Burgers Model Research Articles

Viscoelastic models in green composites from PLA and hazelnut shell fillers with a natural plasticizer from epoxidized linseed oil

In a same way to polymeric materials, some composite materials as it is the case of green composites, are characterized by a viscoelastic behaviour which plays a key role in their mechanical properties with time. The use of some engineering materials could be restricted as their mechanical properties could be highly affected by temperature or time. For this reason, this work is focused on the modeling of the viscoelastic behaviour of this biomaterial composite with a biobased polymer matrix from poly(lactic acid) and a lignocellulosic reinforcement/filler coming from hazelnut shell with different plasticizer content. In particular, a biobased plasticizer, namely epoxidized linseed oil (ELO) has been employed. A first approach to the viscoelastic behaviour of these composites is summarized in this work. The Maxwell model considers a series combination of the elastic reponse (represented by a spring) and the viscous contribution (represented by a dashpot). The Kelvin-Voigt model considers the same physical elements (spring and dashpot) but coupled in parallel. As these two basic visceolastic models show important restrictions regarding the real viscoelastic behaviour, this work also considers a series combination of the Maxwell model and the Kelvin-Voigt model, known as Burgers model. This works focuses on determining the different parameters of the Burgers model to fit experimental data from PLA-hazelnut shell flour biocomposites with varying plasticizer (ELO) content.

Measuring Subsidence Over Soft Clay Highways Using a Novel Time-Series InSAR Deformation Model With an Emphasis on Rheological Properties and Environmental Factors (NREM)

Long-term monitoring of highways in soft soil areas, especially during the postconstruction period, is of great significance to ensure transportation safety and the quality of highway construction. Multitemporal interferometric synthetic aperture radar (MTInSAR) provides an effective tool for soft clay highway monitoring. However, most time-series models used in MTInSAR modeling are empirical mathematical functions, which ignores the physical properties of the observed objects and may limit the accuracy of the retrieved deformation and the understanding of the underground settlement dynamics. We propose a novel InSAR time-series deformation model (namely, NREM) with an emphasis on the rheological mechanisms for soft soil highways and environmental factors (temperature, humidity, and precipitation) to improve the accuracy of the traditional InSAR model and assist in the analyzing the rheological properties of soft soil. The NREM is constructed based on a combination of the seasonal model and the Burgers model introduced from the field of rheology. The primary parameters (i.e., viscosity and elastic modulus) are introduced in the NREM and estimated with the generation of time-series surface deformation. In the real data experiments, two highways are selected as the test areas. The results show that the standard deviations (STDs) of the high-pass deformation, which can reflect the modeling accuracy, derived by the NREM are lower than those of the three traditional models, yielding an improvement of 45% for the Lungui Highway (LH) and 50% for the G1508 Highway (GH). The root mean square errors (RMSEs) for deformation results derived from NREM are estimated to be ±5.1 mm compared with the leveling measurements, which outperforms the traditional models. The obtained rheological parameters can broaden the application of InSAR technology and provide a reference for highway engineering.

水稻土受压蠕变特性及预测模型构建

In order to study the compressive creep properties and laws of paddy soil, multi-stress creep experiments of paddy soil with different moisture content were carried out. The results show that the creep deformation of paddy soil, subjected to compressive loads effect, develops stably and the paddy soil is not destructed under the yield strength when the stress is low. When the stress level is higher than the yield strength, the internal damage of paddy soil would be caused at the moment of loading. With the extension of creep time, the cracks would gradually expand, resulting in the soil to yield, break and disintegrate. According to the analysis of the deformation properties of paddy soil under compression and the change trend of creep curve, the nonlinear viscoelastic-plastic model was composed of the nonlinear viscoplastic model and Burgers model in series. The creep test curve was introduced into the model for fitting, and the coefficient of determination reached more than 0.96. Based on the model, the strain composition, strain proportion, and strain rate of paddy soil were studied. Finally, the nonlinear model was compared with Burgers model by verification test. The fitting accuracy of the nonlinear model was better than Burgers model, and the coefficient of determination and relative error were 0.997 and 0.437%, respectively, which proved the rationality and correctness of the nonlinear viscoelastic-plastic model. This study can provide a theoretical basis for the optimization of tillage machinery structure and the simulation analysis of soil tillage and compaction.

