycle. The dynamic stress–dynamic strain curve calculation method is established based on the hyperbolic model and linear visco-elastic model, and the verification shows that the effect is better. The research findings provide guidance for the improvement of expansive soil in seasonally frozen regions.

Multi-Channel Signals in Dynamic Force-Clamp Mode of Microcantilever Sensors for Detecting Cellular Peripheral Brush.

The development of numerous diseases, such as renal cyst, cancer, and viral infection, is closely associated with the pathological changes and defects in the cellular peripheral brush. Therefore, it is necessary to develop a potential new method to detect lesions of cellular peripheral brush. Here, a piecewise linear viscoelastic constitutive model of cell is established considering the joint contribution of the peripheral brush and intra-cellular structure. By combining the Laplace transformation and its inverse transformation, and the differential method in the temporal domain and differential quadrature method (DQM) in the spatial domain, the signal interpretation models for quasi-static and dynamic signals of microcantilever are solved. The influence mechanisms of the peripheral brush on the viscoelastic properties of cells and quasi-static/dynamic signals of microcantilever are clarified. The results not only reveal that the peripheral brush has significant effects on the complex modulus of the cell and multi-channel signals of the microcantilever, but also suggest that an alternative mapping method by collecting multi-channel signals including quasi-static and higher frequency signals with more brush indexes could be potentially used to identify cancerous cells.

Nonlinear viscoelastic effect on the fatigue performance of wood tar-based rejuvenated asphalt

The nonlinear viscoelasticity (NLVE) effects of rejuvenated asphalt are often neglected during fatigue degradation, potentially leading to misjudgment of its true fatigue performance. To more accurately quantify the fatigue life of rejuvenated asphalt under NLVE effects, frequency sweep (FS), incremental stress sweep (ISS), and linear amplitude sweep (LAS) tests were used to study two types of rejuvenated asphalt. FS and ISS tests respectively obtained the dynamic modulus |G*|LVE and |G*|NLVE representing the linear viscoelasticity (LVE) and NLVE of rejuvenated asphalt, and incorporated them into the simplified viscoelastic continuum damage (S-VECD) model to establish the fatigue failure criterion and predict the fatigue life of rejuvenated asphalt under high strain levels in LAS tests. The findings indicate that the NLVE-based-S-VECD model quantifies fatigue damage in rejuvenated asphalt lower than the LVE model, and the fatigue life of rejuvenated asphalt increases significantly after considering the NLVE effect. Besides, the failure difference (∆GR) and failure area difference (∆A) defined during the modeling process explain the impact of NLVE on the fatigue failure criterion average pseudo strain energy release rate (GR) of rejuvenated asphalt, validating the necessity of incorporating NLVE into the fatigue performance analysis of rejuvenated asphalt. Therefore, it's necessary to account for the impact of NLVE effect on the fatigue performance of rejuvenated asphalt in engineering practice, which will contribute to the development and application of rejuvenator.

Thermomechanical characterisation and plane stress linear viscoelastic modelling of ethylene-tetra-fluoroethylene foils

Ethylene-tetra-fluoroethylene (ETFE) is a polymer employed in tension membrane structures with mechanical properties that strongly depend on time and temperature effects. A comprehensive understanding of the mutual influence of these variables and a unified viscoelastic constitutive model design can enable wider exploitation of ETFE in sustainable lightweight construction. This study presents a thermomechanical characterisation of ETFE foils through quasi-static tensile experiments spanning two orders of magnitude of strain rates, creep, relaxation, shear and dynamic cyclic tests in a wide range of temperatures suitable for building applications, from −20∘ C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$-20^{\\circ }\ ext{ C}$\\end{document} to 60∘ C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$60^{\\circ }\ ext{ C}$\\end{document}. The experimental results in different material orientations are used to identify the limits of the linear viscoelastic domain, define the direction-dependent creep compliance master curves and calibrate the parameters of a plane stress orthotropic linear viscoelastic model, employing the Boltzmann superposition and the time-temperature superposition principles. The model has been numerically implemented using a recursive integration algorithm and its code is provided open source. A validation on independently acquired data shows the accuracy of the constitutive model in predicting ETFE behaviour within the linear viscoelastic regime usually adopted during structural design, with excellent extrapolation capabilities outside the range of the calibration data.

