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Recent advances in origami science and engineering have particularly focused on the challenges of dynamics. While research has primarily focused on statics and kinematics, the need for effective and processable dynamic models has become apparent. This paper evaluates various dynamic modelling techniques for rigid-foldable origami, particularly focusing on their ability to capture nonlinear dynamic behaviours. Two primary methods, the lumped mass–spring–damper approach and the energy-based method, are examined using a bistable stacked Miura-origami (SMO) structure as a case study. Through systematic dynamic experiments, we analyse the effectiveness of these models in predicting bistable dynamic responses, including intra- and interwell oscillations, in different loading conditions. Our findings reveal that the energy-based approach, which considers the structure's inertia and utilizes dynamic experimental data for parameter identification, outperforms other models in terms of validity and accuracy. This model effectively predicts the dynamic response types, the rich and complex nonlinear characteristics and the critical frequency where interwell oscillations occur. Despite its relatively increased complexity in model derivation, it maintains computational efficiency and shows promise for broader applications in origami dynamics. By comparing model predictions with experimental results, this study enhances our understanding of origami dynamics and contributes valuable insights for future research and applications. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'. [ABSTRACT FROM AUTHOR]

Recent advances in multistable metamaterials reveal a link between structural configuration transition and Boolean logic, heralding a new generation of computationally capable intelligent materials. To enable higher‐level computation, existing computational frameworks require the integration of large‐scale networked logic gates, which places demanding requirements on the fabrication of materials counterparts and the propagation of signals. Inspired by cellular automata, a novel computational framework based on multistable origami metamaterials by incorporating reservoir computing is proposed, which can accomplish high‐level computation tasks without the need to construct a logic gate network. This approach thus eliminates the demanding requirements for the fabrication of materials and signal propagation when constructing large‐scale networks for high‐level computation in conventional mechanical logic. Using the multistable stacked Miura‐origami metamaterial as a validation platform, digit recognition is experimentally implemented by a single actuator. Moreover, complex tasks, such as handwriting recognition and 5‐bit memory tasks, are also shown to be feasible with the new computation framework. The research represents a significant advancement in developing a new generation of intelligent materials with advanced computational capabilities. With continued research and development, these materials can have a transformative impact on a wide range of fields, from computational science to material mechano‐intelligence technology and beyond. [ABSTRACT FROM AUTHOR]

Transitions of multistability in materials are exploited for various functions and applications, such as spectral gap tuning, impact energy trapping, and wave steering. However, a fundamental and comprehensive understanding of the transitions, either quasistatic or dynamic transitions, has not yet been acquired, especially in terms of the sequence predictability and tailoring mechanisms. This research, utilizing the stacked Miura‐ori‐variant (SMOV) structure that has multistable shape reconfigurability as a platform, uncovers the deep knowledge of quasistatic and dynamic transitions and proposes the corresponding versatile formation and tuning of mechanical logic gates. Through theoretical, numerical, and experimental means, discriminative and deterministic quasistatic transition sequences, including reversible and irreversible ones, are uncovered, where they constitute a transition map that is editable upon adjusting the design parameters. Via applying dynamic excitations and tailoring the excitation conditions, reversible transitions between all stable configurations become attainable, generating a fully connected transition map. Benefiting from the nonlinearity of the quasistatic and dynamic transitions, basic and compound mechanical logic gates are achieved. The versatility of the scheme is demonstrated using a single SMOV to realize different complex logic operations without increasing structural complexity, showing its unique computing power and inspiring the avenue for efficient physical intelligence. [ABSTRACT FROM AUTHOR]

Self-locking origami structures are characterized by their piecewise linear constitutive relations between force and deformation, which, in practice, are always completely opaque and unmeasurable: the number of piecewise segments, the positions of non-smooth points, and the linear parameters of each segment are unknown a priori. However, acquiring this information is of fundamental importance for understanding the origami structure's dynamic folding process and predicting its dynamic behaviors. This, therefore, arouses our interest in adopting a dynamical identification process to determine the model and to estimate the parameters. In this research, based on the piecewise linear assumption, a physically-interpretable neural-fuzzy network is built to correlate the measured input and output data. Unlike the conventional approaches, the constructed neural network possesses specific physical meaning of its components: the number of neurons relates to the number of piecewise segments, the coefficients of the local linear models relate to the parameters of the constitutive relations, and the validity functions relate to the positions of non-smooth points. By addressing several examples with different backgrounds, the network's underlying data training methods are illustrated, including the local linear optimization for linear parameters, nested optimization for nonlinear partitions, and Local Linear Model Tree optimization for model selection. Noting that the tackled origami problem holds strong universality in terms of the unknown piecewise characteristics, the proposed approach would thus provide an effective, generic, and physically significant means for handling piecewise linear dynamical systems and meanwhile bring fresh vitality to the artificial neural network research. [ABSTRACT FROM AUTHOR]

