Finding the Optimal Nets for Self-Folding Kirigami

Inverse Design of Self-Folding 3D Shells

Self-folding is an emerging paradigm for the inverse design of three-dimensional structures. While most efforts have concentrated on the shape of the net, our approach introduces a new design dimension-bond specificity between the edges. We transform this design process into a Boolean satisfiability problem to derive solutions for various target structures. This method significantly enhances the yield of the folding process. Furthermore, by linearly combining independent solutions, we achieve designs for shape-shifting nets wherein the dominant structure evolves with varying external conditions. This approach is demonstrated through coarse-grained simulations on two examples of triangular and square nets capable of folding into multiple target shapes.

Optimal face-to-face coupling for fast self-folding kirigami

Kirigami-inspired designs can enable self-folding three-dimensional materials from flat, two-dimensional sheets. Hierarchical designs of connected levels increase the diversity of possible target structures, yet they can lead to longer folding times in the presence of fluctuations. Here, we study the effect of rotational coupling between levels on the self-folding of two-level kirigami designs driven by thermal noise in a fluid. Naturally present due to hydrodynamic resistance, we find that this coupling parameter can significantly impact a structure's self-folding pathway, thus enabling us to assess the quality of a kirigami design and the possibility for its optimization in terms of its folding rate and yield.

Microelectronic Morphogenesis: Smart Materials with Electronics Assembling into Artificial Organisms

Microelectronic morphogenesis is the creation and maintenance of complex functional structures by microelectronic information within shape-changing materials. Only recently has in-built information technology begun to be used to reshape materials and their functions in three dimensions to form smart microdevices and microrobots. Electronic information that controls morphology is inheritable like its biological counterpart, genetic information, and is set to open new vistas of technology leading to artificial organisms when coupled with modular design and self-assembly that can make reversible microscopic electrical connections. Three core capabilities of cells in organisms, self-maintenance (homeostatic metabolism utilizing free energy), self-containment (distinguishing self from nonself), and self-reproduction (cell division with inherited properties), once well out of reach for technology, are now within the grasp of information-directed materials. Construction-aware electronics can be used to proof-read and initiate game-changing error correction in microelectronic self-assembly. Furthermore, noncontact communication and electronically supported learning enable one to implement guided self-assembly and enhance functionality. Here, the fundamental breakthroughs that have opened the pathway to this prospective path are reviewed, the extent and way in which the core properties of life can be addressed are analyzed, and the potential and indeed necessity of such technology for sustainable high technology in society is discussed.

Theorem for the design of deployable kirigami tessellations with different topologies

The concept of kirigami has been extensively utilized to design deployable structures and reconfigurable metamaterials. Despite heuristic utilization of classical kirigami patterns, the gap between complex kirigami tessellations and systematic design principles still needs to be filled. In this paper, we develop a unified design method for deployable quadrilateral kirigami tessellations perforated on flat sheets with different topologies. This method is based on the parametrization of kirigami patterns formulated as the solution of a linear equation system. The geometric constraints for the deployability of parameterized cutting patterns are given by a unified theorem covering different topologies of the flat sheets. As an application, we employ the design method to achieve desired shapes along the deployment path of kirigami tessellations, while preserving the topological characteristics of the flat sheets. Our approach introduces interesting perspectives for the topological design of kirigami-inspired structures and metamaterials.

Lattice model for self-folding at the microscale

Three-dimensional shell-like structures can be obtained spontaneously at the microscale from the self-folding of 2D templates of rigid panels. At least for simple structures, the motion of each panel is consistent with a Brownian process and folding occurs through a sequence of binding events, where pairs of panels meet at a specific closing angle. Here, we propose a lattice model to describe the dynamics of self-folding. As an example, we study the folding of a pyramid of N lateral faces. We combine analytical and numerical Monte Carlo simulations to find how the folding time depends on the number of faces, closing angle, and initial configuration. Implications for the study of more complex structures are discussed.

Universal folding pathways of polyhedron nets

Low-dimensional objects such as molecular strands, ladders, and sheets have intrinsic features that affect their propensity to fold into 3D objects. Understanding this relationship remains a challenge for de novo design of functional structures. Using molecular dynamics simulations, we investigate the refolding of the 24 possible 2D unfoldings ("nets") of the three simplest Platonic shapes and demonstrate that attributes of a net's topology-net compactness and leaves on the cutting graph-correlate with thermodynamic folding propensity. To explain these correlations we exhaustively enumerate the pathways followed by nets during folding and identify a crossover temperature [Formula: see text] below which nets fold via nonnative contacts (bonds must break before the net can fold completely) and above which nets fold via native contacts (newly formed bonds are also present in the folded structure). Folding above [Formula: see text] shows a universal balance between reduction of entropy via the elimination of internal degrees of freedom when bonds are formed and gain in potential energy via local, cooperative edge binding. Exploiting this universality, we devised a numerical method to efficiently compute all high-temperature folding pathways for any net, allowing us to predict, among the combined 86,760 nets for the remaining Platonic solids, those with highest folding propensity. Our results provide a general heuristic for the design of 2D objects to stochastically fold into target 3D geometries and suggest a mechanism by which geometry and folding propensity are related above [Formula: see text], where native bonds dominate folding.