A comparison of finite strain viscoelastic models based on the multiplicative decomposition

The constitutive equations of several finite strain viscoelastic models, based on the multiplicative decomposition of the deformation gradient tensor and formulated in a thermodynamically consistent framework, are reviewed to demonstrate their similarities and differences. The proposed analysis shows that dissipation formulations, which may appear different, are similar when expressed in the same configuration, enabling the definition of a unified general model. The ability of this general model to reproduce the main features of the behavior of rubbers is then explored. First, its responses are compared to those of finite linear viscoelastic models commonly implemented in commercial finite element codes. Cases of monotonic uniaxial tension and simple shear, relaxation, and sinusoidal simple shear are considered. Second, a comparison is made between a classic generalized Maxwell rheological scheme and a Zener one with a non-constant viscosity, exploring the relevance of both options within the general model’s constitutive equations.

Numerical modelling of multiple sclerosis: A tissue-scale model of brain lesions

Multiple Sclerosis (MS) is an autoimmune condition leading to the degeneration of brain tissue, occurring when the immune system attacks the myelin sheath surrounding axons of white brain matter thereby disrupting brain signals. This study aimed to evaluate how MS lesions alter stress distribution through grey and white brain matter with lesions (active, chronic, and inactive). A linear viscoelastic model represents the tissue-scale dynamic deformation and time dependency of brain tissue. A Prony series expansion was used to model viscous effects including stress relaxation. An elastic modulus, within the viscoelastic model, was either reduced by 11 % for active lesions, or increased by 35 % increase for inactive lesions. These material properties were then implemented to model healthy tissue, active, chronically inflamed, and inactive lesions. Finite element analysis enabled stress evaluation in response to a peak cyclic displacement of 0.5 mm (1 % strain) with the healthy model acting as a control model. Chronic lesions had the largest effect on stress induced, in terms of high (171 Pa) and low stress (108 Pa). Inactive lesions induced an increase in stress of 11 Pa with areas of low stress (105 Pa). Active lesions caused the least deviation in peak induced stress (7 Pa). In conclusion, a hierarchy in stress induced across the lesion types has been found, from highest to lowest: chronic, inactive and active, with potential implications for lesion progression. In conclusion, MS lesions within brain tissue should model lesions, avoid assuming homogeneity during degeneration, and should distinguish between active and passive lesions.

Multi-Step Relaxation Characterization and Viscoelastic Modeling to Predict the Long-Term Behavior of Bitumen-Free Road Pavements Based on Polymeric Resin and Thixotropic Filler.

Asphalt pavements are fundamental to modern transportation infrastructure, requiring elasticity, firmness, and longevity. However, traditional asphalt, based on bitumen, faces several limitations. To improve pavement performance, polymer resins are being used to substitute bitumen and improve requirements. Therefore, a deep understanding of the material behavior is required. This study presents the analysis of the relaxation behavior of a poly(methyl methacrylate)-based pavement and the influence of mineral fillers. An approach using a linear elastic-viscoelastic material model was selected based on evidence and validated across the linear and nonlinear deformation range. The results reveal no influence of the mineral fillers on the relaxation behavior. The presented modification of the linear elastic and viscoelastic modeling reveals accurate results to predict long-term pavement performance. This approach offers a practical method for forecasting asphalt behavior. Further research is needed to incorporate deformation behavior into the model.

Dynamic mechanical response and failure behavior of solid propellant under shock wave impact

Solid rocket motor propellants are typically subjected to shock wave loads during ignition. To analyze the dynamic mechanical response and failure behavior of hydroxyl-terminated polybutadiene (HTPB) propellant under varying shock intensities, this study innovatively employed a shock tube apparatus in conjunction with schlieren imaging and 3D-DIC techniques. Shock loading experiments were conducted on propellant samples of three different thicknesses under pressures ranging from 0.3 to 0.7 MPa, capturing the dynamic deformation processes. Results revealed that deformation initiated at the clamped region, extending towards the center and forming a parabolic shape. The maximum deformation of the samples shows an approximately linear relationship with the launch pressure and decreases with increasing sample thickness. The 5 mm sample failed under a 0.6 MPa shock pressure, with electron microscopy images identifying matrix damage, particle debonding, and particle fracture as the principal failure mechanisms. Finite element simulations based on the generalized Maxwell linear viscoelastic constitutive model were conducted, demonstrating good agreement with experimental data. The critical stress for fracture was determined to be 4.12 MPa, and the ultimate shock wave pressures for 3, 6, 9, and 12 mm thicknesses were approximately 0.3 MPa, 0.65 MPa, 1.1 MPa, and 1.4 MPa, respectively. These findings provide valuable insights for assessing the structural integrity of solid rocket motors under ignition shock conditions.

