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1
Dacol, Vitor, Elsa Caetano, and João R. Correia. "A Combined Exponential-Power-Law Method for Interconversion between Viscoelastic Functions of Polymers and Polymer-Based Materials." Polymers 12, no. 12 (December 16, 2020): 3001. http://dx.doi.org/10.3390/polym12123001.
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Understanding and modeling the viscoelastic behavior of polymers and polymer-based materials for a wide range of quasistatic and high strain rates is of great interest for applications in which they are subjected to mechanical loads over a long time of operation, such as the self-weight or other static loads. The creep compliance and relaxation functions used in the characterization of the mechanical response of linear viscoelastic solids are traditionally determined by conducting two separate experiments—creep tests and relaxation tests. This paper first reviews the steps involved in conducting the interconversion between creep compliance and relaxation modulus in the time domain, illustrating that the relaxation modulus can be obtained from the creep compliance. This enables the determination of the relaxation modulus from the results of creep tests, which can be easily performed in pneumatic equipment or simple compression devices and are less costly than direct relaxation tests. Some existing methods of interconversion between the creep compliance and the relaxation modulus for linear viscoelastic materials are also presented. Then, a new approximate interconversion scheme is introduced using a convenient Laplace transform and an approximated Gamma function to convert the measured creep compliance to the relaxation modulus. To demonstrate the accuracy of the fittings obtained with the method proposed, as well as its ease of implementation and general applicability, different experimental data from the literature are used.
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Sagar, Gautam, Dong Zheng, Anuwat Suwannachit, Maik Brinkmeier, Kristin Fietz, and Carsten Hahn. "On the Development of Creep Laws for Rubber in the Parallel Rheological Framework." Tire Science and Technology 47, no. 1 (March 1, 2019): 2–30. http://dx.doi.org/10.2346/tire.18.470104.
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ABSTRACT It is widely known that filler-reinforced rubber material in tires shows a very complicated material behavior when subjected to cyclic loadings. One of the most interesting effects for rolling tires is the nonlinear rate-dependent behavior, which is implicitly linked to the amplitude dependency of dynamic stiffness (Payne effect) at a given frequency and temperature. This effect, however, cannot be described by a conventional linear viscoelastic constitutive law, e.g., the Prony series model. Several nonlinear viscoelastic material models have been proposed in the last decades. Among others, Lapczyk et al. (Lapczyk, I., Hurtado, J. A., and Govindarajan, S. M., “A Parallel Rheological Framework for Modeling Elastomers and Polymers,” 182nd Technical Meeting of the Rubber Division of the American Chemical Society, Cincinnati, Ohio, October 2012) recently proposed a quite general framework for the class of nonlinear viscoelasticity, called parallel rheological framework (PRF), which is followed by Abaqus. The model has an open option for different types of viscoelastic creep laws. In spite of the very attractive nonlinear rate-dependency, the identification of material parameters becomes a very challenging task, especially when a wide frequency and amplitude range is of interest. This contribution points out that the creep law is numerically sound if it can be degenerated to the linear viscoelastic model at a very small strain amplitude, which also significantly simplifies model calibration. More precisely, the ratio between viscoelastic stress and strain rate has to converge to a certain value, i.e., the viscosity in a linear viscoelastic case. The creep laws implemented in Abaqus are discussed in detail here, with a focus on their fitting capability. The conclusion of the investigation consequently gives us a guideline to develop a new creep law in PRF. Here, one creep law from Abaqus that meets the requirements of our guideline has been selected. A fairly good fit of the model is shown by the comparison of the simulated complex modulus in a wide frequency and amplitude range with experimental results.
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Dai, H. L., and H. Y. Zheng. "Creep Buckling and Post-Buckling Analyses of a Viscoelastic FGM Cylindrical Shell with Initial Deflection Subjected to a Uniform In-Plane Load." Journal of Mechanics 28, no. 2 (May 8, 2012): 391–99. http://dx.doi.org/10.1017/jmech.2012.44.
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AbstractIn this paper, based on the viscoelastic theory, the creep buckling and post-buckling behaviors of a viscoelastic functionally graded material (FGM) cylindrical shell with initial deflection subjected to a uniform in-plane load are investigated. The material properties of the viscoelastic FGM cylindrical shell are assumed to vary through the structural thickness according to a power law distribution of the volume fraction of constituent materials and Poisson's ratio is assumed as a constant. Considering the transverse shear deformation and geometric nonlinearity, the constitutive relation of the viscoelastic FGM cylindrical shell is established. By means of the Newton-Newmark method and the Boltzmann superposition principle, the problem for the creep buckling and post-buckling of the FGM cylindrical shell is solved. The numerical results reveal that the transverse shear deformation, volume fraction and geometric parameters have significant effects on the creep buckling and post-buckling of the viscoelastic FGM cylindrical shell.
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Zou, Yong, Chin Jian Leo, and Henry Wong. "Time Dependent Viscoelastic Behaviour of EPS Geofoam." Applied Mechanics and Materials 330 (June 2013): 1095–99. http://dx.doi.org/10.4028/www.scientific.net/amm.330.1095.
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A series of laboratory tests was carried out to assess the time-dependent creep behaviour of EPS geofoam at room temperature (23°C) and at 40°C. The experimental data were then used to calibrate and to validate mechanical viscoelastic models along with an empirical Power Law model, at these two temperatures. The viscoelastic models examined were the 3-element (Maxwell-Kelvin), the 4-element (Burgers) and the Modified 4-element models. The modified 4-element model and the base case, the empirical power law model, were found to give the best predictions. As anticipated, the experimental results show that creep rate is higher at elevated temperatures. The results, at 23°C and 40°C, offer a means to assess and model creep behavior in geotechnical applications at normal, and at a practical elevated, temperature where use of EPS geofoam in warmer climate may be a concern.
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Pereira, Ayrton Alef Castanheira, José Roberto Moraes d'Almeida, and Thiago Motta Linhares Castro. "Evaluation of Short-term Creep Behavior of PE-HD after Aging in Oil Derivatives." Polymers and Polymer Composites 26, no. 3 (March 2018): 243–50. http://dx.doi.org/10.1177/096739111802600304.
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The creep behavior of a high density polyethylene (PE-HD) was evaluated before and after aging in contact with gasoline and diesel oil. Four viscoelastic models were used to assess changes in creep properties of the material: three parameters model, four parameters model, stretched Burgers model and Findley Law. Viscoelastic properties, stationary creep rate and compliance were used to analyze and compare the behavior between samples. A strain increase could be seen in aged samples in comparison with as-received ones, caused by plasticization due to aging effects. An increase in flexibility and decrease in stiffness in aged samples was also noted. This work also shows that the effects of aging on the creep response of a polymeric material can be analyzed using short term creep tests.
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Hagin, Paul N., and Mark D. Zoback. "Viscous deformation of unconsolidated reservoir sands—Part 2: Linear viscoelastic models." GEOPHYSICS 69, no. 3 (May 2004): 742–51. http://dx.doi.org/10.1190/1.1759460.
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Laboratory creep experiments show that dry unconsolidated reservoir sands follow a power law function of time (at constant stress), and cyclic loading tests (at quasi‐static frequencies of 10−6 to 10−2 Hz) show that the bulk modulus increases by a factor of two with increasing frequency while attenuation remains constant. In this paper, we attempt to model these observations using linear viscoelasticity theory by considering several simple phenomenological models. We investigated two classes of models: spring‐dashpot models, which are represented by exponential functions with a single relaxation time, and power law models. Although almost all of the models considered were capable of fitting the creep data with time, they result in very different predictions of attenuation and bulk modulus dispersion. We used the model parameters derived from fitting the creep strain to predict the bulk modulus dispersion and attenuation as a function of frequency, to find a single phenomenological model (and model parameters) that could explain the material's creep response with time as well as its dispersion and attenuation characteristics. Spring‐dashpot models, such as the Burgers and standard linear solid models, produce reasonable fits to the creep strain and bulk modulus dispersion data, but do not reproduce the attenuation data. We find that a combined power law–Maxwell creep model adequately fits all of the data. Extrapolating the power law–Maxwell creep model out to 30 years (to simulate the lifetime of a reservoir) predicts that the static bulk modulus is only 25% of the dynamic modulus. Including the instantaneous component of deformation into the previous prediction results in 2% total vertical strain at the wellbore, in good agreement with field observations.
