Comparison of Relaxation Modulus Converted from Frequency- and Time-Dependent Viscoelastic Functions through Numerical Methods

Abstract

Due to the difficulty of obtaining relaxation modulus directly from experiments, many interconversion methods from other viscoelastic functions to relaxation modulus were developed in previous years. The objectives of this paper were to analyze the difference of relaxation modulus converted from dynamic modulus and creep compliance and explore its potential causes. The selected methods were the numerical interconversions based on Prony series representation. For the dynamic to relaxation conversion, the time spectrum was determined by the collocation method. Meanwhile, for the creep to relaxation conversion, both the collocation method and least squares method were adopted to perform the Laplace transform. The results show that these two methods do not present a significant difference in estimating relaxation modulus. Their difference mostly exists in the transient reduced time region. Calculating the average of two methods is suggested to avoid great deviation of single experiment. To predict viscoelastic responses from creep compliance, the collocation method yields comparable results to the least squares method. Thus, simply-calculated collocation method may be preferable in practice. Further, the master curve pattern is sensitive to the Prony series coefficients. The difference in transient reduced time region may be attributed to the indeterminate Prony series coefficients.

Comparative Analysis of Viscoelastic Properties of Open Graded Friction Course under Dynamic and Static Loads

“…According to the coefficients of the generalized Maxwell model, the storage modulus and the loss modulus can be calculated by Equations (15) and (16), respectively [ 16 , 28 , 29 ]: …”

“…According to the coefficients of the generalized Maxwell model, the storage modulus G and the loss modulus G can be calculated by Equations ( 15) and ( 16), respectively [16,28,29]: 10 °C, 20 °C, 30 °C, 40 °C, and 50 °C was tested and calculated, and shown in Figure 2. As shown in Figure 2, at the initial stage of loa ance of OGFC grows rapidly with the loading time; when the load 500 s, the creep compliance of OGFC grows gently, showing a nea It can also be found from Figure 2 that the creep compliance of O cantly with the increase in test temperature.…”

“…However, the related studies have pointed out that there is an inherent relationship between dynamic modulus parameters and static creep compliance parameters of asphalt mixtures, and the creep compliance in the time domain can be transformed into dynamic modulus in the frequency domain according to the relevant mathematical theories [ 16 , 17 ]. Furthermore, the relationship between the creep compliance, relaxation modulus and dynamic modulus of asphalt mixtures can be established, so as to realize the prediction of dynamic modulus parameters.…”

Investigation of flexible pavement maintenance patching factors using a finite element model

“…where G(t) is the shear relaxation modulus; G 0 is instantaneous shear modulus; G 0 = lim t→0 G(0); t is the loading [11] and fatigue tests [15]. Through Laplace transformation and intercoversion [16][17][18], the creep compliance results can be converted into corresponding relaxation results. Furthermore, if with relaxation tests results, parameters including shear modulus components and relaxation times required to fit a Prony series can be obtained by fitting test data [19,20].…”

Detection of Dynamic Modulus and Crack Properties of Asphalt Pavement Using a Non-Destructive Ultrasonic Wave Method

“…The selection of a finite element number per wavelength is critical and greatly affects simulative accuracy. At least seven finite elements per wavelength is suggested to achieve satisfyingly accurate results [14][15][16]. In this study, the element per wavelength was determined as 20 based on a sensitivity analysis, which was conducted to determine the proper element number per wavelength.…”