scholarly journals Polyconvex hyperelastic modeling of rubberlike materials

2021 ◽  
Vol 43 (7) ◽  
Author(s):  
Cyprian Suchocki ◽  
Stanisław Jemioło
Keyword(s):  
Experimental Data ◽  
Power Law ◽  
Curve Fitting ◽  
Constitutive Relations ◽  
Data Sets ◽  
Power Law Model ◽  
Stored Energy ◽  
Data Approximation ◽  
Exponential Power ◽  
Hyperelastic Models

AbstractIn this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

scholarly journals Modeling of the Strain Rate Dependency of Polycarbonate’s Yield Stress: Evaluation of Four Constitutive Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Abdullah A. Al-Juaid ◽  
Ramzi Othman
Keyword(s):  
Experimental Data ◽  
Strain Rate ◽  
Yield Stress ◽  
Power Law ◽  
Constitutive Relations ◽  
Stress Sensitivity ◽  
Strain Rate Range ◽  
Rate Dependency ◽  
Rate Range ◽  
Strain Rate Dependency

The main focus of this paper is in evaluating four constitutive relations which model the strain rate dependency of polymers yield stress. Namely, the two-term power-law, the Ree-Eyring, the cooperative, and the newly modified-Eyring equations are used to fit tensile and compression yield stresses of polycarbonate, which are obtained from the literature. The four equations give good agreement with the experimental data. Despite using only three material constants, the modified-Eyring equation, which considers a strain rate-dependent activation volume, gives slightly worse fit than the three other equations. The two-term power-law and the cooperative equation predict a progressive increase in the strain rate sensitivity of the yield stress. Oppositely, the Ree-Eyring and the modified-Eyring equations show a clear transition between the low and high strain rate ranges. Namely, they predict a linear dependency of the yield stress in terms of the strain rate at the low strain rate range. Crossing a threshold strain rate, the yield stress sensitivity sharply increases as the strain rate increases. Hence, two different behaviors were observed though the four equations fit well the experimental data. More experimental data, mainly at the intermediate strain rate range, are needed to conclude which, of the two behaviors, is more appropriate for polymers.

scholarly journals Modeling the Deformation of Shear Thinning Droplets Suspended in a Newtonian Fluid

2020 ◽  
Vol 30 (1) ◽  
pp. 151-165
Author(s):  
Abdulwahab S. Almusallam ◽  
Isameldeen E. Daffallah ◽  
Lazhar Benyahia
Keyword(s):  
Experimental Data ◽  
Numerical Modeling ◽  
Large Deformation ◽  
Power Law ◽  
Simple Shear ◽  
Shear Thinning ◽  
Power Law Model ◽  
Flow Strength ◽  
Volume Model ◽  
Droplet Phase

Abstract In this work, we carried out numerical modeling of the large deformation of a shear thinning droplet suspended in a Newtonian matrix using the constrained volume model. The adopted approach was to consider making incremental corrections to the evolution of the droplet anisotropy equation in order to capture the experimental behavior of a shear thinning droplet when subjected to deformation due to imposed flow. The constrained volume model was modified by using different models to describe the viscosity of droplet phase: the Bautista et al. model, the Carreau-Yasuda model and the Power-law model. We found that by combining the constrained volume model with a simple shear thinning viscosity model we were able to describe the available experimental data for large deformation of a shear thinning droplet suspended in a Newtonian matrix. Moreover, we developed an equation approximating flow strength during droplet retraction, and we found that the model can accurately describe the experimental data of the retraction of a shear thinning droplet.

‘Window’ Effect in the Analysis of Universal Dynamic Response

2012 ◽  
Vol 519 ◽  
pp. 24-27
Author(s):  
Xiao Yang Gong ◽  
Zhi Feng Gu ◽  
Tong Wei Li
Keyword(s):  
Experimental Data ◽  
Dynamic Response ◽  
Power Law ◽  
Curve Fitting ◽  
Ac Conductivity ◽  
Simple Method ◽  
Ion Motion ◽  
Window Effect ◽  
Glassy Materials ◽  
Frequency Window

Studies of ion motion in crystalline and glassy materials, Jonscher power law, which was frequently referred to as the so-called universal dynamic response (UDR) is an effective method, but the power law exponents obtained from curve-fitting are sensitively affected by the frequency window employed in the analysis. So how to choose frequency window and which window can truly describe the nature of the materials, are important for every researcher. In this paper, through analyzing the experimental data of frequency dependence of ac conductivity in 50Li2O–50P2O5 glasses, a simple method to choose frequency window was found and further discussions indicated our choice was reasonable.