Abstract Conventional sound barriers are constrained by fixed geometry which results in many limitations. In this research, origami , the paper folding technique, is exploited as a platform to design deployable and reconfigurable sound barriers, as well as to actively tailor the attenuation performance. As a proof of concept, a three-dimensional barrier structure is constructed based upon Miura-ori unit cells, whose shape can be significantly altered via folding with a single degree of freedom. Folding also generates periodic corrugations on the origami sheets, which can be exploited as backing cavities to form resonant sound absorbers with a micro-perforated membrane. The absorption performance of the constructed absorber and the insertion loss of the origami barrier are investigated using both numerical and experimental tools. The proposed origami barrier involves two fundamental mechanisms: sound reflection and absorption, and the origami offers unique tunability to enrich both mechanisms owing to the folding-induced geometric evolutions. Specifically, the sound reflection effect can be effectively tuned via changing the acoustic shadow zone and the diffracted sound paths by folding, and the sound absorption effect can also be regulated by altering the depth/shape of the backing cavities during folding. Overall, the results of this research offer fundamental insights into how folding would affect the acoustic performance and open up new opportunities for designing innovative origami-inspired acoustic devices. [ABSTRACT FROM AUTHOR]

• The effects of inter-cell connections on multi-cell origami dynamics are studied. • A refined and processible dynamic model of dual-cell SMO structures is developed. • The differences are revealed in terms of configuration switches and response types. • Global dynamics are examined via basins of attraction and basin stability. • Dynamic experiments verify the predicted connection-induced differences. Origami has become an important source for the development of mechanical metamaterials because folding can often lead to enhanced or unconventional mechanical properties. Metamaterials are always made of repeating cells by stacking and tessellating. The inter-cell connection thus plays a key role in determining the overall mechanics and dynamics of the metamaterial, but current studies mainly focus on the effects of inter-cell connection on statics. To overcome the shortcomings and advance the state of the art, this research employs the dual-cell stacked Miura-origami (SMO) structure as a platform to comprehensively dissect the effects of inter-cell connection forms on the dynamics. The two constituent SMO cells, by design, can be bi-stable such that the dual-cell structure possesses four stable states that are fundamentally different in configuration. Two inter-cell connection forms, a rod connection and a crease connection, are examined both theoretically and experimentally in this research. Assuming rigid-foldability of the constituent SMO structures and by equivalently quantifying the inter-cell connection constraint via additional elastic potential energy, a refined and processible dynamic model of the multi-stable dual-cell SMO structure is developed. Comprehensive numerical calculations reveal, on the one hand, the rich and complex dynamics of the dual-cell structure and, on the other hand, uncover the significant differences caused by the inter-cell connection forms. With relatively weak inter-cell constraint (e.g., the rod connection), dynamic configuration switches would occur at low excitation amplitudes, and the dynamic response types of the two cells can be fundamentally different; however, with relatively strong inter-cell constraint (e.g., the crease connection), more energy input is required to switch the configuration, and the dynamic response types of the two cells remain consistent. Such findings are qualitatively verified via dynamic experiments on the dual-cell SMO structures. We also extend our research to global dynamics by analyzing the basins of attraction and basin stability, which demonstrates from a probabilistic viewpoint that stronger inter-cell constraint would converge the dynamics to synchronous response types. The results of this research would offer a solid foundation for regulating the multi-stable dynamics of multi-cell origami structures/metamaterials and advancing their dynamic applications. [ABSTRACT FROM AUTHOR]

