Thin elastic sheets bend easily and, if they are patterned with cuts, can deform in sophisticated ways. Here we show that carefully tuning the location and arrangement of cuts within thin sheets enables the design of mechanical actuators that scale down to atomically-thin 2D materials. We first show that by understanding the mechanics of a single non-propagating crack in a sheet, we can generate four fundamental forms of linear actuation: roll, pitch, yaw, and lift. Our analytical model shows that these deformations are only weakly dependent on thickness, which we confirm with experiments on centimeter-scale objects and molecular dynamics simulations of graphene and MoS nanoscale sheets. We show how the interactions between non-propagating cracks can enable either lift or rotation, and we use a combination of experiments, theory, continuum computational analysis, and molecular dynamics simulations to provide mechanistic insights into the geometric and topological design of kirigami actuators.
A fractal design is shown to be highly efficient both as a load bearing structure and as a general metamaterial. Through changing the hierarchical order of the structure, the scaling of material required for stability against loading can be manipulated. We show that the transition from solid to hollow beams changes the scaling in a manner analogous to increasing the hierarchical order by one. An example second order solid beam frame is constructed using rapid prototyping techniques. The optimal hierarchical order of the structure is found for different values of loading. Possible fabrication methods and applications are then discussed.
DNA origami is a powerful method for the creation of 3D nanoscale objects, and in the past few years, interest in wireframe origami designs has increased due to their potential for biomedical applications. In DNA wireframe designs, the construction material is double-stranded DNA, which has a persistence length of around 50 nm. In this work, we study the effect of various design choices on the stiffness versus final size of nanoscale wireframe rods, given the constraints on origami designs set by the DNA origami scaffold size. An initial theoretical analysis predicts two competing mechanisms limiting rod stiffness, whose balancing results in an optimal edge length. For small edge lengths, the bending of the rod's overall frame geometry is the dominant factor, while the flexibility of individual DNA edges has a greater contribution at larger edge lengths. We evaluate our design choices through simulations and experiments and find that the stiffness of the structures increases with the number of sides in the cross-section polygon and that there are indications of an optimal member edge length. We also ascertain the effect of nicked DNA edges on the stiffness of the wireframe rods and demonstrate that ligation of the staple breakpoint nicks reduces the observed flexibility. Our simulations also indicate that the persistence length of wireframe DNA structures significantly decreases with increasing monovalent salt concentration.
Mechanical metamaterial actuators achieve predetermined input-output operations exploiting architectural features encoded within a single 3D printed element, thus removing the need for assembling different structural components. Despite the rapid progress in the field, there is still a need for efficient strategies to optimize metamaterial design for a variety of functions. We present a computational method for the automatic design of mechanical metamaterial actuators that combines a reinforced Monte Carlo method with discrete element simulations. 3D printing of selected mechanical metamaterial actuators shows that the machine-generated structures can reach high efficiency, exceeding human-designed structures. We also show that it is possible to design efficient actuators by training a deep neural network which is then able to predict the efficiency from the image of a structure and to identify its functional regions. The elementary actuators devised here can be combined to produce metamaterial machines of arbitrary complexity for countless engineering applications.
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