Fractional Burgers wave equation on a finite domain

Dynamic response of the one-dimensional viscoelastic rod of finite length, that has one end fixed and the other subject to prescribed either displacement or stress, is analyzed by the analytical means of Laplace transform, yielding the displacement and stress of an arbitrary rod’s point as a convolution of the boundary forcing and solution kernel. Thermodynamically consistent Burgers models are adopted as the constitutive equations describing mechanical properties of the rod. Short-time asymptotics implies the finite wave propagation speed in the case of the second class models, contrary to the case of the first class models. Moreover, Burgers model of the first class yield quite classical shapes of displacement and stress time profiles resulting from the boundary forcing assumed as the Heaviside function, while model of the second class yield responses that resemble to the sequence of excitation and relaxation processes.

Parameter optimization study based on co-briquetting tests of corn straw and potato residue

Corn straw and potato residue are common agricultural biomass. Although they have a wide range of applications, the disadvantages of low bulk density and high storage and transportation cost hinder their utilization. The densification of these biomass into briquettes facilitates their storage, transportation, and reuse. The rheological properties of corn straw and potato residue during co-briquetting were investigated in creep tests. The Four-element Burgers Model accurately and intuitively fit the creep curves of the mixed materials, with fitting coefficients above 0.99. The experiment used the relaxation ratio as an indicator, and the influence of compression speed, dwell time, feeding amount, loading force, mass ratio, and temperature were obtained. The response surface analysis indicated that all factors except compression speed had an effect on the relaxation ratio. The results suggested that compressing corn straw and potato residue in a feeding amount of 28 g with a mass ratio of 1:5 at 101 °C under 35 KN loading force and 918 s dwell time produces cost-effective agricultural biomass briquettes. This study provides a reference for improving the co-briquetting process of corn straw and potato residue.

Effects of environmental conditions on the micro-mechanical properties of formulated waterborne coatings

Waterborne colloidal polymer coatings are widely used in architectural and agricultural applications where they are subject to challenging environments, such as extremes of temperatures and relative humidities (RH). This research investigates the effects of adding two common co-formulants, poly(acrylic acid) (PAA) and xanthan gum (XG), to waterborne polymer composite coatings in these environments. The mechanical properties of the resulting coatings are of particular interest. Hardness, creep and tack properties of thick (~400 μm) formulated model coatings were characterized using a micro-indentation technique operating in a single cycle within a bespoke environmental chamber. Measurements were made at three temperatures (16, 20 and 30 °C), which span the glass transition temperature (Tg) of the acrylic copolymer binder, and over three RH values of 10%, 43%, and 90%. The creep data were analysed using the Burgers model to extract characteristic viscoelastic properties. The tack was found by recording the force when withdrawing the probe from the sample and using it to obtain nominal stress (knowing the indentation depth and probe geometry) during the indenter's withdrawal and hence the work of adhesion (WAdh) to detach from the coating. Tack adhesion is completely lost below the binder's Tg but increases when the ambient temperature increases. In formulated coatings, both the tack and creep deformation increase as the relative humidity increases, and this trend is observed at each temperature. There is no evidence from thermal analysis for plasticization of the acrylic polymer by moisture sorption, but the two co-formulants are hydrophilic. The observed softening of the coatings at high RH can be attributed to water sorption in the components. The presence of glassy PAA has the effect of raising the hardness of glassy coatings, but only at low RH when there is no plasticization by water. The addition of hydrophilic XG surprisingly reduces tack adhesion while also raising the viscosity of the coating. These findings will inform the formulation of waterborne colloidal coatings to function in a range of environments.

Creep Modelling of Rootstock during Holding in Watermelon Grafting

The fragile structure of a rootstock predisposes the stem to mechanical damage during grafting. Thus, it is necessary to take into account the rootstock’s rheological properties under mechanical compression when designing a clamping mechanism. This study focused on cucurbit, a typical rootstock for watermelon grafting. Firstly, we adopted a four-element Burgers model to analyze viscoelastic behavior and deformation characteristics of the rootstock, then conducted creep tests to obtain the parameters of the viscoelastic model. Next, we developed a model for the rootstock during holding based on viscoelastic parameters, loading force and contact time. Moreover, we evaluated the effect of various loading forces and test velocities on creep deformation to reveal the least damage on the rootstock. Results showed that the influence of loading force on the creep deformation was greater than test velocity. Finally, the holding test indicated that the clamping mechanism with silicone rubber can effectively prevent the damage to the stem. Specifically, the loading force should be controlled below 4 N to reduce the associated damage. Taken together, our findings provide a theoretical basis for analyzing the holding damage mechanism during watermelon grafting.

