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We present a design optimization and manufacturing approach for the creation of complex three-dimensional (3D) curved rod structures with spatially variable material distributions that exhibit active deformation behavior, enabled by the shape memory effect (SME) of 3D printed photopolymers—so-called four-dimensional (4D) printing. Our framework optimizes the cross-sectional properties of a rod structure, in particular the Young's modulus, such that under given loading conditions it can obtain one or more target shapes resulting from geometrically nonlinear deformation, from which the structure can then actively deform back to the original shape due to the SME. Our approach includes a novel algorithm to generate physical realizations from the computational design model, which allows their direct fabrication via printing of shape memory composites with voxel-level compositional control with a multi-material 3D printer. Our design and manufacture digital toolchain allows the continuous variation of multiple active materials as a route to optimize mechanical as well as active behavior of a structure, without changing the original shape of the 3D rod structure, which is not possible with a single material. We demonstrate the entire design-fabrication-test approach and illustrate its capabilities with examples including 3D characters, personalized medical applications, and complex structures that exhibit instabilities during their nonlinear deformation.

Keywords: 4D printing, active structures, design optimization, functionally graded materials, multi-material 3D printing, voxel control of material properties