The role of unit cell topology in modulating the compaction response of additively manufactured cellular materials using simulations and validation experiments

Additive manufacturing has enabled a transformational ability to create cellular structures (or foams) with tailored topology. Compared to their monolithic polymer counterparts, cellular structures are potentially suitable for systems requiring materials with high specific energy-absorbing capability to provide enhanced damping. In this work, we demonstrate the utility of controlling unit-cell topology with the intent of obtaining a desired stress–strain response and energy density. Using mesoscale simulations that resolve the unit-cell sub-structures, we validate the role of unit-cell topology in selectively activating a buckling mode and thereby modulating the characteristic stress–strain response. Simulations incorporate a linear viscoelastic constitutive model and a hyperelastic model for simulating large deformation of the polymer under both tension and compression. Simulated results for nine different cellular structures are compared with experimental data to gain insights into three different modes of buckling and the corresponding stress–strain response.

Rate-dependent energy dissipation of graded viscoelastic structures fabricated by grayscale vat photopolymerization

A major benefit of additive manufacturing technologies is precise control over structural topologies and material properties, which allows to tailor, for instance, energy absorption and dissipation. While vat photopolymerization is generally restricted to a single material, grayscale masked stereolithography (gMSLA) allows to customize material behavior by grading the light intensity within a structure. This study investigates the impact and opportunities of grayscale grading strategies on the rate-dependent mechanical behavior of structures fabricated by gMSLA. Considering the viscoelastic nature of polymers, rate-dependent energy dissipation is explored, introducing a parametric linear viscoelastic constitutive model for varying grayscales. The investigation includes the comprehensive characterization of mechanical properties, numerical finite element simulation, validation through experimental procedures, and exploration of dissipation energy under different strain rates. In this way, a rational function successfully determines the critical strain rate at which the maximum dissipation occurs. Overall, the research offers a comprehensive investigation of the mechanical dissipation behavior of graded 3D printed structures, laying the foundation for further studies and advancements aimed at optimizing these structures for enhanced energy absorption capabilities.

Modeling and FE simulation of coupled water diffusion and viscoelasticity in relaxation tests of polyamide 6

Polyamides can absorb or desorb water from or to their surrounding environment. The impact of this process is significant as water molecules lead locally to a swelling and a coupling of diffusion and deformation behavior. To model these phenomena, a strongly coupled chemo-mechanical (or diffuso-mechanical) model is required, considering both local water concentration and the viscoelastic material behavior of polyamide. In the present work, we derive and apply such a model to polyamide 6. A diffusion equation describing changes in water concentration is coupled to the balance of linear momentum in polyamide 6. The interaction between deformation and concentration is derived from thermodynamic considerations by introducing a free energy consisting of a mechanical and a chemical part. The mechanical part describes a linear viscoelastic model and includes chemical strains due to the presence of water molecules. The chemical part builds upon the theory of Flory and Huggins, that takes into account changes in enthalpy and entropy of mixing due to the interaction of polymer and water molecules. The coupling of deformation to water concentration arises due to a dependency of the water flux on the hydrostatic stress inside the polyamide. We successfully apply the derived model in Finite-Element simulations to predict the drying of polyamide 6 specimens without any coupling to mechanical loads. In addition, we reproduce experimentally obtained data from relaxation measurements, where the drying of polyamide specimens leads to an increase in relaxation modulus.