• A pneumatic Yoshimura-origami (PYO) cell is designed and prototyped. • The tunable statics and dynamics of the PYO cell are experimentally demonstrated. • The dynamic model of the PYO cell is established by an identification approach. • The model could predict pressure-induced tunable dynamics of the PYO cell. • Tunable passbands and transmissibility of the 6-cell PYO structure are achieved. • Programmable stopbands of the PYO metamaterial are numerically demonstrated. The unique merits of origami structures and origami metamaterials are the folding-induced shape reconfigurability and the associated evolution of mechanical properties. However, currently, there is a lack of mature solutions on how to achieve active tuning, and the tunability is stuck in static properties. Therefore, this study proposes a pneumatic scheme to overcome the above two bottleneck problems. Specifically, by integrating a pneumatic bladder with a monostable Yoshimura-ori structure, a pneumatic Yoshimura origami (PYO) cell is designed. Compared with the conventional approach making use of the origami multistability, the pressure scheme is simpler in design, more accurate in regulation, and richer in configurations. To exploit the PYO structure for tunable dynamics, the dynamic model is developed via a nonlinear system identification approach, in which the overall system, including the structure itself and the friction contact, is represented as a nonlinear spring-damper element, with the constitutive profile identified via the weighted least square method from the dynamic experimental data. Based on the developed model, the pressure tunability is then explored in a 6-cell PYO structure and a PYO metamaterial. Through comprehensive linear dispersion analyses and numerical simulations, we reveal that pressure could effectively tune the passbands of the 6-cell structure so that the transmission of vibration, at certain frequencies, can be qualitatively switched between amplification and attenuation; from another perspective, pressure could also be tailored for programming the stopbands of the PYO metamaterial to achieve the shift between propagation and prohibition. The results of this investigation could provide useful guidelines for the development of intelligent origami structures/metamaterials with excellent tunability, and meanwhile, open a new perspective of origami dynamics research. [ABSTRACT FROM AUTHOR]

In recent years, multi-stable origami structures have garnered increasing attention for their applications in dynamic scenarios such as robotic arm motions, impact energy absorption, and spectrum gap regulation. Understanding the intricate working mechanisms and exploring the rich dynamics of these structures necessitate the development of dynamic models. However, existing dynamic modeling methods for origami structures are often cumbersome, and the resulting dynamic models often lack interpretability. To overcome these limitations, we propose a novel data-driven dynamic modeling approach based on B-spline Galerkin method and subset selection strategy. This approach directly captures the dynamics of multi-stable origami structures using measured data, eliminating the need for reliance on empirical or prior knowledge. To validate the effectiveness of the proposed approach, we first evaluate it on the Duffing system, which has explicit expressions, successfully reconstructing the governing equation. Subsequently, we apply this method to the dynamic modeling of the origami ball structure with tri-stability and the multi-cell stacked Miura-origami (SMO) structure with high dimensionality through simulation, showing favorable results. Finally, using experimental data collected from a bi-stable SMO structure prototype, we employ the proposed method to obtain a global model that can accurately predict different dynamic behaviors over a broad range of excitation frequencies, including intra-well periodic vibrations, inter-well periodic vibrations, and inter-well chaotic vibrations. Overall, our method showcases outstanding efficacy in formulating interpretable, manageable, and comprehensive dynamic models. It plays a pivotal role in delving into the intricate dynamics of multi-stable origami structures. [ABSTRACT FROM AUTHOR]

Origami structures with reconfigurable mechanical properties are increasingly in demand in engineering applications. The Square-Twist (S-T) origami, featured with excellent reconfigurability and torsional bistability, has a broad application prospect. However, there are relatively few reports on the abundant mechanical properties of S-T origami, especially for those uncommon configurations. In this paper, to analyze the kinematics and mechanics of the unfolding motion, an equivalent theoretical model of the S-T origami is established, which could effectively solve the challenging issues of facet bending, self-contact, and diverse loading directions. With systematic finite element analyses and experimental tests of the S-T origami structures, the effectiveness of the theoretical model along with the optimization-based numerical approach is verified. During the unfolding process, significant distinctions in the potential energy profile and the force–displacement relations among the four different configurations of the S-T origami structure are uncovered. The effects of the design geometry and the material property on the constitutive relations of the S-T origami structure are comprehensively elucidated. Finally, we demonstrate that through folding reconfiguration, an S-T origami structure could exhibit five types of force–displacement relation that are qualitatively different, including bi-stable and mono-stable profiles. [ABSTRACT FROM AUTHOR]