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Osman, Ekhlas A., and Saad A. Mutasher. "Viscoelastic properties of kenaf reinforced unsaturated polyester composites." International Journal of Computational Materials Science and Engineering 03, no. 01 (March 2014): 1450004. http://dx.doi.org/10.1142/s2047684114500043.
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In order to quantify the effect of temperature on the mechanical and dynamic properties of kenaf fiber unsaturated polyester composites, formulations containing 10 wt.% to 40 wt.% kenaf fiber were produced and tested at two representative temperatures of 30°C and 50°C. Dynamic mechanical analysis was performed, to obtain the strain and creep compliance for kenaf composites at various styrene concentrations. It is possible to obtain creep curves at different temperature levels which can be shifted along the time axis to generate a single curve known as a master curve. This technique is known as the time–temperature superposition principle. Shift factors conformed to a William–Landel–Ferry (WLF) equation. However, more long term creep data was needed in order to further validate the applicability of time-temperature superposition principle (TTSP) to this material. The primary creep strain model was fitted to 60 min creep data. The resulting equation was then extrapolated to 5.5 days; the creep strain model of power-law was successfully used to predict the long-term creep behavior of natural fiber/thermoset composites.
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Alrubaie, Murtada Abass A., Roberto A. Lopez-Anido, Douglas J. Gardner, Mehdi Tajvidi, and Yousoo Han. "Modeling the hygrothermal creep behavior of wood plastic composite (WPC) lumber made from thermally modified wood." Journal of Thermoplastic Composite Materials 33, no. 8 (January 9, 2019): 1109–24. http://dx.doi.org/10.1177/0892705718820404.
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The viscoelastic behavior of an extruded wood plastic composite (WPC) made from thermally modified wood under hygrothermal treatment was studied and modeled. Multiple three-point bending creep/recovery tests were carried out using a dynamic mechanical thermal analyzer (DMTA) equipped with a submersible clamp. WPC specimens with a 15-mm span were subjected to two initial applied stresses; 9% and 14% of the flexural strength in 30 min of creep and 30 min of creep recovery under the combined effects of temperature (25°C, 35°C, and 45°C) and water immersion (saltwater (SW) and distilled water). A dry condition WPC control was used to compare the hygrothermal effects with respect to the control conditions. The WPC material in this article exhibited a linear viscoelastic behavior under the effect of temperature, whereas a nonlinear viscoelastic behavior was observed under immersion conditions. A power law model is considered a useful model to describe the creep behavior of WPC specimens with a 15-mm span in the control and the SW conditions and at 45°C. A power law model was used to describe 180-day creep deflection of WPC lumber beams with an 853-mm span subjected to 12 MPa of the flexural strength in four-point bending at 50% relative humidity and at 21°C. The power law model predicts that the WPC lumber will reach a flexural strain in outer fiber of 1% in approximately 150 years.
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Marklund, Erik, Janis Varna, and Lennart Wallström. "Nonlinear Viscoelasticity and Viscoplasticity of Flax/Polypropylene Composites." Journal of Engineering Materials and Technology 128, no. 4 (June 30, 2006): 527–36. http://dx.doi.org/10.1115/1.2345444.
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In tensile tests the flax/polypropylene composites clearly show nonlinear behavior in loading and hysteresis loops in unloading. In creep tests performed at different load levels the response was nonlinear viscoelastic, and after recovery, viscoplastic strains were detected. No degradation in stiffness could be seen and thus nonlinear viscoelasticity and viscoplasticity were assumed to be the main cause for the observed behavior. The fracture surface of a specimen that experienced creep rupture at 24 MPa was investigated using a scanning electron microscope. The viscoplastic response was studied experimentally and described by a power law with respect to time and stress level in the creep test. The nonlinear viscoelasticity was described using Schapery’s model. The application of Prony series and a power law to approximate the viscoelastic compliance was investigated. Both descriptions have accuracy sufficient for practical applications. However, at high stresses the attempts to describe the viscoelastic compliance by a power law with a stress-independent exponent failed and therefore stress dependence of this exponent was included in the data analysis. The accuracy within the considered stress range is good, but the thermodynamic consistency of this procedure has to be proven.
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Orlet, M. W., and C. E. Bakis. "Viscoelastic Characterization of High Fiber Content Filament Wound Polyurethane Matrix Composites." Rubber Chemistry and Technology 71, no. 5 (November 1, 1998): 1042–58. http://dx.doi.org/10.5254/1.3538509.
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Abstract Elastomeric matrix composites (EMCs) consisting of a polyurethane matrix unidirectionally reinforced with high volume fractions of high strength fibers have interesting and unique mechanical properties such as high strength and stiffness in the fiber direction and high ductility perpendicular to the fibers. The aim of this investigation is to explore the quasi-static mechanical properties of glass and carbon fiber EMCs in the direction transverse to the fibers and to measure and model the creep of the monolithic matrix material and the transverse creep of the glass EMC. In the quasi-static tests, glass and carbon EMCs followed a monotonic stress—strain curve that was essentially flat from approximately 1–2% to over 10% strain. The maximum stresses obtained in the quasi-static tests were approximately 3.5 and 7 MPa in the carbon and glass EMCs, respectively. The monolithic matrix and the glass EMC loaded transversely to the fibers both showed highly nonlinear creep behaviors. The former creep behavior was modeled successfully with a standard power law expression. The nonlinear creep behavior of the glass EMC cannot be modeled with a standard power law expression, possibly due to creep damage.
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Abuzeid, Osama M., and Peter Eberhard. "Linear Viscoelastic Creep Model for the Contact of Nominal Flat Surfaces Based on Fractal Geometry: Standard Linear Solid (SLS) Material." Journal of Tribology 129, no. 3 (February 16, 2007): 461–66. http://dx.doi.org/10.1115/1.2736427.
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The objective of this study is to construct a continuous mathematical model that describes the frictionless contact between a nominally flat (rough) viscoelastic punch and a perfectly rigid foundation. The material’s behavior is modeled by assuming a complex viscoelastic constitutive law, the standard linear solid (SLS) law. The model aims at studying the normal compliance (approach) of the punch surface, which will be assumed to be quasistatic, as a function of the applied creep load. The roughness of the punch surface is assumed to be fractal in nature. The Cantor set theory is utilized to model the roughness of the punch surface. An asymptotic power law is obtained, which associates the creep force applied and the approach of the fractal punch surface. This law is only valid if the approach is of the size of the surface roughness. The proposed model admits an analytical solution for the case when the deformation is linear viscoelastic. The modified analytical model shows a good agreement with experimental results available in the literature.
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Ngudiyono, Bambang Suhendro, Ali Awaludin, and Andreas Triwiyono. "Review of creep modelling for predicting of long-term behavior of glued-laminated bamboo structures." MATEC Web of Conferences 258 (2019): 01023. http://dx.doi.org/10.1051/matecconf/201925801023.
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Glued-laminated bamboo has been widely used to substitute timber as a building material. This material classified as a viscoelastic material because it exhibiting properties that are common to both solid and liquid. Under long-term constant loading, the glued-laminated bamboo structures will experience creep deformation. The mechanical, power law and finite element models are common methods that used to predict the creep for viscoelastic material, some of them have advantages and disadvantages. In this manuscript, modelling of long-term creep is reviewed. The fundamental concepts of creep modelling, the influence of variable load level, and humidity were discussed to develop for computational applications. By using FEA program, a subroutine has been developed by previous researchers to accommodate the effect of orthotropic properties. In the future, the subroutine will be used and developed for numerical creep analysis of glued-laminated bamboo.