Convolution quadrature time-domain boundary element method for antiplane anisotropic viscoelastic wave propagation

This paper presents a Convolution Quadrature Time-Domain Boundary Element Method (CQBEM) for antiplane anisotropic viscoelastodynamics. The proposed CQBEM formulation employs the standard linear viscoelastic model and the fundamental solution developed by Wang and Achenbach for expressing viscoelastic and anisotropic properties, respectively. This fundamental solution, which involves integration over the unit circle, is evaluated numerically. After offering a comprehensive overview of the proposed CQBEM formulation, we demonstrate the effectiveness of the proposed method by analyzing the scattering of elastic waves by cavities in certain types of anisotropic viscoelastic materials. Additionally, the use of group velocity curves further validates the numerical results, confirming the anisotropic and viscoelastic effects and thus substantiates the proposed CQBEM for antiplane anisotropic viscoelastic wave propagation.

Structural response analysis of a solid rocket motor charge under temperature and internal pressure loads

To study the structural integrity of a solid rocket motor under low temperature load, internal pressure load, and two combined loads, based on the linear viscoelastic model, the structural response of a solid rocket motor under low temperature load, internal pressure load and two combined loads were analyzed by ANSYS finite element software, and the temperature field and strain field of charge loading were obtained. The Von Mises strain distribution of the solid rocket motor along the axial characteristic line is obtained. The results are: Under the combined action of low temperature load, internal pressure load, and two kinds of loads, the maximum Von Mises strain appears at the transition position between the blade joint and the barrel section, which is the most dangerous position for charging.

Phase inversion detection in immiscible binary polymer blends via zero‐shear viscosity measurements

AbstractIn the present work, we demonstrate that zero‐shear viscosity is a sensitive rheological function to detect phase inversion in immiscible binary polymer blends characterized by a viscosity ratio larger than one. The phase inversion of poly(propylene) (PP)/low‐density poly(ethylene) (LDPE) and poly(styrene) (PS)/LDPE, at various compositions, was assessed via our novel approach. For both blends, three distinctive regions could be determined through zero‐shear viscosity measurements; the LDPE matrix, the co‐continuous phase, and the PS or PP matrix. For PP/LDPE blends, the co‐continuous structure was between 50 and 75 wt.% PP, and for PS/LDPE blends the co‐continuous structure was between 45 and 75 wt.% PS, in agreement with scanning electron microscopy analysis, empirical model predictions, and literature data.Highlights Phase inversion revealed via viscosity measurements. Limitations of linear viscoelastic models for immiscible blends assessed.

The linear viscoelastic fracture theory applies to soft solids better when they are…viscoelastic

Over the last half-century, linear viscoelastic models for crack growth in soft solids have flourished but their predictions have rarely been compared to experiments. In fact, most available models are either very approximate or cast in forms which are not quite suitable for the analysis of actual data. Here, we propose a linear viscoelastic approach which consistently exploits the dynamic mechanical analysis data. We apply this method to four sets of results documenting fracture or adhesion rupture in soft solids with various degrees of viscoelasticity. For elastomers, the results reproduce the well-known inconsistency of the process zone size. In more viscoelastic systems, however, the present approach is able to match the measured velocity dependence of the rupture energy with physically acceptable process zone sizes. Moreover, our predictions agree with the damage zone sizes measured by mechanoluminescence. Building on these results, we discuss various issues arising when evaluating the linear viscoelastic contribution to the rupture/adhesion energy in soft solids: data quality, physical interpretation of the parameters, validity of simpler approximations and limitations of the present approach.

