In recent developments in the field of multi-material additive manufacturing, differences in material properties are exploited to create printed shape memory structures, which are referred to as 4D-printed structures. New printing techniques allow for deliberate introduction of prestresses in the specimen during manufacturing. This prestress is combined with a heat-induced glass transition, which lowers the materials Young's modulus. Upon the decrease in stiffness, the prestress is released, which results in the realization of a pre-programmed deformation. Coupled with the right design, this enables new functionalities. As the design of such functional multi-material structures is crucial but far from trivial, a systematic methodology is developed, where a finite element model is combined with a density-based topology optimization method to describe the material layout. The coupling between the definition of the prestress and the material interpolation function used in the topology description is addressed. The efficacy of topology optimization to design 4D-printed structures is explored by applying the methodology to a variety of design problems. Tests are performed with printed samples to calibrate the prestress and to validate the modeling approach. This study demonstrates that by combining topology optimization and 4D-printing concepts, stimuli-responsive structures with specific properties can be designed and realized.
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