We explore a new design strategy of leveraging kinematic bifurcation in creating origami/kirigami-based three-dimensional (3D) hierarchical, reconfigurable, mechanical metamaterials with tunable mechanical responses. We start from constructing three basic, thick, panel-based structural units composed of 4, 6 and 8 rigidly rotatable cubes in close-looped connections. They are modelled, respectively, as 4R, 6R and 8R (R stands for revolute joint) spatial looped kinematic mechanisms, and are used to create a library of reconfigurable hierarchical building blocks that exhibit kinematic bifurcations. We analytically investigate their reconfiguration kinematics and predict the occurrence and locations of kinematic bifurcations through a trial-correction modelling method. These building blocks are tessellated in 3D to create various 3D bifurcated hierarchical mechanical metamaterials that preserve the kinematic bifurcations in their building blocks to reconfigure into different 3D architectures. By combining the kinematics and considering the elastic torsional energy stored in the folds, we develop the geometric mechanics to predict their tunable anisotropic Poisson’s ratios and stiffnesses. We find that kinematic bifurcation can significantly effect mechanical responses, including changing the sign of Poisson’s ratios from negative to positive beyond bifurcation, tuning the anisotropy, and overcoming the polarity of structural stiffness and enhancing the number of deformation paths with more reconfigured shapes. This article is part of the theme issue ‘Origami/Kirigami-inspired structures: from fundamentals to applications’. 
                        more » 
                        « less   
                    This content will become publicly available on November 18, 2025
                            
                            Toward mechanical proprioception in autonomously reconfigurable kirigami-inspired mechanical systems
                        
                    
    
            Mechanical metamaterials have recently been exploited as an interesting platform for information storing, retrieval and processing, analogous to electronic devices. In this work, we describe the design and fabrication a two-dimensional (2D) multistable metamaterial consisting of building blocks that can be switched between two distinct stable phases, and which are capable of storing binary information analogous to digital bits. By changing the spatial distribution of the phases, we can achieve a variety of different configurations and tunable mechanical properties (both static and dynamic). Moreover, we demonstrate the ability to determine the phase distribution via simple probing of the dynamic properties, to which we refer as mechanical proprioception. Finally, as a simple demonstration of feasibility, we illustrate a strategy for building autonomous kirigami systems that can receive inputs from their environment. This work could bring new insights for the design of mechanical metamaterials with information processing and computing functionalities. This article is part of the theme issue ‘Origami/Kirigami-inspired structures: from fundamentals to applications’. 
        more » 
        « less   
        
    
    
                            - PAR ID:
- 10584379
- Publisher / Repository:
- The Royal Society
- Date Published:
- Journal Name:
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Volume:
- 382
- Issue:
- 2283
- ISSN:
- 1364-503X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
- 
            
- 
            null (Ed.)Kirigami, the art of paper cutting, has become a paradigm for mechanical metamaterials in recent years. The basic building blocks of any kirigami structures are repetitive deployable patterns that derive inspiration from geometric art forms and simple planar tilings. Here, we complement these approaches by directly linking kirigami patterns to the symmetry associated with the set of 17 repeating patterns that fully characterize the space of periodic tilings of the plane. We start by showing how to construct deployable kirigami patterns using any of the wallpaper groups, and then design symmetry-preserving cut patterns to achieve arbitrary size changes via deployment. We further prove that different symmetry changes can be achieved by controlling the shape and connectivity of the tiles and connect these results to the underlying kirigami-based lattice structures. All together, our work provides a systematic approach for creating a broad range of kirigami-based deployable structures with any prescribed size and symmetry properties.more » « less
- 
            The concepts of origami and kirigami have often been presented separately. Here, we put forth a synergistic approach—the folded kirigami—in which kirigami assemblies are complemented by means of folding, typical of origami patterns. Besides the emerging patterns themselves, the synergistic approach also leads to topological mechanical metamaterials. While kirigami metamaterials have been fabricated by various methods, such as 3D printing, cutting, casting, and assemblage of building blocks, the “folded kirigami” claim their distinctive properties from the universal folding protocols. For a target kirigami pattern, we design an extended high-genus pattern with appropriate sets of creases and cuts, and proceed to fold it sequentially to yield the cellular structure of a 2D lattice endowed with finite out-of-plane thickness. The strategy combines two features that are generally mutually exclusive in canonical methods: fabrication involving a single piece of material and realization of nearly ideal intercell hinges. We test the approach against a diverse portfolio of triangular and quadrilateral kirigami configurations. We demonstrate a plethora of emerging metamaterial functionalities, including topological phase-switching reconfigurability between polarized and nonpolarized states in kagome kirigami, and availability of nonreciprocal mechanical response in square-rhombus kirigami.more » « less
- 
            Kirigami (cutting and/or folding) offers a promising strategy to reconfigure metamaterials. Conventionally, kirigami metamaterials are often composed of passive cut unit cells to be reconfigured under mechanical forces. The constituent stimuli-responsive materials in active kirigami metamaterials instead will enable potential mechanical properties and functionality, arising from the active control of cut unit cells. However, the planar features of hinges in conventional kirigami structures significantly constrain the degrees of freedom (DOFs) in both deformation and actuation of the cut units. To release both constraints, here, we demonstrate a universal design of implementing folds to reconstruct sole-cuts–based metamaterials. We show that the supplemented folds not only enrich the structural reconfiguration beyond sole cuts but also enable more DOFs in actuating the kirigami metasheets into 3 dimensions (3D) in response to environmental temperature. Utilizing the multi-DOF in deformation of unit cells, we demonstrate that planar metasheets with the same cut design can self-fold into programmable 3D kirigami metastructures with distinct mechanical properties. Last, we demonstrate potential applications of programmable kirigami machines and easy-turning soft robots.more » « less
- 
            Abstract This study investigates the programming of elastic wave propagation bandgaps in periodic and multi‐stable metamaterials by intentionally and uniquely sequencing its constitutive mechanical bits. To this end, stretched kirigami is used as a simple and versatile testing platform. Each mechanical bit in the stretched kirigami can switch between two stable equilibria with different external shapes (aka. “(0)” and “(1)” states). Therefore, by designing the sequence of (0) and (1) bits, one can fundamentally change the underlying periodicity and thus program the phononic bandgap frequencies. This study develops an algorithm to identify the unique periodicities generated by assembling “n‐bit strings” consisting ofnmechanical bits. Based on a simplified geometry of thesen‐bit strings, this study also formulates a theory to uncover the rich mapping between input sequencing and output bandgaps. The theoretical prediction and experiment results confirm that the (0) and (1) bit sequencing is effective for programming the phonic bandgap frequencies. Moreover, one can additionally fine‐tune the bandgaps by adjusting the global stretch. Overall, the results of this study elucidate new strategies for programming the dynamic responses of architected material systems.more » « less
 An official website of the United States government
An official website of the United States government 
				
			 
					 
					
