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

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.

A Simplified Viscoelastic Solution of the Frost Heaving Force of Cavity Water behind Tunnel Linings

With the high demand for construction of tunnels in China’s severe cold regions, the problem of frost heaving has become an important factor that endangers tunnel safety. This paper attempts to investigate the effect of frost heave of cavity water that widely exists in the tunneling engineering on the tunnel stability. According to the actual deformation of the surrounding rock of the tunnel, the viscoelastic behavior is considered to the surrounding rock. On the premise of the elastic solution of stagnant water frost heave, the viscoelastic solution of frost heaving pressure is deduced by Laplace transform using the generalized Kelvin model based on the elastic-viscoelastic correspondence principle. The frost heaving force is analyzed through a case study with variations in the size of the cavity defect as well as the constitutive model parameters. It is concluded that the frost heaving force increases with the cavity defect size; over time, the frost heaving force gradually increases, but it will eventually stabilize. It is found that when the frost heaving force reaches a certain level, the surrounding rock with low strength or the lining with insufficient strength will crack, and the frost heaving force will not continue to increase.

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

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.

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

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.

Experimental Identification of the Constitutive Model of Viscoelastic Non-Standard Materials

There is an increasing interest towards the use of non-conventional material such as Functionally Graded Materials (FGM) for aerospace and automotive mechanical applications. Classical material models, e.g. Kelvin or Zener, can show some limitations in describing the viscoelastic behavior of these materials. A numerical and experimental approach to identify the optimal model order and the parameters of the constitutive material relationship in the frequency domain is proposed. The constitutive equation is modeled by means of a generalized Kelvin model and expressed in the form of a rational function. To describe the complex material behavior, high order polynomials are needed for the rational function and the problem of finding the function coefficients can be ill-conditioned. Different approaches for the rational function parameters identification are compared. A least square error identification technique adopting Forsythe orthogonal polynomials is proposed. The selected procedure is first applied on numerically estimated measurements with noise, and then on real measurement data obtained by forced vibration testing of Polytetrafluoroethylene specimens.

Vibration of Micro-Scale Structures: Accurate SPH Approach and Simplified Generalized Kelvin Model

Recent advances in polymer technology together with the growing need of smaller and lighter electronic components and biomedical equipment led to the development of new applications of polymers at micro scale. However, unlike traditional materials (e.g., metal silicon), polymers exhibit a significant time dependency in their response to load (e.g., viscoelastic, hyperelastic). Therefore, predicting the behavior of such polymer components at small scale requires accurate simulations of the effects of creep and relaxation within the systems. The current study uses a mesh-free particle method (smoothed particle hydrodynamics) to predict time-dependent mechanical response of polymers. As a first step towards investigating the response of a polymer microstructure under load, we simulate the behavior of a slender polymer rod compressed and tangentially dragged against a smooth glass surface. It is shown that although accurate prediction of polymer deformation cannot be achieved with a fully analytic model, a simplified generalized Kelvin model could calibrated to capture most of the characteristics of the fully numerical model. This cold be used for predicting the behavior under load of a passive subsystem of imbedded in a control algorithm to extend the measuring domain of a possible sensor or prevent potentially dangerous operating conditions.

Variable Parameters-Based Damage Creep Model of Weak Rock Layer and its Engineering Application

In order to study the deformation mechanism of the weak layer in diabase dikes under long-term loading at a hydropower dam foundation, in situ plate loading tests were performed. A damage creep model which improved the five-parameter generalized Kelvin model was established to describe the creep behavior of the weak layer. In this model, the deterioration effect of the rock parameters is considered and the creep parameters of the rock deteriorate gradually. This model is applied in a slope design for a dam foundation at a hydropower station. Long-term stability of the slope after excavation is evaluated. It shows that when damage creep is considered, the displacement is larger compared with the case of ignoring damage creep. The study shows that the deterioration effect of the rock parameters is of full importance for the project design and construction safety.

Experimental Studies of Creep Characters of Tunnel Lining Concrete

Adopting MTS815 hydraulic servo system, through triaxial compressive deformation and triaxial creep experiment result of tunnel supports, research the stress-strain and creep properties of tunnel supports. Test results show that deformation process of support concrete displays obvious strain softening, instantaneous elastic strain increments with stress level and strain of creep curve appears increased trend with time. Creep curve of concrete drive to a fixed value when stress level is lower and strain rate of concrete more and more small. The generalized Kelvin model of three element and LUBBY2 model are feasible as creep model of concrete support. Based on the relation of creep characteristic curves for rock salt, the creep parameters of generalized Kelvin model and LUBBY2 model are advanced.