Tenreiro Machado J A, Lopes António M, de Camposinhos Rui
Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, Porto, Portugal.
UISPA-LAETA/INEGI, Faculty of Engineering, University of Porto, Porto, Portugal.
Philos Trans A Math Phys Eng Sci. 2020 May 29;378(2172):20190292. doi: 10.1098/rsta.2019.0292. Epub 2020 May 11.
This paper describes epoxy resins by means of electrical impedance spectroscopy (EIS) and the mathematical tool of fractional calculus (FC). Two stages are considered: first, the EIS is used for testing the samples and, second, the measured data are approximated using integer and fractional order models. The FC-based modelling describes the epoxy resins using a small number of parameters that reflect their main characteristics. The EIS data gathered for the epoxies samples are compared with those of different adhesives and sealants by means of a hierarchical clustering algorithm that unravels the relationships between the distinct materials. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.
本文通过电阻抗谱（EIS）和分数阶微积分（FC）这一数学工具对环氧树脂进行了描述。考虑了两个阶段：第一，使用EIS对样品进行测试；第二，使用整数阶和分数阶模型对测量数据进行近似。基于FC的建模使用少量反映环氧树脂主要特性的参数来描述它们。通过一种层次聚类算法，将收集到的环氧树脂样品的EIS数据与不同粘合剂和密封剂的数据进行比较，该算法揭示了不同材料之间的关系。本文是主题为“通过分数阶微积分进行先进材料建模：挑战与展望”的一部分。
