In the materials design domain, much of the data from materials calculations is stored in different heterogeneous databases with different data and access models. Therefore, accessing and integrating data from different sources is challenging. As ontology-based access and integration alleviates these issues, in this paper we address data access and interoperability for computational materials databases by developing the Materials Design Ontology. This ontology is inspired by and guided by the OPTIMADE effort that aims to make materials databases interoperable and includes many of the data providers in computational materials science. In this paper, first, we describe the development and the content of the Materials Design Ontology. Then, we use a topic model-based approach to propose additional candidate concepts for the ontology. Finally, we show the use of the Materials Design Ontology by a proof-of-concept implementation of a data access and integration system for materials databases based on the ontology.