4D프린팅에서 목적한 3D 형상으로 변형하는 초기 출력 모델 설계 방법

Abstract

Recent uses of smart materials for 3D printing introduced the production of objects that change their morphology through controlled stimulation. This technology is called 4D printing. To make this technology any useful, there should be a design tool that can calculate the initial 3D printed shape with proper material compositions that will transform into the final shape after being exposed to the stimulation. In this study, we present a mathematical foundation based on polygonal model planarization. The proposed method is quite similar to the parameterization problem in computer graphics but it is more difficult because of the added constraint that all basic elements that constitute the 3D printed initial shape need to expand to reach the final shape. The expansion rate can vary among the elements and this is physically realizable by controlling the mixing ratio of two materials of different expansion ratios. Also, we calculated the angle of the edge that also modified with respect to the vertex as it was flattened. Finally, we proposed a 4D printing structure that can be transformed into a 3D shape using expansion rate and distortion angle of edges.