EXPERIMENTAL RESEARCH ON VISCOELASTICITY PROPERTY OF DIFFERENT LAYERS PERIODONTAL LIGAMENT UNDER COMPRESSION

2021 ◽  
pp. 2150050
Author(s):  
JINLAI ZHOU ◽  
YANG SONG ◽  
CHENGUANG XU ◽  
CHUNQIU ZHANG ◽  
XUE SHI
Keyword(s):  
Elastic Modulus ◽  
Periodontal Ligament ◽  
Creep Compliance ◽  
Relaxation Modulus ◽  
Maxwell Model ◽  
Kelvin Model ◽  
Generalized Maxwell Model ◽  
Relaxation Stress ◽  
Generalized Kelvin Model ◽  
Fitting Accuracy

The periodontal ligament (PDL) exhibits different material mechanical properties along the long axis of the teeth. To explore the creep and the relaxation effects of dissimilar layers of PDL, this paper took the central incisors of porcine mandibular as experimental subjects and divided them perpendicular to the teeth axis into five layers. Creep experiments and relaxation experiments on five layers were conducted to obtain the creep compliance and relaxation modulus at different layers. Linear elastic model, generalized Kelvin model, and generalized Maxwell model were used to describe the major characteristics of the PDL: Instantaneous elasticity, creep and relaxation. Fitting accuracy of three-parameter, five-parameter, and seven-parameter of the model was compared, and the constitutive equations of different layers were established by the least square method. The results presented that the creep strain and the relaxation stress of PDL were exponentially correlated with time under different loading conditions. Different layers showed a significant effect on the creep strain and relaxation stress of PDL. Along the long axis of the teeth, the changing rule of the creep compliance and relaxation modulus of each layer showed quite the contrary, and the instantaneous elastic modulus first decreased to the minimum, then increased to the maximum. Higher instantaneous elastic modulus led to lower creep compliance and higher relaxation modulus. The generalized Kelvin model and the generalized Maxwell model well characterized the creep and relaxation properties of PDL. Fitting accuracy increased with the number of model parameters. The relaxation time of PDL was about one order of magnitude shorter than the creep retardation time, which indicated that the relaxation effect lasted shorter than the creep effect.

scholarly journals Viscoelastic Properties of Asphalt Mixtures with Different Modifiers at Different Temperatures Based on Static Creep Tests

2019 ◽  
Vol 9 (20) ◽  
pp. 4246 ◽  
Author(s):  
Yongchun Cheng ◽  
He Li ◽  
Liding Li ◽  
Yuwei Zhang ◽  
Haitao Wang ◽  
...  
Keyword(s):  
Viscoelastic Properties ◽  
Asphalt Mixture ◽  
Maxwell Model ◽  
Asphalt Mixtures ◽  
Creep Tests ◽  
Kelvin Model ◽  
Static Creep ◽  
Generalized Maxwell Model ◽  
Different Temperatures ◽  
Generalized Kelvin Model

To obtain the viscoelastic parameters of asphalt mixtures and analyze the effect of temperatures and modifiers on viscoelastic properties of asphalt mixtures, the creep compliances of the neat asphalt mixture (AM), compound diatomite and basalt fibers reinforced asphalt mixture (DBFAM), and styrene-butadiene-styrene modified asphalt mixture (SBSAM) were tested and calculated by the static creep tests. And the creep compliances of the three asphalt mixtures at −20 °C, −10 °C, and 0 °C are deducted by the time–temperature equivalence principle (TTEP) and Arrhenius equation. Further, the relaxation modulus of the three asphalt mixtures from −20 °C to 50 °C at 10 °C increments are calculated by the convolution integral and Simpson method. Subsequently, the Burgers model, the generalized Kelvin model, and the generalized Maxwell model are applied to analyze the viscoelastic properties of the three asphalt mixtures at different temperatures. The results show that the generalized Kelvin model and the generalized Maxwell model are superior to the Burgers model in describing the variation of viscoelastic properties of asphalt mixtures with loading time. At low temperatures, asphalt mixtures have excellent properties in resisting permanent deformation and releasing internal stress. Besides, the addition of SBS modifier and compound diatomite and basalt fibers modifier can significantly raise the viscosity η1 and the elastic modulus E1 of the asphalt mixture, respectively.

scholarly journals Visco-thermo-elastic Simulation Approach For Prediction of Cure-induced Residual Stresses in Fiber Reinforced Composites

