Conceptual design aims at developing design concepts that can satisfy the specified design requirements, where the design concepts are normally in the form of a physical structure. There has been quite a lot of work done in this area of design research, from which it is now generally agreed that functional decomposition and function to structure mapping are two fundamental steps of design task in synthesis for design solution. However, there have not been many strategies to support these design tasks, especially for the function to structure mapping. In addition, design solutions may not just consist of physical structure. Sometimes only materials can provide a feasible design solution; sometimes a materials solution might be more effective and/or more economic than a structural solution. Again, there have not been many strategies that explicitly considered materials solution at the early design stage. To address these problems, this paper proposes three mappings from function to both structure and material. Several embodiment strategies supporting these mappings are also proposed, including four functional matches used for identifying functional design solutions, and a performance match used for ensuring that the identified solution can satisfy the performance requirements or constraints. A design case is also studied to illustrate as well as to test the effectiveness of these strategies.