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Fan, Xiyan, Wenling Jiang, Ning Mei, and Chuanqi Su. "Nonlinear Creep Model and Parameter Determination of Asphalt." Journal of Physics: Conference Series 2174, no. 1 (January 1, 2022): 012090. http://dx.doi.org/10.1088/1742-6596/2174/1/012090.
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Abstract Asphalt is a kind of typical viscoelastic material. Adding different materials in asphalt composite materials is an important way in road engineering materials. The creep experiments under different stress of asphalt, we used the multivariate model to fit the experimental data to get Burgers model and the creep law of asphalt correlation is best. The Burgers model be expanded by Taylor series, the polynomial creep model of creep compliance and relaxation characterized the coefficient of asphalt specimen can be obtained. Compared to other models, the creep law of asphalts well characterized by polynomial model, multivariate model has a wider range of adaptability compared to polynomial model, and polynomial model of mathematical calculation more simple than multivariate model.
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Zhu, Yuan, Pei Ying Liu, and Zhi Hong Jiang. "The Creep Behavior of Wood-Polymer Composites." Advanced Materials Research 815 (October 2013): 632–38. http://dx.doi.org/10.4028/www.scientific.net/amr.815.632.
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The creep behavior of WPCs needs to be addressed when developing and using this kind of materials. In this paper, the creep behavior of WPCs under linear viscoelastic region was investigated at different temperatures and bamboo flours levels. The creep compliance increase with the rise of temperature, the addition of bamboo flour has a positive effect on the creep behavior. Burgers model, Findley power law and TTSP were used to predict the long-term behavior of this kind material. Finely power law can well describe the creep properties of WPCs while Burgers model begins to diverge from measured data at about 100min. The application of TTSP was used to create master curve covered more than 108 from 30-min short-term creep compliance curves.
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Riesen, P., K. Hutter, and M. Funk. "A viscoelastic Rivlin-Ericksen material model applicable to glacier ice." Nonlinear Processes in Geophysics 17, no. 6 (December 1, 2010): 673–84. http://dx.doi.org/10.5194/npg-17-673-2010.
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Abstract. We present a viscoelastic constitutive relation which describes transient creep of a modified second grade fluid enhanced with elastic properties of a solid. The material law describes a Rivlin-Ericksen material and is a generalization of existing material laws applied to study the viscoelastic properties of ice. The intention is to provide a formulation tailored to reproduce the viscoelastic behaviour of ice ranging from the instantaneous elastic response, to recoverable deformation, to viscous, stationary flow at the characteristic minimum creep rate associated with the deformation of polycrystalline ice. We numerically solve the problem of a slab of material shearing down a uniformly inclined plate. The equations are made dimensionless in a form in which elastic effects and/or the influence of higher order terms (i.e., strain accelerations) can be compared with viscous creep at the minimum creep rate by means of two dimensionless parameters. We discuss the resulting material behaviour and the features exhibited at different parameter combinations. Also, a viable range of the non-dimensional parameters is estimated in the scale analysis.
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Garrido, Mário, and João R. Correia. "Elastic and viscoelastic behaviour of sandwich panels with glass-fibre reinforced polymer faces and polyethylene terephthalate foam core." Journal of Sandwich Structures & Materials 20, no. 4 (June 30, 2016): 399–424. http://dx.doi.org/10.1177/1099636216657388.
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This paper presents experimental and analytical investigations about the elastic and viscoelastic (creep) behaviour of sandwich panels made of glass-fibre reinforced polymer faces and a polyethylene terephthalate foam core, produced by vacuum infusion for civil engineering structural applications. First, the elastic response of the panels’ constituent materials (glass-fibre reinforced polymer and polyethylene terephthalate) in tension, compression and shear was experimentally assessed; shear tests on the foam were carried out using a novel test method, the diagonal tension shear test. The creep behaviour in shear of the polyethylene terephthalate foam was evaluated for different load levels. The effective flexural properties of the full-scale sandwich panels as well as their flexural behaviour up to failure were experimentally assessed. Flexural creep and subsequent recovery experiments were also conducted for different load levels, to characterise the viscoelastic behaviour of the full-scale sandwich panels. Creep deformations of the polyethylene terephthalate foam and of the sandwich panels were found to be significantly lower than those corresponding to polyurethane foam and balsa wood reported in the literature; unrecoverable viscoelastic deformations were observed in the full-scale panels. In the analytical study, the creep response of the panels was modelled using Findley’s power law and the composite creep modelling approach. The composite creep modelling predictions were reasonably accurate and allowed assessing the relative contributions of bending and shear deformations to the total sandwich panel creep deflections.
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Bogobowicz, A. "Non-Newtonian Creep Into a Two-Dimensional Cavity of Near-Rectangular Shape." Journal of Applied Mechanics 63, no. 4 (December 1, 1996): 1047–51. http://dx.doi.org/10.1115/1.2787230.
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The plane-strain formulation for the steady-state closure of a near-rectangular, single isolated opening in an indefinite viscoelastic medium is presented. A power creep law describes the creep behavior of the viscous medium. Because of the highly nonlinear nature of the creep, an analytic solution is not possible for the proposed opening geometry, hence an approximation method based upon the minimum principle for velocities is used. The analytic function is used to describe the shape of opening (circular, elliptical, and rectangular with rounded corners).
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Fu, Jianghua, Yang Liu, Jintao Su, Bao Chen, and Zheming Chen. "Rubber Creep Model and Its Influence on Mounting Stiffness." Applied Sciences 12, no. 24 (December 12, 2022): 12764. http://dx.doi.org/10.3390/app122412764.
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The mount of the engine will creep under the action of long-term load. Creep will change its original structure, resulting in changes in static and dynamic characteristics and fatigue life. In order to solve the problem of mounting rubber creep, the creep characteristics were studied in this paper. In order to study the influence of creep characteristics on engine mounting stiffness, a theoretical model of mount creep was established based on the creep mechanism of rubber. The effects of different loads on the creep characteristics of engine mount were studied. The static viscoelastic parameters and creep analysis of rubber mounting were analyzed numerically. The creep variation law of suspension under different loads is obtained. By analyzing the static and dynamic characteristics of no creep, 2.98 mm creep and 3.83 mm creep of engine mount, the creep characteristics and the variation law of mount stiffness of rubber mount were revealed. The results show that the static stiffness of suspension increases with the increase of creep. When the frequency is constant and the creep increases, the dynamic stiffness of the suspension increases obviously. In this paper, the creep characteristics of rubber mount are analyzed, and the results of the analysis provide a design method for rubber mount design.
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Abdullah, Orhan Sabah, Shaker S. Hassan, and Ahmed N. Al-Khazraji. "Evaluating and Modeling of Tensile Creep Rupture Behavior for Neat and Reinforced Polyamide 6.6." Materials Science Forum 1002 (July 2020): 95–103. http://dx.doi.org/10.4028/www.scientific.net/msf.1002.95.
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Generally, thermoplastic polymers due to their viscoelastic behavior tend to appear creep deformation at low temperature compared to metals; this continuous creep deformation caused irregular shapes with time and resultant unstable dimensional parts. Therefore, the investigation of creep behavior in thermoplastic polymers must be considered as an essential requirement in the design process. This work exanimated the creep rupture behavior for Polyamide 6.6 and their composites which content of 1%MWCNTS or 30 short carbon fibers under variant applied stresses and temperatures, as well as, to create analytical model to the obtained results Findley power law model was employed for this purpose with a comprehensive verification to their compatibility to the experimental results. The results appeared that the addition of reinforced materials and decreasing applied stresses and temperatures will cause an enhancement in creep resistance by increasing rupture time and decreasing the minimum creep rate values. On the other hand, using of Findley power law model gives a good agreement to the obtained experimental results.
