Design rationale (DR) explains why an artifact is designed the way it is. An explicit representation of DR is helpful to designers, allowing them to understand, improve, and reuse previous designs. The argumentation-based representation is the mainstream approach to DR representation. It has a semiformal graphical format to depict the structure of arguments for solving a design problem. This paper argues that because the design is not just a problem-solving process but also a cognitive activity that is continuously iterative and evolving, the conventional argumentation-based representation of DR has some inherent limitations. An improved, intent-driven representation model is proposed to capture and formalize the DR and its evolving history to support DR reuse. The model's knowledge structure, consisting of DR elements and their relationships, is detailed. A preliminary knowledge representation of the model based on Web Ontology Language is introduced. Furthermore, the context of DR is defined to document the complete DR and support effective traceability of design thinking. A graphical DR modeling system is developed, and an example is demonstrated to verify the system's application and the effectiveness of the proposed representation model. The paper provides an effective method to retain and manage a designer's implicit design knowledge, which has the potential to significantly improve the integrated management of product development knowledge.