Application of Modified Power Law and Arrhenius Relationship in Studying Rheological Behavior of Bio-Oils

2006 ◽  
Vol 517 ◽  
pp. 147-152 ◽  
Author(s):  
W.S. Wan Nik ◽  
S.G. Eng Giap ◽  
H.H. Masjuki ◽  
H.B. Senin
Keyword(s):  
Experimental Data ◽  
Shear Rate ◽  
Power Law ◽  
Corn Oil ◽  
Flow Behavior ◽  
Type Equation ◽  
Power Law Model ◽  
Flow Behavior Index ◽  
Different Temperatures ◽  
Modified Power Law

Tribological aspects of bio-oils have to be investigated before they are used as industrial fluids. In this paper rheological (fluid deformation under shear) properties of four bio-oils are presented. A Couette type viscometer was used to evaluate flow behavior of the oils at seven discrete temperatures. Commercial coconut, canola, sunflower and corn oil were used in this study. For all the oil samples, viscosities were affected by the change of shear rate and temperature. Two rheological models, temperature dependence and shear rate dependence, were used in the study. The original power law gives contradict picture of flow curves and flow parameters. Thus, modified power law model was proposed. The modified model was fitted to experimental data to obtain the flow behavior index. Arrhenius type equation was fitted to experimental data to obtain the activation energy due to different temperatures and shear rates. Evaluation of rheological properties by modified power law model indicates that these bio-oils belong to the pseudo-plastic group.

Estimating ink mileage of dry toners in electrophotography

TAPPI Journal ◽  
2013 ◽  
Vol 12 (3) ◽  
pp. 9-14
Author(s):  
RENMEI XU ◽  
CELESTE M. CALKINS
Keyword(s):  
Experimental Data ◽  
Curve Fitting ◽  
Graphite Furnace ◽  
Atomic Absorption Spectrometer ◽  
Density Region ◽  
Coated Papers ◽  
Graphite Furnace Atomic Absorption ◽  
S Model ◽  
Better Than ◽  
Film Weight

This work investigates the ink mileage of dry toners in electrophotography (EP). Four different substrates were printed on a dry-toner color production Xerox iGen3 EP press. The print layout contained patches with different cyan, magenta, yellow, and black tonal values from 10% to 100%. Toner amounts on cyan patches were measured using an analytical method. Printed patches and unprinted paper samples, as well as dry toners, were dissolved in concentrated nitric acid. The copper concentrations in the dissolved solutions were analyzed by a Zeeman graphite furnace atomic absorption spectrometer. Analytical results were calculated to determine the toner amounts on paper for different tonal values. Their corresponding reflection densities were also measured. All data were plotted with OriginPro® 8 software, and four mathematical models were used for curve fitting. It was found that the C-S model fitted the experimental data of the two uncoated papers better than the other three models. None of the four models fitted the experimental data of the two coated papers, while the linear model was found to fit the data well. Linear fitting was the best in the practical density region for the two coated papers. Ink mileage curves obtained from curve fitting were used to estimate how much ink was required to achieve a target density for each paper; hence, the ink mileage was calculated. The highest ink mileage was 3.39 times the lowest ink mileage. The rougher the paper surface, the higher the requirement for ink film weight, and the lower ink mileage. No correlation was found between ink mileage and paper porosity.

scholarly journals Unsteady thermal Maxwell power law nanofluid flow subject to forced thermal Marangoni Convection

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Muhammad Jawad ◽  
Anwar Saeed ◽  
Taza Gul ◽  
Zahir Shah ◽  
Poom Kumam
Keyword(s):  
Relaxation Time ◽  
Power Law ◽  
Marangoni Convection ◽  
Power Law Model ◽  
Analysis Method ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Welan Gum ◽  
Homotopy Analysis ◽  
Power Law Nanofluid

AbstractIn the current work, the unsteady thermal flow of Maxwell power-law nanofluid with Welan gum solution on a stretching surface has been considered. The flow is also exposed to Joule heating and magnetic effects. The Marangoni convection equation is also proposed for current investigation in light of the constitutive equations for the Maxwell power law model. For non-dimensionalization, a group of similar variables has been employed to obtain a set of ordinary differential equations. This set of dimensionless equations is then solved with the help of the homotopy analysis method (HAM). It has been established in this work that, the effects of momentum relaxation time upon the thickness of the film is quite obvious in comparison to heat relaxation time. It is also noticed in this work that improvement in the Marangoni convection process leads to a decline in the thickness of the fluid’s film.

