Innovations in Cyber-Physical System (CPS) are driven by functionalities and features. Mechanical Engineering is mainly concerned with the physical product architecture that is not explicitly linked to these functions. A holistic model-driven engineering approach for CPS, therefore, needs to bridge the gap between functions and the physical product architecture. In mechanical design methodology, functional architectures describe the functionality of the system under development but are typically neither considered nor modeled in practice. Existing approaches utilizing mechanical functional architectures, however, do not formalize a relation between the functional architecture and the geometric design. Therefore, we conceived a meta-model that defines modeling-languages for modeling functional architectures of mechanical systems and physical solutions, i.e., interconnections of physical effects and geometries, as refinements of the functional components. We have encoded the meta-model as a SysML profile and applied it within an interdisciplinary, industrial project to model an automotive cooling system. Our contribution signposts the potential of functional structures to not only bridge the gap between function and geometry in mechanics but also to integrate the heterogeneous domains participating in CPS engineering.