Chen Songqiang, Chen Bin, Wu Xi, Zhou Jian
Zhejiang Engineering Research Center of Intelligent Urban Infrastructure, Hangzhou City University, Hangzhou 310015, China.
Balance Building Research Center, Zhejiang University, Hangzhou 310058, China.
Materials (Basel). 2023 Sep 6;16(18):6097. doi: 10.3390/ma16186097.
The conversion between the relaxation modulus and creep compliance is a traditional research topic in viscoelastic materials. Generally, different methods have been used to solve the numerical solution based on convolution theory. However, the initial relaxation modulus (relaxation modulus at = 0) has been difficult to obtain. This paper aimed to propose a fast calculation method to derive the initial relaxation modulus from the creep compliance. First, three groups of uniaxial static creep tests of asphalt mixtures were conducted to determine the creep compliance of the experimental data. Then, the calculation of the initial relaxation modulus from the creep compliance by three inversion methods (midpoint method, approximate method, and Laplace numerical inversion method) was evaluated. The results indicate that approximate method and Laplace numerical inversion method cannot calculate the initial relaxation modulus value, and the calculation results of the midpoint method can only approach the exact value infinitely, for which calculating the relaxation modulus at 0.0005 s requires 2000 s. The results can only approach the exact value infinitely and take a lot of computing time. Finally, a fast calculation method for the initial relaxation modulus is proposed and verified by Laplace initial value theorem, and this method can directly derive a simple expression for calculating the initial relaxation modulus without requiring computational time. The proposed calculation methods of the initial relaxation modulus for various viscoelastic models were then put forward. The research results provide an effective tool for obtaining the initial relaxation modulus accurately.
松弛模量与蠕变柔量之间的转换是粘弹性材料领域的一个传统研究课题。一般来说，基于卷积理论有不同的方法来求解数值解。然而，初始松弛模量（即时间为0时的松弛模量）一直难以获得。本文旨在提出一种快速计算方法，从蠕变柔量中推导初始松弛模量。首先，对沥青混合料进行了三组单轴静态蠕变试验，以确定试验数据的蠕变柔量。然后，评估了通过三种反演方法（中点法、近似法和拉普拉斯数值反演法）从蠕变柔量计算初始松弛模量的情况。结果表明，近似法和拉普拉斯数值反演法无法计算出初始松弛模量值，中点法的计算结果只能无限趋近于精确值，例如计算0.0005 s时的松弛模量需要2000 s，其结果只能无限趋近于精确值且需要大量计算时间。最后，提出了一种初始松弛模量的快速计算方法，并通过拉普拉斯初值定理进行了验证，该方法可以直接推导出一个计算初始松弛模量的简单表达式，无需计算时间。随后提出了针对各种粘弹性模型的初始松弛模量计算方法。研究结果为准确获取初始松弛模量提供了一种有效工具。