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Mainardi, Francesco, and Giorgio Spada. "On the viscoelastic characterization of the Jeffreys–Lomnitz law of creep." Rheologica Acta 51, no. 9 (May 16, 2012): 783–91. http://dx.doi.org/10.1007/s00397-012-0634-x.
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Brown, Christopher U., Timothy L. Norman, Vincent L. Kish, Thomas A. Gruen, and J. David Blaha. "Time-Dependent Circumferential Deformation of Cortical Bone Upon Internal Radial Loading." Journal of Biomechanical Engineering 124, no. 4 (July 30, 2002): 456–61. http://dx.doi.org/10.1115/1.1488168.
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Short and long duration tests were conducted on hollow femoral bone cylinders to study the circumferential (hoop) creep response of cortical bone subjected to an intramedullary radial load. It was hypothesized that there is a stress threshold above which nonlinear creep effects dominate the mechanical response and below which the response is primarily determined by linear viscoelastic material properties. The results indicate that a hoop stress threshold exists for cortical bone, where creep strain, creep strain rate and residual strain exhibited linear behavior at low hoop stress and nonlinear behavior above the hoop stress threshold. A power-law relationship was used to describe creep strain as a function of hoop stress and time and damage morphology was assessed.
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Cheng, Yang-Tse, and Fuqian Yang. "Obtaining shear relaxation modulus and creep compliance of linear viscoelastic materials from instrumented indentation using axisymmetric indenters of power-law profiles." Journal of Materials Research 24, no. 10 (October 2009): 3013–17. http://dx.doi.org/10.1557/jmr.2009.0365.
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Using Laplace transform, we solve the inverse problem of obtaining the shear relaxation modulus and creep compliance of linear viscoelastic solids from indentation by axisymmetric indenters of power-law profiles. We identify several simple, though nontrivial, loading paths for carrying out indentation measurements such that the inverse problem has analytical solutions. We show that the shear relaxation modulus and creep compliance may be readily obtained using the newly derived analytical expressions together with proposed indentation loading paths.
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Alrubaie, Murtada Abass A., Douglas J. Gardner, and Roberto A. Lopez-Anido. "Modeling the Long-Term Deformation of a Geodesic Spherical Frame Structure Made from Wood Plastic Composite Lumber." Applied Sciences 10, no. 14 (July 21, 2020): 5017. http://dx.doi.org/10.3390/app10145017.
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The long-term deformation of a geodesic spherical frame structure with a diameter of 20 m made from wood plastic composite (WPC) lumber (struts) is described using the Norton-Bailey power law model to predict the service life creep behavior (the creep strain ( ε c r )) of the WPC. The Norton-Bailey power law model parameters, A the power law multiplier, n the stress order, and m the time order, were obtained from experimental four-point bending flexural creep measurements of WPC lumber subjected to three levels of flexural stress: 7, 14, and 29% of the ultimate flexural strength for 200 days. The parameters obtained from the experiments showed good agreement to the model of the WPC lumber in flexure. The Norton-Bailey power law parameters were then implemented to describe the long-term deformation of the spherical frame structure. The limit of failure was considered when the WPC creep strain reaches the value of 1%. However, the FEA predicted the maximum creep strain to be 20% of the failure strain. This modeling approach is considered useful to describe and predict the long-term deformation of aquacultural structures made from viscoelastic materials during the envisioned service life (10 years) based on experimental creep data for the members that form the structure.
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Morland, L. W. "Primary, secondary and tertiary creep of ice modelled as a viscoelastic fluid." Journal of Glaciology 55, no. 189 (2009): 170–78. http://dx.doi.org/10.3189/002214309788608976.
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AbstractAs an ice sheet evolves, there are ice elements near the surface only recently subjected to stress following deposition, and others that have been subjected to stress over many ranges of time. The constant stress and constant strain-rate responses of ice in uniaxial compressive stress exhibit non-viscous behaviour, that is, the strain rate is not fixed by the stress (and conversely) but both vary with time. At constant stress the initial primary strain rate decreases with time to a minimum, described as secondary creep. It then increases and approaches an asymptotic limit, described as tertiary creep. Analogously, at constant strain rate the initial stress increases to a maximum then decreases to an asymptotic limit. These responses are used to construct a simple viscoelastic fluid constitutive law of differential type. Such a time-dependent law, with timescales changing widely with temperature, can be expected to yield a flow field in an ice sheet that is very different from that obtained from the viscous law. Only comparison solutions for both constitutive laws can determine the differences and significance of the non-viscous behaviour, and the simple law constructed would be a candidate for such comparisons.
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Heinrich, S. M., S. Shakya, J. Liang, and P. S. Lee. "An Analytical Model for Time-Dependent Shearing Deformation in Area-Array Interconnects." Journal of Electronic Packaging 122, no. 4 (January 28, 2000): 328–34. http://dx.doi.org/10.1115/1.1289631.
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An analytical model is developed for predicting the time-dependent shearing displacement in area-array solder interconnects due to global CTE mismatch under thermal cycling. As a first step toward incorporating the creep deformation of the solder, the material is modeled as viscoelastic and temperature-independent. This permits one to invoke the correspondence principle of viscoelasticity to map the authors’ previously derived, closed-form solution for an elastic nonprismatic (concave, convex, or cylindrical) Timoshenko beam under shear loading into the associated viscoelastic solution. This leads to general analytical results for the frequency-dependent shear displacement amplitude in the critical joint. The results are expressed conveniently in terms of a “full-creep correction factor” and a “frequency correction factor,” which explicitly show the effects of the following parameters on the joint deformation: joint shape; array population; array, component, and substrate dimensions; viscoelastic material properties of the interconnect material; elastic properties of the component and substrate materials; and loading frequency. To demonstrate the technique for a particular viscoelastic constitutive law, the solder is assumed to behave elastically under hydrostatic loads and as a viscoelastic Kelvin solid under deviatoric conditions. For this special case the creep portion of the deformation is shown to be dependent upon only two dimensionless parameters: a dimensionless loading frequency and a material- and shape-dependent joint parameter. The results of the study may be useful in identifying design and process modifications that may improve the thermal fatigue life of area arrays. [S1043-7398(00)00404-7]
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Dacol, Vitor, Elsa Caetano, and João Correia. "A New Viscoelasticity Dynamic Fitting Method Applied for Polymeric and Polymer-Based Composite Materials." Materials 13, no. 22 (November 18, 2020): 5213. http://dx.doi.org/10.3390/ma13225213.
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The accurate analysis of the behaviour of a polymeric composite structure, including the determination of its deformation over time and also the evaluation of its dynamic behaviour under service conditions, demands the characterisation of the viscoelastic properties of the constituent materials. Linear viscoelastic materials should be experimentally characterised under (i) constant static load and/or (ii) harmonic load. In the first load case, the viscoelastic behaviour is characterised through the creep compliance or the relaxation modulus. In the second load case, the viscoelastic behaviour is characterised by the complex modulus, E*, and the loss factor, η. In the present paper, a powerful and simple implementing technique is proposed for the processing and analysis of dynamic mechanical data. The idea is to obtain the dynamic moduli expressions from the Exponential-Power Law Method (EPL) of the creep compliance and the relaxation modulus functions, by applying the Carson and Laplace transform functions and their relationship to the Fourier transform, and the Theorem of Moivre. Reciprocally, once the complex moduli have been obtained from a dynamic test, it becomes advantageous to use mathematical interconversion techniques to obtain the time-domain function of the relaxation modulus, E(t), and the creep compliance, D(t). This paper demonstrates the advantages of the EPL method, namely its simplicity and straightforwardness in performing the desirable interconversion between quasi-static and dynamic behaviour of polymeric and polymer-composite materials. The EPL approximate interconversion scheme to convert the measured creep compliance to relaxation modulus is derived to obtain the complex moduli. Finally, the EPL Method is successfully assessed using experimental data from the literature.