Dynamic modulus, internal friction, and transient creep at high temperature in austenitic stainless steel

Dynamic shear modulus and internal friction of a coarse-grained austenitic stainless-steel sample (AISI 304) were measured by mechanical spectroscopy technique at elevated temperatures to 1200 ℃ and oscillation periods ranging from 1 s to 1000 s. The results were fitted to an extended Burgers model, showing a new thermally activated dissipation peak with relaxation strength 0.075 ± 0.005 superimposed on the high-temperature background. Across the temperature interval 1000–750 ℃, the dissipation peak traverses the 1–1000 s observational window with an activation energy of 210 ± 14 kJ/mol. Complementary time-domain information acquired by microcreep testing within the same temperature range reveals the extent to which the inelastic strain is recoverable (i.e. anelastic). A transient creep map was constructed to quantitatively analyze the contribution of different deformation mechanisms. The combined analysis involving Burgers model and a transient creep map highlights the likely role of stress-induced migration of dislocations in both the anelastic relaxation and the viscous deformation. This study thus provides a more robust understanding of the mechanical behavior of austenitic stainless steel at high temperatures and low strain amplitudes with implications, for example, for its use in jacketing other materials for mechanical testing under conditions of high temperature and pressure.

Nonlinear Models of Thermo-Viscoelastic Materials.

The paper develops a general scheme for viscoelastic materials, where the constitutive properties are described by means of measures of strain, stress, heat flux, and their time derivatives. The constitutive functions are required to be consistent with the second law of thermodynamics. Indeed, a new view is associated with the second law: the non-negative expression of the entropy production is set equal to a further constitutive function. The introduction of the entropy production as a constitutive function allows for a much wider range of models. Within this range, a scheme to obtain nonlinear models of thermo-viscoelastic materials subject to large deformations is established. Notably, the Kelvin–Voigt, Maxwell, Burgers, and Oldroyd-B viscoelastic models, along with the Maxwell–Cattaneo heat conduction, are obtained as special cases. The scheme allows also for modelling the visco-plastic materials, such as the Prandtl–Reuss work-hardening function and the Bingham–Norton fluid.

Uncovering the creep deformation mechanism of rock-forming minerals using nanoindentation

The creep phenomenon of rocks is quite complex and the creep mechanisms are far from being well understood. Although laboratory creep tests have been carried out to determine the creep deformation of various rocks, these tests are expensive and time-consuming. Nanoindentation creep tests, as an alternative method, can be performed to investigate the mechanical and viscoelastic properties of granite samples. In this study, the reduced Young’s modulus, hardness, fracture toughness, creep strain rate, stress exponent, activation volume and maximum creep displacement of common rock-forming minerals of granite were calculated from nanoindentation results. It was found that the hardness decreases with the increase of holding time and the initial decrease in hardness was swift, and then it decreased slowly. The stress exponent values obtained were in the range from 4.5 to 22.9, which indicates that dislocation climb is the creep deformation mechanism. In addition, fracture toughness of granite’s rock-forming minerals was calculated using energy-based method and homogenization method was adopted to upscale the micro-scale mechanical properties to macro-scale mechanical properties. Last but not least, both three-element Voigt model and Burgers model fit the nanoindentation creep curves well. This study is beneficial to the understanding of the long-term mechanical properties of rock samples from a micro-scale perspective, which is of great significance to the understanding of localized deformation processes of rocks.

Creep damage model of rock with varying-parameter under the step loading and unloading conditions

The creep characteristics of rock under step loading and unloading conditions were investigated in this study. Based on the generalized Burgers model, the total strain of rock was decomposed into elastic, viscoelastic, varying-parameter viscoelastic, and viscoplastic strains considering the damage. The four strains were connected in series to establish a new varying-parameter creep damage model that can characterize the creep characteristics of rock under step loading and unloading conditions as well as identify and verify the model parameters. The study results showed that the varying-parameter creep damage model could better describe the creep characteristics of rock under step loading and unloading conditions, significantly the non-linear both the strain and time of attenuation creep and accelerated creep. The model fitting curve was highly consistent with the experimental data, and the correlation coefficient R2 was greater than 0.98, which thoroughly verified the accuracy and rationality of the model. These findings can provide theoretical support for analyzing the deformation and long-term stability of rock and soil.