2021 ◽  
Author(s):  
Jonas Müller ◽  
Michael Müller-Pabel ◽  
Niklas Lorenz ◽  
Benjamin Gröger ◽  
Johannes Gerritzen ◽  
...  
Keyword(s):  
Residual Stresses ◽  
Composite Structures ◽  
Relaxation Modulus ◽  
Maxwell Model ◽  
Liquid Composite Molding ◽  
Simulation Approach ◽  
Fiber Reinforced ◽  
Cycle Times ◽  
Generalized Maxwell Model ◽  
Elastic Simulation

Liquid composite molding (LCM) has established as a high quality manufacturing process for fiber reinforced composite structures. In order to reduce cycle times significantly, novel fast curing matrix resins are being introduced into series production. These put high requirements on process control and part reproducibility. Problems that may be encountered in this context involve process-induced distortion and surface waviness resulting from anisotropic and cure-dependent material properties. Numerical simulations represent a powerful approach to avoid the use of costly trial-and-error methods. For this reason, a simulation approach is being developed which aims at the prediction of residual stresses and accompanying effects on different length scales. Based on a resin characterization comprising reaction kinetics, cure-dependent relaxation modulus as well as thermal expansion and pressure-dependent chemical shrinkage, a generalized MAXWELL model is selected to describe the process-related mechanical behavior of the thermoset. Taking into account the influence of the process parameters on the resin properties enables a detailed analysis of process-property-relationships. By this, the developed simulation approach offers the possibility of a comprehensive analysis of both local and global process-induced phenomena and hence prevention of flaws.

Strain and Age Effects on Behavior of a Concrete Pavement Joint Sealant Material

1996 ◽  
Vol 1529 (1) ◽  
pp. 95-100
Author(s):  
Ashok Gurjar ◽  
Dan G. Zollinger ◽  
Tianxi Tang
Keyword(s):  
Master Curve ◽  
Superposition Principle ◽  
Relaxation Modulus ◽  
Maxwell Model ◽  
Material Model ◽  
Concrete Pavement ◽  
Age Effects ◽  
Joint Analysis ◽  
Generalized Maxwell Model ◽  
Sealant Material

A one-part self-leveling silicone joint sealant material was experimentally investigated in the laboratory. It was found that strain and age had apparent effects on the relaxation modulus of the material. Relaxation tests were conducted under different strain levels. The test samples were exposed to ultraviolet radiation and moisture for artificial aging before testing. For this largely deformable material, finite strain formulas were used in analysis of experimental data. Strain and age effects were successfully normalized in the relaxation master curve by using the superposition principle. On the basis of the master curve, a material model of the generalized Maxwell model in parallel type was constructed. The real time was scaled to the reduced time by time-strain shift and time-age shift factors so as to characterize the strain and age effects. This model is mathematically simple and can be easily applied in finite element programs for concrete pavement joint analysis.

Effect of Cure State on Stress Relaxation in 3501-6 Epoxy Resin

1997 ◽  
Vol 119 (3) ◽  
pp. 262-265 ◽  
Author(s):  
S. R. White ◽  
A. B. Hartman
Keyword(s):  
Stress Relaxation ◽  
Epoxy Resin ◽  
Creep Compliance ◽  
Numerical Technique ◽  
Matrix Material ◽  
Relaxation Modulus ◽  
Master Curves ◽  
Creep Tests ◽  
Three Point Bending ◽  
Direct Inversion

Little experimental work has been done to characterize how the viscoelastic properties of composite material matrix resins develop during cure. In this paper, the results of a series of creep tests carried out on 3501–6 epoxy resin, a common epoxy matrix material for graphite/epoxy composites, at several different cure states is reported. Beam specimens were isothermally cured at increasing cure temperatures to obtain a range of degrees of cure from 0.66 to 0.99. These specimens were then tested in three-point bending to obtain creep compliance over a wide temperature range. The master curves and shift functions for each degree of cure case were obtained by time-temperature superposition. A numerical technique and direct inversion were used to calculate the stress relaxation modulus master curves from the creep compliance master curves. Direct inversion was shown to be adequate for fully cured specimens, however it underpredicts the relaxation modulus and the transition for partially cured specimens. Correlations with experimental stress relaxation data from Kim and White (1996) showed that reasonably accurate results can be obtained by creep testing followed by numerical conversion using the Hopkins-Hamming method.

scholarly journals Research on Rock Creep Characteristics Based on the Fractional Calculus Meshless Method