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DI MINO, Gaetano, Gordon AIREY, Mario DI PAOLA, Francesco Paolo PINNOLA, Giacomo D’ANGELO, and Davide LO PRESTI. "LINEAR AND NONLINEAR FRACTIONAL HEREDITARY CONSTITUTIVE LAWS OF ASPHALT MIXTURES." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 22, no. 7 (July 12, 2016): 882–89. http://dx.doi.org/10.3846/13923730.2014.914104.
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The aim of this paper is to propose a fractional viscoelastic and viscoplastic model of asphalt mixtures using experimental data of several tests such as creep and creep recovery performed at different temperatures and at different stress levels. From a best fitting procedure it is shown that both the creep one and recovery curve follow a power law model. It is shown that the suitable model for asphalt mixtures is a dashpot and a fractional element arranged in series. The proposed model is also available outside of the linear domain but in this case the parameters of the model depend on the stress level.
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Sorvari, Joonas, Teemu Leppänen, and Jukka Silvennoinen. "The effect of the through-thickness moisture content gradient on the moisture accelerated creep of paperboard: Hygro-viscoelastic modeling approach." Nordic Pulp & Paper Research Journal 33, no. 1 (May 23, 2018): 122–32. http://dx.doi.org/10.1515/npprj-2018-3001.
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Abstract Paper-based materials are viscous materials, the time-dependent behavior of which depends strongly on moisture content. Particularly the creep of paperboard containers under compressive forces is greatly affected by changes in the relative humidity. In the present paper, we examine the creep behavior of paperboard under cyclic humidity conditions using the finite element method. Especially the shape and rate of the through-thickness moisture content gradient on moisture accelerated creep are studied. An isotropic hygro-viscoelastic constitutive law is used for paperboard. The results of the simulations are compared with experiments. It is concluded that the through-thickness moisture gradients have a great impact on the moisture accelerated creep of paperboard. Furthermore, the results show that depending on the direction of external load the through-thickness moisture content gradient may increase or decrease creep rate.
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Lavergne, François A., Peter Sollich, and Véronique Trappe. "Delayed elastic contributions to the viscoelastic response of foams." Journal of Chemical Physics 156, no. 15 (April 21, 2022): 154901. http://dx.doi.org/10.1063/5.0085773.
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We show that the slow viscoelastic response of a foam is that of a power-law fluid with a terminal relaxation. Investigations of the foam mechanics in creep and recovery tests reveal that the power-law contribution is fully reversible, indicative of a delayed elastic response. We demonstrate how this contribution fully accounts for the non-Maxwellian features observed in all tests, probing the linear mechanical response function. The associated power-law spectrum is consistent with soft glassy rheology of systems with mechanical noise temperatures just above the glass transition [Fielding et al., J. Rheol. 44, 323 (2000)] and originates from a combination of superdiffusive bubble dynamics and stress diffusion, as recently evidenced in simulations of coarsening foam [Hwang et al., Nat. Mater. 15, 1031 (2016)].
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Minárová, Mária. "Isothermal viscoelasticity and energy." MATEC Web of Conferences 310 (2020): 00043. http://dx.doi.org/10.1051/matecconf/202031000043.
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Within the scope of the linear viscoelasticity theory, the change in the inner energy of a viscoelastic body is induced either by heat exchange or by a work performance. The first law of thermodynamics, balance equation of a closed system is mostly referred when the thermodynamic consistency of some rheological model is required. Accordingly, within the frame of the isothermal viscoelastic investigation we just distinguish between the stored and dissipated energy. And this is the issue that the paper is focused on. Subjected to a load, the one degree of freedom viscoelastic models’ behaviour is traced, together with the observation of the energy – total, stored and dissipated. Nevertheless, the only stored energy in viscoelastic model is potential energy. General considerations are applied on Maxwell model subjected to the standard both creep and relaxation tests.
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Johnson, A. R., A. Tessler, and M. Dambach. "Dynamics of Thick Viscoelastic Beams." Journal of Engineering Materials and Technology 119, no. 3 (July 1, 1997): 273–78. http://dx.doi.org/10.1115/1.2812256.
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A viscoelastic higher-order thick beam finite element formulation is extended to include elastodynamic deformations. The material constitutive law is a special differential form of the Maxwell solid, which employs viscous strains as internal variables to determine the viscous stresses. The total time-dependent stress is the superposition of its elastic and viscous components. In the constitutive model, the elastic strains and the conjugate viscous strains are coupled through a system of first-order ordinary differential equations. The use of the internal strain variables allows for a convenient finite element formulation. The elastodynamic equations of motion are derived from the virtual work principle. Computational examples are carried out for a thick orthotropic cantilevered beam. Relaxation, creep, relaxation followed by free damped vibrations, and damping related modal interactions are discussed.
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Vena, P., D. Gastaldi, and R. Contro. "A Constituent-Based Model for the Nonlinear Viscoelastic Behavior of Ligaments." Journal of Biomechanical Engineering 128, no. 3 (December 12, 2005): 449–57. http://dx.doi.org/10.1115/1.2187046.
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This paper presents a constitutive model for predicting the nonlinear viscoelastic behavior of soft biological tissues and in particular of ligaments. The constitutive law is a generalization of the well-known quasi-linear viscoelastic theory (QLV) in which the elastic response of the tissue and the time-dependent properties are independently modeled and combined into a convolution time integral. The elastic behavior, based on the definition of anisotropic strain energy function, is extended to the time-dependent regime by means of a suitably developed time discretization scheme. The time-dependent constitutive law is based on the postulate that a constituent-based relaxation behavior may be defined through two different stress relaxation functions: one for the isotropic matrix and one for the reinforcing (collagen) fibers. The constitutive parameters of the viscoelastic model have been estimated by curve fitting the stress relaxation experiments conducted on medial collateral ligaments (MCLs) taken from the literature, whereas the predictive capability of the model was assessed by simulating experimental tests different from those used for the parameter estimation. In particular, creep tests at different maximum stresses have been successfully simulated. The proposed nonlinear viscoelastic model is able to predict the time-dependent response of ligaments described in experimental works (Bonifasi-Lista et al., 2005, J. Orthopaed. Res., 23, pp. 67–76;Hingorani et al., 2004, Ann. Biomed. Eng., 32, pp. 306–312;Provenzano et al., 2001, Ann. Biomed. Eng., 29, pp. 908–214;Weiss et al., 2002, J. Biomech., 35, pp. 943–950). In particular, the nonlinear viscoelastic response which implies different relaxation rates for different applied strains, as well as different creep rates for different applied stresses and direction-dependent relaxation behavior, can be described.
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Bartelt, Perry, and Markus Von Moos. "Triaxial tests to determine a microstructure-based snow viscosity law." Annals of Glaciology 31 (2000): 457–62. http://dx.doi.org/10.3189/172756400781819761.
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AbstractThis paper describes a new triaxial testing apparatus designed to determine the creep (viscoelastic) behavior of snow. The device is deformation-controlled and can apply strain rates between 10–7 s–1 and 10–2s–1 in tension and compression. The sample volume change is determined by measuring the displaced pore-air volume. During winters 1997/98 and 1998/99, >100 compression and tension tests were carried out. It is shown that snow is a highly non-linear but ideal viscoelastic material with a strong strain-rate dependency. A selection of test results is provided. We show how snow viscosity varies with density and strain rate. In a final analysis we interpret our results with respect to snow microstructure in order to develop microstructure-based constitutive relations which can be implemented in finite-element programs. Our results clearly show that for snow densities and strain rates tested, straining of the grain bonds is the primary mechanism of deformation within the snow ice lattice.
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Patnaik, S. Srikant, and Tarapada Roy. "Viscoelastic and mechanical properties of CNT-reinforced polymer-based hybrid composite materials using hygrothermal creep." Polymers and Polymer Composites 29, no. 9_suppl (November 2021): S1386—S1402. http://dx.doi.org/10.1177/09673911211052730.
