Digital Twins (DTs) are real-time digital models that allow for self-diagnosis, self-optimization and self-configuration without the need for human input or intervention. While DTs are a central aspect of the ongoing fourth industrial revolution (I4.0), this leap forward may be reserved for the established, large-cap companies since the adoption of digital technologies among Small and Medium-size Enterprises (SMEs) is still modest. The aim of the H2020 European Project ”DIGITbrain” is to support a modular construction of DTs by reusing their fundamental building blocks, i.e., the Models that describe the behavior of the DT, their associated Algorithms and the Data required for the evaluation. By offering these building blocks as a service via a DT Platform (a Digital Twin Environment), the technical barriers among SMEs to adopt these technologies are lowered. This paper describes how digital models can be classified, reused and authored on such DT Platforms. Through experimental analyses of three industrial cases, the paper exemplifies how DTs are employed in relation to product assembly of agricultural robots, polymer injection molding, as well as laser-cutting and sheet-metal forming of aluminum.