Comparative analysis on rheological characteristics of different modified asphalt based on DSR and BBR evaluation

PurposeIn order to evaluate the rheological properties of asphalt more comprehensively and effectively, and to explore and discuss the practicability of relevant models in the evaluation of the rheological properties of asphalt.Design/methodology/approachBased on the rheological and viscoelastic theories, temperature scanning, frequency scanning and multiple stress creep recovery (MSCR) tests of different modified asphalt were carried out by dynamic shear rheometer (DSR) to obtain relevant viscoelastic parameters and evaluate the high temperature properties of different modified asphalt. Based on the time-temperature equivalence principle, the main curve was constructed to study the viscoelastic properties of asphalt in a wider frequency domain. The main curve was fitted with the CAM model, and the rheological properties of different modified asphalt were evaluated through the analysis of model parameters. The creep stiffness and creep velocity of different modified asphalt were obtained through the rheological test of bending beam (BBR), and the low-temperature performance of different modified asphalt was analyzed by using Burgers model to fit the creep compliance.FindingsThe results show that the high temperature rheological properties of several modified asphalt studied in the test are ranked from best to worst as follows: PE modified asphalt > SBS modified asphalt > SBR modified asphalt. Short-term aging can improve the high temperature performance of asphalt, and different types of modifiers can promote or inhibit this improvement effect. Based on BBR test and Burgers model fitting analysis, SBR modified asphalt has the best low temperature performance, followed by SBS modified asphalt, while PE modified asphalt has poor low temperature performance, so it is not suitable to be used as road material in low temperature area.Originality/valueCombined with effective evaluation methods, the rheological properties of asphalt at different temperatures and angles were systematically evaluated, and the evolution of rheological properties of asphalt characterized by model parameters was further analyzed by advanced model simulation.

Soil-Water Characteristics and Creep Deformation of Unsaturated Expansive Subgrade Soil: Experimental Test and Simulation

The creep deformation of expansive soil has been considered as a vital threat to the safety in engineering construction because it may cause serious slope diseases in geological engineering. Meanwhile, since expansive soil usually remains in unsaturated state, its mechanical property is significantly affected by the seasonal environment. Therefore, the nonlinear deformation of expansive soil has received increasing attention, especially the humidity-dependent creep properties. This study focused on the stability of the unsaturated expansive soil subgrade considering rainfall and the creep behavior. Pressure plate extractor and direct shear tests were performed to investigate the hydro-mechanical and creep characteristics of the unsaturated expansive soil. Both the Van-Genuchten and Burgers models were applied to analyze the test results and inserted into the numerical model of the slope under rainfall infiltration. Results show that the compaction degree and the stress state was closely related to the water holding capacity of the expansive soil. The nonlinearity of the creep behavior became increasingly obvious with the increase of time and the stress level. The safety factor of the slope decreased as the rainfall time increased, and the most dangerous slide of the slope moved toward the foot of the slope. Considering the long-term creep process, there was a period of rapid growth in horizontal displacement that is detrimental to the stability of the slope. Besides, the rainfall infiltration could accelerate the slope failure before and after this creep process.

Determination of asphalt mixture’s viscoelastic constitutive parameters for pavement response analysis using dynamic modulus transformation

Asphalt mixture is a kind of typical viscoelastic material, whose viscoelastic property is much affected by test temperature and loading rate. This feature makes it difficult to accurately determine the mixture’s viscoelastic constitutive parameters, which is crucial for pavement mechanical analysis, and results in a large discrepancy between the calculated results and in situ measured data if parameters are not properly determined. Considering the background discussed above, this paper develops a theoretical method to determine asphalt mixture’s Burgers model parameters through transforming dynamic modulus, which bases the extreme value characteristics of asphalt mixture’s dynamic modulus and the theory of linear viscoelastic mechanics. Next, this paper conducts a series of laboratory experiments, analytical derivation and numerical modeling to verify this developed method’s efficiency and accuracy, and obtains a satisfying result. In the latter part of this paper, a viscoelastic numerical modeling for Cagliari Elmas airport asphalt pavement’s mechanical response is conducted, which just utilizes this developed method to determine a mixture’s viscoelastic constitutive parameters and a comparison of pavement response among modeling results, in situ measured data and Flexpave modeling results verify this method again.

