The Digital Twin is one of the major technology trends of the last decade. During the course of its rapid expansion into various fields of application, many definitions of the Digital Twin emerged, tailored to its respective applications. Taxonomies can cluster the diversity and define application-specific archetypes. This paper presents a systematic characterization of the Digital Twin in the context of structural mechanics and lightweight design. While the importance of a shared understanding and the development of holistic solutions for implementing Digital Twins in various application areas is widely recognized, a general framework for implementing Digital Twins in structural mechanics has not yet been established. In this paper, we systematically characterize Digital Twins and develop a framework for their application in structural mechanics, enabling the digital design and monitoring of structures for improved performance and maintenance strategies. The key contributions include collecting and clustering design and operational requirements and deriving two central archetypes: structure-designing and structure-monitoring Digital Twins. The primary goal is to reduce the complexity of conceptualizing Digital Twins of structures by providing a preliminary framework and reconsidering the Digital Twins of structures as a holistic system throughout the product life cycle. Overall, in this paper, we take a systematic approach to enhancing the conceptualization and implementation of Digital Twins in structural mechanics.