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The stimuli-responsive self-folding structure is ubiquitous in nature, for instance, the mimosa folds its leaves in response to external touch or heat, and the Venus flytrap snaps shut to trap the insect inside. Thus, modeling self-folding structures has been of great interest to predict the final configuration and understand the folding mechanism. Here, we apply a simple yet effective method to predict the folding angle of the temperature-responsive nanocomposite hydrogel/elastomer bilayer structure manufactured by 3D printing, which facilitates the study of the effect of the inevitable variations in manufacturing and material properties on folding angles by comparing the simulation results with the experimentally measured folding angles. The defining feature of our method is to use thermal expansion to model the temperature-responsive nanocomposite hydrogel rather than the nonlinear field theory of diffusion model that was previously applied. The resulted difference between the simulation and experimentally measured folding angle ( i.e. , error) is around 5%. We anticipate that our method could provide insight into the design, control, and prediction of 3D printing of stimuli-responsive shape morphing ( i.e. , 4D printing) that have potential applications in soft actuators, robots, and biomedical devices. 

Abstract With the rapid developments of advanced manufacturing and its ability to manufacture microscale features, architected materials are receiving ever increasing attention in many physics fields. Such a design problem can be treated in topology optimization as architected material with repeated unit cells using the homogenization theory with the periodic boundary condition. When multiple architected materials with spatial variations in a structure are considered, a challenge arises in topological solutions, which may not be connected between adjacent material architecture. This paper introduces a new measure, connectivity index (CI), to quantify the topological connectivity, and adds it as a constraint in multiscale topology optimization to achieve connected architected materials. Numerical investigations reveal that the additional constraints lead to microstructural topologies, which are well connected and do not substantially compromise their optimalities.