Creep behavior of full-culm Moso bamboo under long-term bending

Bamboo can be easily cultivated and harvested in a relatively short time and has been widely known as a sustainable building material. The study on the long-term creep behavior of full-culm bamboo members is of great significance for the design and use of bamboo structures in engineering, but there are few studies. This paper presents an experimental and numerical study on the creep behavior of full-culm original bamboo beams. In this study, two groups of bamboo beams with different stress levels were analyzed, and the fitting results based on Burger model were obtained. Short-term material properties test was firstly carried out to determine the ultimate strength of Phyllostachys edulis (or Moso bamboo). Secondly, in the creep test, 15 full-culm original bamboo beams were subjected to different constant stress levels for 180 days in an indoor environment, and the creep behavior of bamboo beams was observed and measured over time. Then a creep model of numerical analysis procedure based on the Burger model was established to simulate the creep behavior of each beam. By comparing the numerical analysis results with the test results, basic creep behavior characteristics including creep rate and proportion of each deformation (instantaneous elastic deformation, viscoelastic deformation and viscous deformation) were analyzed and discussed in depth. Finally, the creep behavior of full-culm original bamboo beams was evaluated by the acceptance criteria used for wood and wood-based products. The results indicated that the developed Burger model can well capture the trend of creep behavior including low and high stress level, and the full-culm original bamboo beam under lower stress level has the potential to replace timber in terms of withstanding long-term load. The creep test and numerical analysis of the full-culm original bamboo beams in this paper can provide a reference for follow-up study.

The shear-creep behavior of the weak interlayer mudstone in a red-bed soft rock in acidic environments and its modeling with an improved Burgers model

The shear-creep behavior of the weak interlayer mudstone in a red-bed soft rock in acidic environments and its modeling with an improved Burgers model

Examining mechanical behavior of steel-bamboo composite I-section column under long-term loading

The steel-bamboo composite structure is a novel composite structure, which is characterized by light weight and high bearing capacity of structural components, as well as excellent seismic performance and good thermal performance of fabricated buildings. To facilitate its engineering application and better understanding the deformation law of composite column during design reference period, mechanical properties of steel-bamboo composite column under long-term loads are investigated in this paper. 27 composite I-section columns were designed and fabricated, among which 18 specimens were first investigated in static loading test with steel ratio and slenderness ratio as main parameters, failure modes and effect of each parameter on the axial compression performance was observed and analyzed. Then, a self-balanced loading device was designed to perform long-term loading test on 6 specimens with loading level and steel ratio as main parameters, and the other 3 specimens were adopted to monitor the temperature effect on creep. The creep process of specimens was observed and the nonlinear fitting analysis of creep data was carried out using Burger model. Once the predetermined long-term loading duration was reached, the secondary static loading test were carried out to study the influencing factors of bearing capacity and deformation, as well as their variation laws. Further, calculation formula of yield bearing capacity was derived by analyzing yield conditions of composite column, as two calculation methods of ultimate bearing capacity were proposed based on superposition principle and limit equilibrium theory. Results show that the composite columns have good integrity, high deformation capacity and bearing capacity, which improves significantly with the increase of steel ratio and decreases with the increase of slenderness ratio. Creep deformation become basically stable after 90 days of loading, which can be accurately described by Burger model. After the long-term loading, ductility and ultimate strain of the specimens were obviously increased, while the bearing capacity was not significantly affected. The average error between the theoretical and experimental results of yield and ultimate bearing capacity is smaller than 7%, which indicates that the established calculation methods have high accuracy and are suitable for predicting the bearing capacity of steel-bamboo composite I-section columns. It is proved that scientifically designed steel-bamboo composite columns have reliable bearing capacities and controllable deformations, and can be safely applied to practical projects.