scholarly journals X-ray Properties of 3C 111: Separation of Primary Nuclear Emission and Jet Continuum

Universe ◽  
2020 ◽  
Vol 6 (11) ◽  
pp. 219
Author(s):  
Elena Fedorova ◽  
B.I. Hnatyk ◽  
V.I. Zhdanov ◽  
A. Del Popolo
Keyword(s):  
Accretion Disk ◽  
Power Law ◽  
Line Emission ◽  
High Energy ◽  
Power Law Model ◽  
X Ray ◽  
Additional Information ◽  
Observational Dataset ◽  
Simple Power ◽  
Photon Index

3C111 is BLRG with signatures of both FSRQ and Sy1 in X-ray spectrum. The significant X-ray observational dataset was collected for it by INTEGRAL, XMM-Newton, SWIFT, Suzaku and others. The overall X-ray spectrum of 3C 111 shows signs of a peculiarity with the large value of the high-energy cut-off typical rather for RQ AGN, probably due to the jet contamination. Separating the jet counterpart in the X-ray spectrum of 3C 111 from the primary nuclear counterpart can answer the question is this nucleus truly peculiar or this is a fake “peculiarity” due to a significant jet contribution. In view of this question, our aim is to estimate separately the accretion disk/corona and non-thermal jet emission in the 3C 111 X-ray spectra within different observational periods. To separate the disk/corona and jet contributions in total continuum, we use the idea that radio and X-ray spectra of jet emission can be described by a simple power-law model with the same photon index. This additional information allows us to derive rather accurate values of these contributions. In order to test these results, we also consider relations between the nuclear continuum and the line emission.

scholarly journals Spatial Heterogeneity of the Incidence of Powdery Mildew on Hop Cones

Plant Disease ◽  
2006 ◽  
Vol 90 (11) ◽  
pp. 1433-1440 ◽  
Author(s):  
David H. Gent ◽  
Walter F. Mahaffee ◽  
William W. Turechek
Keyword(s):  
Powdery Mildew ◽  
Spatial Heterogeneity ◽  
Power Law ◽  
Binomial Distribution ◽  
Disease Incidence ◽  
Disease Assessment ◽  
Cluster Sampling ◽  
Data Sets ◽  
Ratio Test ◽  
Frequency Distributions

The spatial heterogeneity of the incidence of hop cones with powdery mildew (Podosphaera macularis) was characterized from transect surveys of 41 commercial hop yards in Oregon and Washington from 2000 to 2005. The proportion of sampled cones with powdery mildew ( p) was recorded for each of 221 transects, where N = 60 sampling units of n = 25 cones assessed in each transect according to a cluster sampling strategy. Disease incidence ranged from 0 to 0.92 among all yards and dates. The binomial and beta-binomial frequency distributions were fit to the N sampling units in a transect using maximum likelihood. The estimation procedure converged for 74% of the data sets where p > 0, and a loglikelihood ratio test indicated that the beta-binomial distribution provided a better fit to the data than the binomial distribution for 46% of the data sets, indicating an aggregated pattern of disease. Similarly, the C(α) test indicated that 54% could be described by the beta-binomial distribution. The heterogeneity parameter of the beta-binomial distribution, θ, a measure of variation among sampling units, ranged from 0.01 to 0.20, with a mean of 0.037 and a median of 0.015. Estimates of the index of dispersion ranged from 0.79 to 7.78, with a mean of 1.81 and a median of 1.37, and were significantly greater than 1 for 54% of the data sets. The binary power law provided an excellent fit to the data, with slope and intercept parameters significantly greater than 1, which indicated that heterogeneity varied systematically with the incidence of infected cones. A covariance analysis indicated that the geographic location (region) of the yards and the type of hop cultivar had little effect on heterogeneity; however, the year of sampling significantly influenced the intercept and slope parameters of the binary power law. Significant spatial autocorrelation was detected in only 11% of the data sets, with estimates of first-order autocorrelation, r1, ranging from -0.30 to 0.70, with a mean of 0.06 and a median of 0.04; however, correlation was detected in only 20 and 16% of the data sets by median and ordinary runs analysis, respectively. Together, these analyses suggest that the incidence of powdery mildew on cones was slightly aggregated among plants, but patterns of aggregation larger than the sampling unit were rare (20% or less of data sets). Knowledge of the heterogeneity of diseased cones was used to construct fixed sampling curves to precisely estimate the incidence of powdery mildew on cones at varying disease intensities. Use of the sampling curves developed in this research should help to improve sampling methods for disease assessment and management decisions.

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