Statistical analysis of identification of linear viscoelastic models

Statistical analysis of identification of linear viscoelastic models

ОЦЕНКА ЗНАЧИМОСТИ И ВЫБОР ПАРАМЕТРОВ КОНТАКТНОЙ МОДЕЛИ ПРИ МОДЕЛИРОВАНИИ СЕМЯН ГОРОХА МЕТОДОМ ДИСКРЕТНЫХ ЭЛЕМЕНТОВ

An integral part of technological operations in agriculture during sowing, harvesting, transportation and post-harvest processing is the impact of the working parts of machines on crop seeds. To increase the efficiency of machines and reduce seed injury, it is necessary to improve the design and technological parameters of the working units. Currently, the most promising method for theoretically substantiating the parameters of machines working with seeds and improving their design is modeling using the discrete element method. The study is carried out to substantiate the parameters of the contact model of discrete elements when modeling pea seeds. The parameters of the contact model were justified based on the results of testing on the angle of slope and arch when pouring seeds. To analyze the angle of repose and vault, a transparent rectangular container was used, when seeds were poured out of the upper part of which, the remaining seeds formed the angle of the vault, and the crumbled ones formed the angle of repose. Evaluation of the coefficients of the regression equations for changes in the angles of the arch and slope when shedding seeds in a container from the parameters of the selected contact linear viscoelastic model made it possible to establish a significant parameter - the coefficient of dynamic friction between particles. The nature of the change in the angle of repose of pea seeds from moisture is identical to the change in this angle for particles modeled by the discrete element method, with their recovery coefficient v = 0.2 and the coefficient of dynamic friction between them fd = 0.15...0.17. The dependences of the angle of repose on the moisture content of pea seeds and the coefficient of dynamic friction between particles obtained during the implementation of experiments represent a nomogram for choosing the coefficient of dynamic friction between particles fd for a contact linear viscoelastic model depending on the moisture content of pea seeds when modeling using the discrete element method.

Electro-mechanical analogy for Prabhakar-like fractional viscoelasticity

The aim of this paper is to set up a formal equivalence between a mechanical system and an electrical one. Specifically, we consider the Maxwell-Prabhakar linear viscoelastic model, based on Prabhakar fractional operators. Therefore, we find the analogous expression for the electric current due to a step potential. The expression for the resulting electric current depends on the variable characterizing the viscoelastic model and its behaviour is then discussed with the support of some interesting plots.

Brain Material Properties and Integration of Arachnoid Complex for Biofidelic Impact Response for Human Head Finite Element Model.

Finite element head models offer great potential to study brain-related injuries; however, at present may be limited by geometric and material property simplifications required for continuum-level human body models. Specifically, the mechanical properties of the brain tissues are often represented with simplified linear viscoelastic models, or the material properties have been optimized to specific impact cases. In addition, anatomical structures such as the arachnoid complex have been omitted or implemented in a simple lumped manner. Recent material test data for four brain regions at three strain rates in three modes of loading (tension, compression, and shear) was used to fit material parameters for a hyper-viscoelastic constitutive model. The material model was implemented in a contemporary detailed head finite element model. A detailed representation of the arachnoid trabeculae was implemented with mechanical properties based on experimental data. The enhanced head model was assessed by re-creating 11 ex vivo head impact scenarios and comparing the simulation results with experimental data. The hyper-viscoelastic model faithfully captured mechanical properties of the brain tissue in three modes of loading and multiple strain rates. The enhanced head model showed a high level of biofidelity in all re-created impacts in part due to the improved brain-skull interface associated with implementation of the arachnoid trabeculae. The enhanced head model provides an improved predictive capability with material properties based on tissue level data and is positioned to investigate head injury and tissue damage in the future.

Viscoelastic Dynamics of Photothermal‐Responsive Liquid Crystal Elastomer Fibers

AbstractLiquid crystal elastomers (LCEs) with photo‐responsive properties, typically driven by either photochemical or photothermal mechanisms, have found extensive applications as, for example, actuators in soft robots. However, intricate temperature‐dependent viscoelasticity of LCEs poses a challenge, leading to a notable gap in the domain of dynamic models for photothermal‐responsive LCE (PTR‐LCE) fibers. Here, a fundamental framework is proposed for accurate modeling and real‐time simulations of PTR‐LCE fiber dynamics. The PTR‐LCE fiber is described as a one‐dimensional (1D) string model that decomposes the fiber deformation into active and passive parts, which are characterized by an order parameter and a temperature‐dependent linear viscoelasticity model, respectively. Then, independent experimental measurements of model parameters are conducted, and a numerical algorithm is developed to solve the model, which is validated for convergence, time efficiency, and accuracy. Finally, the model is employed to simulate both open‐loop and Proportional‐Integral‐Derivative (PID) control of actuators made of PTR‐LCE fibers. The results confirm the advantages of this model over previous models. This work not only reveals the physical mechanisms underlying the PTR‐LCE fiber dynamic behaviors but also provides inspirations for more efficient and precise soft robotic applications.