Rheological characterisation of alginate-like exopolymer gels crosslinked with calcium

Bacterial alginate-like exopolymers (ALE) gels have been used in this work as a model for the extracellular polymeric matrix of biofilms. Aim was to relate the mechanical properties and strength of this matrix that make biofilms as persistent to cleaning as they are, to the complex cohesive molecular interactions involved. Mechanical properties of the gels as a function of CaCO3 concentration were investigated using dynamic and static rheology. Gels with relatively low CaCO3 concentrations, between 100 μmol and 300 μmol per g ALE, were found to exhibit similar viscoelastic behaviour as real biofilms, with elastic moduli between 50 Pa and 100 Pa and dissipation factors between 0.2 and 0.3. Increasing CaCO3 concentrations resulted in an increase of the elastic modulus up to 250 Pa, accompanied by an increase in brittleness. At a CaCO3 concentration of 1250 μmol per g ALE this trend stopped, probably due to disturbance of the continuous ALE network by precipitation of salts. Therefore, overdosing of Ca salts can be an adequate approach for the removal of biofouling. All gels exhibited permanent strain hardening under medium strain, and their mechanical properties showed dependency on their strain history. Even after application of an oscillatory strain with 200% amplitude that caused the gel structure to collapse, the gels recovered 65 to 90% of their original shear modulus, for the major part within the first 20 s. Recovery was slightly less for gels with high CaCO3 concentration. In creep tests fitted with a Burgers model with multiple Kelvin elements at least three different interactions in the ALE gels could be distinguished with characteristic retardation times in the range of 10, 100 and 1000 s. Further identification of the mechanisms underlying the gel mechanics will allow the development of targeted strategies to undermine the mechanical strength of biofouling and aid the cleaning process.

Burger Model as the Best Option for Modeling of Viscoelastic Behavior of Resists for Nanoimprint Lithography.

In this study, Atomic Force Microscopy-based nanoindentation (AFM-NI) with diamond-like carbon (DLC) coated tip was used to analyze the mechanical response of poly(methyl methacrylate) (PMMA) thin films (thicknesses: 235 and 513 nm) on a silicon substrate. Then, Oliver and Pharr (OP) model was used to calculate hardness and Young’s modulus, while three different Static Linear Solid models were used to fit the creep curve and measure creep compliance, Young’s modulus, and viscosity. Values were compared with each other, and the best-suited method was suggested. The impact of four temperatures below the glass transition temperature and varied indentation depth on the mechanical properties has been analyzed. The results show high sensitivity on experiment parameters and there is a clear difference between thin and thick film. According to the requirements in the nanoimprint lithography (NIL), the ratio of hardness at demolding temperature to viscosity at molding temperature was introduced as a simple parameter for prediction of resist suitability for NIL. Finally, thinner PMMA film was tentatively attributed as more suitable for NIL.

Study on the viscoelastic behaviour of the modified asphalt containing multi-walled carbon nanotubes (MWCNTs) and crumb rubber (CR)

Asphalt binder plays an important role on the performance of asphalt mixture, especially for the high-temperature performance. The purpose of this research is to investigate the viscoelastic behaviours of the modified asphalt containing multi-walled carbon nanotubes and crumb rubber. By adding multi-walled carbon nanotubes and crumb rubber to the base asphalt, the multi-walled carbon nanotubes modified asphalt, crumb rubber modified asphalt and multi-walled carbon nanotubes and crumb rubber composite-modified asphalt were prepared. The high-temperature viscosity and rheological property indices were obtained through the viscosity test and small amplitude oscillatory measurement. Besides, multiple stress creep recovery test and stress relaxation test were utilized to explore creep recovery behaviours and stress relaxation characteristics of the asphalt samples. Based on the time-temperature superposition principle, the master curves of complex shear modulus and phase angle were generated. Han curves of the asphalt samples were established based on superposition principle of Blotzmann. Furthermore, the Burgers model was used to model the creep-recovery data. The relaxation functions of Maxwell model and Burgers model were applied to fit stress relaxation curves of the asphalt samples. Results indicate that, the addition of multi-walled carbon nanotubes and crumb rubber caused an increase in high-temperature viscosity, and reduce the temperature susceptibility of base binder. In addition, the permanent deformation resistance, creep-recovery behaviours and stress relaxation characteristics of asphalt were enhanced remarkably by the two modifiers modification. Lastly, the composite-modified asphalt exhibited better viscoelastic behaviours than asphalt modified with either crumb rubber or multi-walled carbon nanotubes alone.