Dacol Vitor, Caetano Elsa, Correia João R
CONSTRUCT (ViBEST), Faculty of Engineering (FEUP), University of Porto, 4200-465 Porto, Portugal.
CERIS, DECivil, IST, University of Lisbon, 1049-001 Lisbon, Portugal.
Polymers (Basel). 2020 Dec 16;12(12):3001. doi: 10.3390/polym12123001.
Understanding and modeling the viscoelastic behavior of polymers and polymer-based materials for a wide range of quasistatic and high strain rates is of great interest for applications in which they are subjected to mechanical loads over a long time of operation, such as the self-weight or other static loads. The creep compliance and relaxation functions used in the characterization of the mechanical response of linear viscoelastic solids are traditionally determined by conducting two separate experiments-creep tests and relaxation tests. This paper first reviews the steps involved in conducting the interconversion between creep compliance and relaxation modulus in the time domain, illustrating that the relaxation modulus can be obtained from the creep compliance. This enables the determination of the relaxation modulus from the results of creep tests, which can be easily performed in pneumatic equipment or simple compression devices and are less costly than direct relaxation tests. Some existing methods of interconversion between the creep compliance and the relaxation modulus for linear viscoelastic materials are also presented. Then, a new approximate interconversion scheme is introduced using a convenient Laplace transform and an approximated Gamma function to convert the measured creep compliance to the relaxation modulus. To demonstrate the accuracy of the fittings obtained with the method proposed, as well as its ease of implementation and general applicability, different experimental data from the literature are used.
理解和模拟聚合物及聚合物基材料在广泛的准静态和高应变率下的粘弹性行为，对于它们在长时间运行中承受机械载荷（如自重或其他静载荷）的应用具有重要意义。传统上，用于表征线性粘弹性固体力学响应的蠕变柔量和松弛函数是通过进行两个单独的实验——蠕变试验和松弛试验来确定的。本文首先回顾了在时域中进行蠕变柔量和松弛模量相互转换所涉及的步骤，说明可以从蠕变柔量获得松弛模量。这使得能够根据蠕变试验结果确定松弛模量，蠕变试验可以在气动设备或简单压缩装置中轻松进行，且成本低于直接的松弛试验。还介绍了一些现有的线性粘弹性材料蠕变柔量和松弛模量相互转换的方法。然后，引入了一种新的近似相互转换方案，使用方便的拉普拉斯变换和近似的伽马函数将测量得到的蠕变柔量转换为松弛模量。为了证明所提出方法得到的拟合结果的准确性，以及其易于实施和普遍适用性，使用了文献中的不同实验数据。