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In the present work, a combination of experimental and numerical procedure is proposed to study the effects of different hygrothermal conditions on the creep strain, viscoelastic properties of nanocomposites, and mechanical properties of such nanocomposite-based carbon fiber–reinforced polymer (CFRP) hybrid composite materials. Ultrasonic probe sonicator is used to randomly disperse the multiwalled carbon nanotubes into an epoxy to minimize agglomerations. Dynamic mechanical analysis is employed to conduct the creep tests under different hygrothermal conditions of such nanocomposite samples. The Findley power law is used to obtain the long-term creep behavior of nanocomposite materials. Prony series is used to determine the viscoelastic properties of nanocomposite material in the frequency domain. Coefficient of moisture expansion (CME) is independent of moisture concentration; thus, CME of the nanocomposite is also determined. Strength of materials and Saravanos–Chamis micromechanics (SCM) have also been utilized to obtain the mechanical properties of such hybrid composite materials under different hygrothermal conditions. It has been found that the inclusion of multiwalled carbon nanotubes in the nanocomposite and hybrid composites improves storage modulus and loss factor (i.e., tan δ) compared to the conventional CFRP-based composite materials under hygrothermal conditions.
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Wang, Shau-Chew, and Eberhard A. Meinecke. "Buckling of Viscoelastic Columns. Part I: Constant Load Buckling." Rubber Chemistry and Technology 58, no. 1 (March 1, 1985): 154–63. http://dx.doi.org/10.5254/1.3536056.
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Abstract The constant load buckling of viscoelastic columns has been studied extensively in the past and equations have been derived to predict the buckling time from the geometry of the columns and the constitutive equation of the material. These theories restrict themselves to columns loaded with an axial load only. A variety of linear as well as nonlinear creep laws have been utilized. In this study, existing creep-buckling equations have been modified to include the effect of lateral loads on the time to buckle. The constitutive equation used is the power law which applies quite well for well-vulcanized elastomers. Furthermore, the viscoelastic response of the material was assumed to be linear, which can be justified by the extremely small compressive strains found before buckling occurs. The validity of the equations has been compared to experimental data obtained on well-vulcanized elastomeric columns of different slenderness ratios under a variety of loading conditions. An attempt has been made to explain some discrepancies between theory and experimental findings.
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Chepurnenko, Anton, Stepan Litvinov, Besarion Meskhi, and Alexey Beskopylny. "Optimization of Thick-Walled Viscoelastic Hollow Polymer Cylinders by Artificial Heterogeneity Creation: Theoretical Aspects." Polymers 13, no. 15 (July 22, 2021): 2408. http://dx.doi.org/10.3390/polym13152408.
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A theoretical solution of the problem of thick-walled shell optimization by varying the mechanical characteristics of the material over the thickness of the structure is proposed, taking into account its rheological properties. The optimization technique is considered by the example of a cylindrical shell made of high-density polyethylene with hydroxyapatite subjected to internal pressure. Radial heterogeneity can be created by centrifugation during the curing of the polymer mixed with the additive. The nonlinear Maxwell–Gurevich equation is used as the law describing polymer creep. The relationship of the change in the additive content along with the radius r, at which the structure is equally stressed following the four classical criteria of fracture, is determined in an elastic formulation. Moreover, it is shown that a cylinder with equal stress at the beginning of the creep process ceases to be equally stressed during creep. Finally, an algorithm for defining the relationship of the additive mass content on coordinate r, at which the structure is equally stressed at the end of the creep process, is proposed. The developed algorithm, implemented in the MATLAB software, allows modeling both equally stressed and equally strength structures.
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Schiffmann, Kirsten Ingolf. "Nanoindentation creep and stress relaxation tests of polycarbonate: Analysis of viscoelastic properties by different rheological models." International Journal of Materials Research 97, no. 9 (September 1, 2006): 1199–211. http://dx.doi.org/10.1515/ijmr-2006-0189.
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Abstract Feedback-controlled nanoindentation with a Berkovich diamond tip has been used to perform creep and stress relaxation tests on polycarbonate at room temperature for a wide range of loads (10 – 30000 μN) and indentation depths (30 – 3000 nm). The creep compliance J(t) and relaxation modulus G(t) have been calculated from experimental data as a function of time in the range t = 0.1 – 100 (1000) s. The data are analysed by different rheological models which are compared: (1) the Burgers model, (2) the generalised Maxwell/generalised Kelvin model, and two empirical approaches: (3) a logarithmic model, and (4) a power law model. The Burgers model gives a poor description of the material behaviour since it assumes a steady-state flow of material which is not observed in the experimental time range. The generalised models yield a set of discrete relaxation- and retardation time constants. It is shown that these time constants do not correlate with specific molecular moving processes in the polymer, but are only one of several possible parameterisations of the creep and relaxation curves. Numerical differentiation of G(t) and J(t) shows that polycarbonate has continuous relaxation- and retardation time spectra, respectively, and the dynamic viscosity η(t) of the material increases linearly with time. The behaviour of polycarbonate is best represented by the empirical power law model, which allows optimum fit of creep/relaxation curves, relaxation and retardation time spectra and time-dependent viscosity.
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MacAyeal, Douglas R., Olga V. Sergienko, and Alison F. Banwell. "A model of viscoelastic ice-shelf flexure." Journal of Glaciology 61, no. 228 (2015): 635–45. http://dx.doi.org/10.3189/2015jog14j169.
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AbstractWe develop a formal thin-plate treatment of the viscoelastic flexure of floating ice shelves as an initial step in treating various problems relevant to ice-shelf response to sudden changes of surface loads and applied bending moments (e.g. draining supraglacial lakes, iceberg calving, surface and basal crevassing). Our analysis is based on the assumption that total deformation is the sum of elastic and viscous (or power-law creep) deformations (i.e. akin to a Maxwell model of viscoelasticity, having a spring and dashpot in series). The treatment follows the assumptions of well-known thin-plate approximation, but is presented in a manner familiar to glaciologists and with Glen’s flow law. We present an analysis of the viscoelastic evolution of an ice shelf subject to a filling and draining supraglacial lake. This demonstration is motivated by the proposition that flexure in response to the filling/drainage of meltwater features on the Larsen B ice shelf, Antarctica, contributed to the fragmentation process that accompanied its collapse in 2002.
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Alotta, Gioacchino, Olga Barrera, and Elise C. Pegg. "Viscoelastic material models for more accurate polyethylene wear estimation." Journal of Strain Analysis for Engineering Design 53, no. 5 (April 24, 2018): 302–12. http://dx.doi.org/10.1177/0309324718765512.
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Wear debris from ultra-high-molecular-weight polyethylene components used for joint replacement prostheses can cause significant clinical complications, and it is essential to be able to predict implant wear accurately in vitro to prevent unsafe implant designs continuing to clinical trials. The established method to predict wear is simulator testing, but the significant equipment costs, experimental time and equipment availability can be prohibitive. It is possible to predict implant wear using finite element methods, though those reported in the literature simplify the material behaviour of polyethylene and typically use linear or elastoplastic material models. Such models cannot represent the creep or viscoelastic material behaviour and may introduce significant error. However, the magnitude of this error and the importance of this simplification have never been determined. This study compares the volume of predicted wear from a standard elastoplastic model, to a fractional viscoelastic material model. Both models have been fitted to the experimental data. Standard tensile tests in accordance with ISO 527-3 and tensile creep recovery tests were performed to experimentally characterise both (a) the elastoplastic parameters and (b) creep and relaxation behaviour of the ultra-high molecular weight polyethylene. Digital image correlation technique was used in order to measure the strain field. The predicted wear with the two material models was compared for a finite element model of a mobile-bearing unicompartmental knee replacement, and wear predictions were made using Archard’s law. The fractional viscoelastic material model predicted almost ten times as much wear compared to the elastoplastic material representation. This work quantifies, for the first time, the error introduced by use of a simplified material model in polyethylene wear predictions, and shows the importance of representing the viscoelastic behaviour of polyethylene for wear predictions.