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Gang Peng ◽  
Zhanqing Chen ◽  
Jiarui Chen
Keyword(s):  
Fractional Calculus ◽  
Meshless Method ◽  
Test System ◽  
Constitutive Relationship ◽  
Creep Process ◽  
Kelvin Model ◽  
Related Data ◽  
Model Based ◽  
Rock Creep ◽  
Generalized Kelvin Model

The application of fractional calculus in the rheological problems has been widely accepted. In this study, the constitutive relationship of the generalized Kelvin model based on fractional calculus was studied, and the meshless method was introduced so as to derive a new meshless algorithm formula based on the fractional calculus of the generalized Kelvin model. By using the MTS815.02 hydraulic servo rock mechanics test system, the creep test of mudstones is carried out, and the related data of the creep process were obtained. Based on the generalized Kelvin model of fractional calculus, the related creep parameters of the argillaceous sandstone under compression were fitted. The results showed that the solution of the generalized Kelvin model based on fractional calculus was greatly consistent with the numerical method solution. Meanwhile, the meshless algorithm based on fractional calculus had a favorable stability and accuracy.

Obtaining shear relaxation modulus and creep compliance of linear viscoelastic materials from instrumented indentation using axisymmetric indenters of power-law profiles

2009 ◽  
Vol 24 (10) ◽  
pp. 3013-3017 ◽  
Author(s):  
Yang-Tse Cheng ◽  
Fuqian Yang
Keyword(s):  
Inverse Problem ◽  
Laplace Transform ◽  
Power Law ◽  
Creep Compliance ◽  
Relaxation Modulus ◽  
Instrumented Indentation ◽  
Loading Paths ◽  
Linear Viscoelastic ◽  
Shear Relaxation ◽  
Analytical Expressions

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.

scholarly journals Study on Relaxation Damage Properties of High Viscosity Asphalt Sand under Uniaxial Compression

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Yazhen Sun ◽  
Zhangyi Gu ◽  
Jinchang Wang ◽  
Chenze Fang ◽  
Xuezhong Yuan
Keyword(s):  
Uniaxial Compression ◽  
Viscoelastic Model ◽  
Relaxation Modulus ◽  
Maxwell Model ◽  
High Viscosity ◽  
Secondary Development ◽  
Compression Tests ◽  
Crack Control ◽  
Different Temperatures ◽  
Damage Process

Laboratory investigations of relaxation damage properties of high viscosity asphalt sand (HVAS) by uniaxial compression tests and modified generalized Maxwell model (GMM) to simulate viscoelastic characteristics coupling damage were carried out. A series of uniaxial compression relaxation tests were performed on HVAS specimens at different temperatures, loading rates, and constant levels of input strain. The results of the tests show that the peak point of relaxation modulus is highly influenced by the loading rate in the first half of an L-shaped curve, while the relaxation modulus is almost constant in the second half of the curve. It is suggested that for the HVAS relaxation tests, the temperature should be no less than −15°C. The GMM is used to determine the viscoelastic responses, the Weibull distribution function is used to characterize the damage of the HVAS and its evolution, and the modified GMM is a coupling of the two models. In this paper, the modified GMM is implemented through a secondary development with the USDFLD subroutine to analyze the relaxation damage process and improve the linear viscoelastic model in ABAQUS. Results show that the numerical method of coupling damage provides a better approximation of the test curve over almost the whole range. The results also show that the USDFLD subroutine can effectively predict the relaxation damage process of HVAS and can provide a theoretical support for crack control of asphalt pavements.

Identification of Viscoelastic Properties of Finite Element Structures With Joints

1997 ◽  
Author(s):  
Torsten Herrmann ◽  
Valdas Chaika
Keyword(s):  
Finite Element ◽  
Viscoelastic Properties ◽  
Sparse Matrix ◽  
Maxwell Model ◽  
Least Square ◽  
Identification Algorithm ◽  
Domain Identification ◽  
Generalized Maxwell Model ◽  
Maxwell Models ◽  
Complex Modal Analysis

Abstract Identification of the damping and stiffness parameters of the composite joints in finite element structures is analyzed. For the modeling of the viscoelastic properties of the joints the classical Voigt-Kelvin and generalized Maxwell model (three parameter solid) are used. A time domain identification algorithm for classically and non-classically damped dynamic systems is developed. It is based on the application of an extended Kalman filter and least square technique. The algorithm uses complex modal analysis and sparse matrix technology. Both force and base excited systems are considered. Experimental verification of the identification results is carried out on a test structure. The accuracy of the modeling of damping in the joint using the Voigt-Kelvin and generalized Maxwell models is investigated.

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