The materials we encounter in our every day lives already extend beyond the traditional materials of wood, metal, ceramics and glass. The characteristics and behavior of materials and material composites are continuously being tweaked. The introduction of new materials that can respond to inputs from the environment has brought about a new movement for material development and interaction design: computational composites. A computational composite is capable of sensing inputs from the environment, processing and controlling the consequent expression or formation of the material. The aim of the thesis was two-fold: to design and develop a soft bodied mechanism inspired by the movement of a caterpillar, using a Shape Memory Alloy-based (SMAs) composite, and to design material concepts based on the qualities of the composite. This was an explorative project, investigating the application of a bio-inspired approach and the Material Driven Design (MDD) approach to the development of a moving material. The first phase of the project focused on uncovering the technical aspects of a SMA-based composites and its relation to a computational composite. To understand caterpillar locomotion, a thorough study on its anatomy and locomotion strategies was performed. A qualitative study on how designers interpret caterpillar-like motion lead to four interesting movements, which were further developed in moving SMA-based composites from silicone and 4D printed textile. One SMA-based composite was selected for further improvement of the mechanism to be capable of translational caterpillar-like motion. The mechanism can also be interpreted and applied in other ways, and thus the experiential characteristics of the material were uncovered to define a material experience vision for further applications. Through a creative session and ideation phase three material concepts were proposed, suited for three types of user input on the computational composite: none, indirect and direct. The ultimate purpose for the material would be to sensitize people to the idea of a world where materials move from passive objects to active elements in our daily lives. It is recommended to do more research on the composite and to apply the materials experience vision to applications beyond every day objects and into the more innovative field of computer interface design and human-material interaction.