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Lakes, R. S., and R. Vanderby. "Interrelation of Creep and Relaxation: A Modeling Approach for Ligaments." Journal of Biomechanical Engineering 121, no. 6 (December 1, 1999): 612–15. http://dx.doi.org/10.1115/1.2800861.
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Experimental data (Thornton et al., 1997) show that relaxation proceeds more rapidly (a greater slope on a log-log scale) than creep in ligament, a fact not explained by linear viscoelasticity. An interrelation between creep and relaxation is therefore developed for ligaments based on a single-integral nonlinear superposition model. This interrelation differs from the convolution relation obtained by Laplace transforms for linear materials. We demonstrate via continuum concepts of nonlinear viscoelasticity that such a difference in rate between creep and relaxation phenomenologically occurs when the nonlinearity is of a strain-stiffening type, i.e., the stress-strain curve is concave up as observed in ligament. We also show that it is inconsistent to assume a Fung-type constitutive law (Fung, 1972) for both creep and relaxation. Using the published data of Thornton et al. (1997), the nonlinear interrelation developed herein predicts creep behavior from relaxation data well (R ≥ 0.998). Although data are limited and the causal mechanisms associated with viscoelastic tissue behavior are complex, continuum concepts demonstrated here appear capable of interrelating creep and relaxation with fidelity.
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Yazyev, Batyr M., Anton S. Chepurnenko, and Anzhelika V. Saibel. "MODELING OF STRESS-STRAIN STATE OF THICK CONCRETE SLABS TAKING THE CREEP OF CONCRETE INTO ACCOUNT." International Journal for Computational Civil and Structural Engineering 13, no. 4 (December 31, 2017): 140–48. http://dx.doi.org/10.22337/2587-9618-2017-13-4-140-148.
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In the article the derivation of the resolving equations for calculation taking into account creep of thick reinforced concrete plates is given. We use the hypothesis of a parabolic law for the distribution of tangential stresses over the thickness of a plate. The problem was reduced to a system of two differential equations with respect to deflection and the function of shear. An example is given of a calculation of a plate hinged on the contour loaded with a uniformly distributed load using a viscoelastic model of hereditary aging of concrete. The solution was carried out using double trigonometric series in combination with the Euler method for determining creep strains.
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ATTIA, MOHAMED A., AHMED G. EL-SHAFEI, and FATIN F. MAHMOUD. "NONLINEAR ANALYSIS OF FRICTIONAL THERMO-VISCOELASTIC CONTACT PROBLEMS USING FEM." International Journal of Applied Mechanics 06, no. 03 (May 6, 2014): 1450028. http://dx.doi.org/10.1142/s1758825114500288.
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This study presents a numerical finite element model to analyze the response of frictional thermo-viscoelastic contact systems, which experience material and geometrical nonlinearities. Thermo-rheologically complex behavior of the contacting bodies is assumed. The nonlinear viscoelastic constitutive model is expressed by an integral form of a creep function, whose elastic and time-dependent properties vary with stresses and temperatures. Adopting the assumption that the hydrostatic and deviatoric responses are uncoupled, the constitutive equation is expressed in an incremental form, with the hereditary integral updated at the end of each time increment by recursive computation. The Lagrange multiplier approach is applied to incorporate the inequality contact constraints, while friction effect along the contact interface is modeled using a local nonlinear friction law. The material and geometrical nonlinearities are modeled in the framework of the total Lagrangian formulation. The developed nonlinear viscoelastic model is verified using the available benchmarks. The applicability of the developed model is demonstrated by solving two thermo-viscoelastic frictional contact problems with different contact natures. Results show a distinct effect of the thermo-rheological behavior on viscoelastic contact status.
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ABDEL RAHMAN, ALAA A., AHMED G. EL-SHAFEI, and FATIN F. MAHMOUD. "NONLINEAR ANALYSIS OF VISCOELASTICALLY LAYERED ROLLS IN STEADY STATE ROLLING CONTACT." International Journal of Applied Mechanics 06, no. 06 (December 2014): 1450065. http://dx.doi.org/10.1142/s1758825114500653.
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The present paper analyzes the steady state rolling contact (SSRC) response of nonlinear viscoelastically layered rigid roll indented by a rigid cylindrical indenter. Both material and geometrical nonlinearities are accounted for in the framework of the updated Lagrangian finite element formulation. The Schapery's viscoelastic creep model is adopted to model the viscoelastic behavior. To accommodate the steady state rolling condition, the constitutive equations are recast into a spatially dependent incremental form. Throughout the contact interface, the Lagrange multiplier method is used to enforce the contact constraints, while the classical Coulomb's law is adopted to simulate friction. The resulting nonlinear equilibrium equations are solved by the Newton–Raphson method. The developed model is applied to analyze a viscoelastically layered rigid roll in steady state rolling and intended by a rigid cylindrical indenter. Results showed the distinct effects of angular velocity, retardation time, indenter radius, and viscoelastic layer thickness on the SSRC configuration.
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Kovalchenko, M. S. "Rheology and Kinetics of Pressure Sintering." Materials Science Forum 835 (January 2016): 76–105. http://dx.doi.org/10.4028/www.scientific.net/msf.835.76.
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The rheological viscous flow model of deformable, irreversibly compressible, porous body based on mechanics of continua, and creep theory of crystalline materials, is used to describe quantitatively the sintering of powder materials with pressure in isothermal and nonisothermal conditions. Densification of the porous body occurs under action of Laplace pressure, generated by surface tension, and applied pressure. The densification kinetics of porous metals and crystalline compounds in initial and intermediate stages of sintering with static external pressure represent nonlinear steady-state creep controlled by a climb dislocation mechanism in solid matrix forming porous material. Activation energies of this mechanism are consistent with the bulk diffusion. A diffusional creep controls the pressure sintering kinetics in a later stage. The rheological models of deformable viscoelastic bodies and the associated dynamic strain theory for viscoelastic irreversibly compressible bodies, based on the energy conservation law, enable a quantitative description of their densification under dynamic loading. At the same time it is taking into account the internal energy of deformable body. The solutions of dynamic systems involve the mechanical interaction of compacting machine with this body. The simulation of impact sintering of porous metals shows that the viscosity of the matrix, that forms the porous body, and the activation energy of viscous deformation dramatically decrease with increasing initial impact velocity. This promotes the compaction of the material to practically nonporous state and enhances its mechanical properties.
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Lenormand, Guillaume, Emil Millet, Ben Fabry, James P. Butler, and Jeffrey J. Fredberg. "Linearity and time-scale invariance of the creep function in living cells." Journal of The Royal Society Interface 1, no. 1 (November 22, 2004): 91–97. http://dx.doi.org/10.1098/rsif.2004.0010.
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We report here the creep function measured in three cell types, after a variety of interventions, and over three time decades (from 3ms to 3.2 s). In each case the response conformed to a power law, implying that no distinct molecular relaxation times or time constants could characterize the response. These results add to a growing body of evidence that stands in contrast to widely used viscoelastic models featuring at most a few time constants. We show instead that the ability of the matrix to deform is time-scale invariant and characterized by only one parameter: the power law exponent that controls the transition between solid-like and liquid-like behaviour. Moreover, we validate linearity by comparison of measurements in the time and frequency domains.
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Li, Sheng-Nan, Zhu Peng, Zhong-Hua Huang, Qiao Liang, Jie Liu, and Wen-Quan Zhou. "Time-Dependent Deformation and Long-Term Strength of Carbonaceous Mudstone under Dry and Wet Cycles." Sustainability 14, no. 19 (September 23, 2022): 12044. http://dx.doi.org/10.3390/su141912044.
