This article presents and illustrates a functional modeling-based representation of digital twinning (DT) architectures. We provide a detailed review of the existing architectures and frameworks intended for use on product digital twins. We identified gaps in the prior work on architectures and frameworks for DT of products, product families, and systems. We identified a need for robust representation schemes that enable product-specific synthesis and analysis of DTs, which the existing DT architecture representations do not offer. We integrated the efforts of the researchers on DT architectures in our functional modeling-based architecture representation approach. We included selected attributes of each reviewed framework and addressed the identified gaps through our functional modeling-based DT architecture representation. The proposed architecture representation approach opens up new avenues of research and can potentially help improve the design process for product DT. This paper illustrates our approach through an instructional example of a COVID-19 testing breathalyzer kiosk designed as a rapid response to the COVID-19 pandemic.