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Clarifying the time-dependent strength deterioration characteristics of carbonaceous mudstone under dry and wet cycles is of great significance to the design of expressway cut slopes. In this work, we conducted triaxial compression creep tests on carbonaceous mudstone specimens that had undergone different numbers of dry and wet cycles to investigate their creep properties. A function was established between the steady-state viscoplastic creep rate and axial compression. The threshold stress of the steady-state viscoplastic creep rate was assumed as the long-term strength, and the long-term strength deterioration law of carbonaceous mudstone under dry and wet cycles was studied. The results showed that the transient strain, viscoelastic creep, and viscoplastic creep of carbonaceous mudstone increased with the number of dry and wet cycles, and the creep failure stress and transient elasticity modulus decreased. Based on the steady-state viscoplastic creep rate method, the long-term strength of carbonaceous mudstone after n (n = 0, 3, 6, 9) dry and wet cycles was found to be 74.25%, 64.88%, 57.56%, and 53.16% of its uniaxial compression strength, respectively. Compared with the isochronous curve method and the transition creep method, the steady-state viscoplastic creep rate method can more accurately determine the long-term rock strength. The long-term strength of carbonaceous mudstone under dry and wet cycles decays exponentially, and the long-term strength decay rate during the first three dry and wet cycles is about 215 times the average decay rate.
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Alrubaie, Murtada Abass A., Roberto A. Lopez-Anido, and Douglas J. Gardner. "Flexural Creep Behavior of High-Density Polyethylene Lumber and Wood Plastic Composite Lumber Made from Thermally Modified Wood." Polymers 12, no. 2 (January 24, 2020): 262. http://dx.doi.org/10.3390/polym12020262.
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The use of wood plastic composite lumber as a structural member material in marine applications is challenging due to the tendency of wood plastic composites (WPCs) to creep and absorb water. A novel patent-pending WPC formulation that combines a thermally modified wood flour (as a cellulosic material) and a high strength styrenic copolymer (high impact polystyrene and styrene maleic anhydride) have been developed with advantageous viscoelastic properties (low initial creep compliance and creep rate) compared with the conventional WPCs. In this study, the creep behavior of the WPC and high-density polyethylene (HDPE) lumber in flexure was characterized and compared. Three sample groupings of WPC and HDPE lumber were subjected to three levels of creep stress; 7.5, 15, and 30% of the ultimate flexural strength (Fb) for a duration of 180 days. Because of the relatively low initial creep compliance of the WPC specimens (five times less) compared with the initial creep compliance of HDPE specimens, the creep deformation of HDPE specimens was six times higher than the creep deformation of WPC specimens at the 30% creep stress level. A Power Law model predicted that the strain (3%) to failure in the HDPE lumber would occur in 1.5 years at 30% Fb flexural stress while the predicted strain (1%) failure for the WPC lumber would occur in 150 years. The findings of this study suggest using the WPC lumber in structural application to replace the HDPE lumber in flexure attributable to the low time-dependent deformation when the applied stress value is withing the linear region of the stress-strain relationship.
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Álvarez-Vázquez, Adrián, Alfonso Fernández-Canteli, Enrique Castillo Ron, Pelayo Fernández Fernández, Miguel Muñiz-Calvente, and María Jesús Lamela Rey. "A Novel Approach to Describe the Time–Temperature Conversion among Relaxation Curves of Viscoelastic Materials." Materials 13, no. 8 (April 11, 2020): 1809. http://dx.doi.org/10.3390/ma13081809.
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Time and temperature, besides pressure in a lesser extent, represent the most significant variables influencing the rheological behavior of viscoelastic materials. These magnitudes are each other related through the well-known Time–Temperature Superposition (TTS) principle, which allows the master curve referred to relaxation (or creep) behavior to be derived as a material characteristic. In this work, a novel conversion law to interrelate relaxation curves at different temperatures is proposed by assuming they to be represented by statistical cumulative distribution functions of the normal or Gumbel family. The first alternative responds to physical considerations while the latter implies the fulfillment of extreme value conditions. Both distributions are used to illustrate the suitability of the model when applied to reliable derivation of the master curve of Polyvinil–Butyral (PVB) from data of experimental programs. The new approach allows not only the TTS shift factors to be estimated by a unique step, but the whole family of viscoelastic master curves to be determined for the material at any temperature. This represents a significant advance in the characterization of viscoelastic materials and, consequently, in the application of the TTS principle to practical design of viscoelastic components.
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Abuzeid, Osama M., Anas N. Al-Rabadi, and Hashem S. Alkhaldi. "Fractal Geometry-Based Hypergeometric Time Series Solution to the Hereditary Thermal Creep Model for the Contact of Rough Surfaces Using the Kelvin-Voigt Medium." Mathematical Problems in Engineering 2010 (2010): 1–22. http://dx.doi.org/10.1155/2010/652306.
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This paper aims at constructing a continuous hereditary creep model for the thermoviscoelastic contact of a rough punch and a smooth surface of a rigid half-space. The used model considers the rough surface as a function of the applied load and temperatures. The material of the rough punch surface is assumed to behave as Kelvin-Voigt viscoelastic material. Such a model uses elastic springs and viscous dashpots in parallel. The fractal-based punch surface is modelled using a deterministic Cantor structure. An asymptotic power law, deduced using approximate iterative relations, is used to express the punch surface creep which is a time-dependent inelastic deformation. The suggested law utilized the hypergeometric time series to relate the variables of creep as a function of remote forces, body temperatures, and time. The model is valid when the approach of punch surface and half space is in the order of the size of the surface roughness. The closed-form results are obtained for selected values of the system parameters; the fractal surface roughness and various material properties. The obtained results show good agreement with published experimental results, and the methodology can be further extended to other structures such as the Kelvin-Voigt medium within electronic circuits and systems.
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Yazyev, S. В., V. I. Andreev, and А. S. Chepurnenko. "Stability analysis of wooden arches with account for nonlinear creep." Advanced Engineering Research 21, no. 2 (July 9, 2021): 114–22. http://dx.doi.org/10.23947/2687-1653-2021-21-2-114-122.
Full textAbstract:
Introduction. The paper deals with the calculation of wooden arches taking into account the nonlinear relationship between stresses and instantaneous deformations, as well as creep and geometric nonlinearity, are considered. The analysis is based on the integral equation of the viscoelastoplastic hereditary aging model, originally proposed by A.G. Tamrazyan [1] to describe the nonlinear creep of concrete.Materials and Methods. The creep measure is taken in accordance with the work of I.E. Prokopovich and V.A. Zedgenidze [2] as a sum of exponential functions. The transition from the integral form of the creep law to the differential form is shown. The relationship between stresses and instantaneous deformations for wood under compression is determined from the Gerstner formula, and elastic work is assumed under tension. The solution is carried out using the finite element method in combination with the Newton-Raphson method and the Euler method according to the scheme that involves a stepwise increase in the load with correction of the stiffness matrix taking into account the change in the coordinates of the nodes with the sequential calculation of additional displacements of the nodes, which are due to the residual forces. The proposed approach for increasing the accuracy of determination of creep deformations at each step provides using the fourth-order Runge-Kutta method instead of the Euler method.Results. Based on the Lagrange variational principle, expressions are obtained for the stiffness matrix and the vector of additional dummy loads due to creep. The method developed by the authors is implemented in the form of a program in the MATLAB environment. Calculation examples are given for parabolic arches simply supported at the ends without an intermediate hinge and with an intermediate hinge in the middle of the span under the action of a uniformly distributed load. The results obtained are compared in the viscoelastic and viscoelastic formulation. The reliability of the results is validated through the calculation in the elastic formulation in the ANSYS software package.Discussion and Conclusions. For the arches considered, it is found that even with a load close to the instant critical, the growth of time travel is limited. Thus, the nature of their work under creep conditions differs drastically from the nature of the deformation of compressed rods.