Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences最新文献

With a focus on a class of origami-inspired metamaterials, this work explores the role of panel confinement in their mechanical response under cyclic loading. The goal is twofold: (i) quantify the magnitude change in snapping force and energy dissipation attained by varying the severity of confinement of selected panels; and (ii) leverage insights to modulate in situ their mechanical response as dictated by a given application, hence propose panel confinement modulation as a practical design route for response reprogrammability. Through computational modelling, proof-of-concept fabrication and cyclic testing, we first identify and characterize the governing factors enabling either the alteration or the preservation of the snapping force magnitude during repeated cycles of forward and backward loading. Then, we demonstrate how the in situ modulation of the constrained distance between selected panels enables reprogramming their snapping sequence and energy dissipation. The results contribute to expanding the versatility and application of this class of origami metamaterial across sectors, from aerospace to protective equipment, requiring precise control of mechanical damping and energy dissipation.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Yoshimura origami is a classical folding pattern that has inspired many deployable structure designs. Its applications span from space exploration, kinetic architectures and soft robots to even everyday household items. However, despite its wide usage, Yoshimura has been fixated on a set of design constraints to ensure its flat foldability. Through extensive kinematic analysis and prototype tests, this study presents a new Yoshimura that intentionally defies these constraints. Remarkably, one can impart a unique meta-stability by using the Golden Ratio angle ([Formula: see text]) to define the triangular facets of a generalized Yoshimura (with [Formula: see text], where [Formula: see text] is the number of rhombi shapes along its cylindrical circumference). As a result, when its facets are strategically popped out, a 'Golden Ratio Yoshimura' boom with [Formula: see text] modules can be theoretically reconfigured into [Formula: see text] geometrically unique and load-bearing shapes. This result not only challenges the existing design norms but also opens up a new avenue to create deployable and versatile structural systems.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Metamaterial design approaches, which integrate structural elements into material systems, enable the control of uncommon behaviours by decoupling local and global properties. Leveraging this conceptual framework, metamaterial adhesives incorporate nonlinear cut architectures into adhesive films to achieve unique combinations of adhesion capacity, release, and spatial tunability by controlling how cracks propagate forward and in reverse directions during separation. Here, metamaterial adhesive designs are explored with triangular cut features while integrating hierarchical and secondary cut patterns among primary nonlinear cuts. Both cut geometry and secondary cut features tune adhesive force capacity and energy of separation. Importantly, the size and spacing of cut features must be designed around a critical length scale. When secondary cut features are greater than a critical length, cracks can be steered in multiple directions, going both forward and backwards within a primary attachment element. This control over crack dynamics enhances the work of separation by a factor of 1.5, while maintaining the peel force relative to a primary cut. If hierarchical cut features are too small or too compliant, they interact and do not distinctly modify crack behaviour. This work highlights the importance of adhesive length scales and stiffness for crack control and attachment characteristics in adhesive films.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Origami folding structures are vital in shaping programmable mechanical material properties. Of particular note, tunable dynamical properties of elastic wave propagation in origami structures have been reported. Despite the promising features of origami metamaterials, the influence of the kinematics of tessellated origami structures on elastic wave propagation remain unexplored. This study proposes elastic metamaterials using connected Miura-ori tubes, the kinematics of which are coupled by folding and unfolding motions in a tubular axis; achieved by periodically connecting non-rotated and rotated Miura-ori tubes. The kinematics generate wave modes with localized deformations within the unit cell of the metamaterials, affecting the global elastic deformation of Miura-ori tubes via the coupling of wave modes. Dispersion analysis, using the generalized Bloch wave framework based on bar-and-hinge models, verifies the influence of kinematics in the connected tubes on elastic wave propagation. Furthermore, folding the connected tubes changes the coupling strength of wave modes between the kinematics and global elastic deformation of the tubes by breaking the ideal kinematics. The coupling of wave modescontributes to the formation of the band gaps and their tunability. These findings enable adaptive and in situ tunability of band structures to prohibit elastic waves in the desired frequency ranges.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Origami-inspired mechanisms provide opportunities for deployable systems, including reflectarray antennas. There is a need for approaches to deploy and stabilize such arrays. Magnetic mechanisms show promise for meeting those needs and how methods for modelling their behaviour would facilitate their design and analysis. We demonstrate the existence of bistability in select configurations of magnetically stabilized hinges and characterize their equilibrium positions as a function of parameters estimated from simulation data for these mechanisms. Other relevant information such as potential energy, axial force data, angular position of unstable equilibria and transition values from bistability to monostability are also modelled. The results are verified through experimental torque and stability data for selected configurations of the mechanisms.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

A periodic surface is one that is invariant by a two-dimensional lattice of translations. Deformation modes that stretch the lattice without stretching the surface are effective membrane modes. Deformation modes that bend the lattice without stretching the surface are effective bending modes. For periodic piecewise smooth simply connected surfaces, it is shown that the effective membrane modes are, in a sense, orthogonal to effective bending modes. This means that if a surface gains a membrane mode, it loses a bending mode, and conversely, in such a way that the total number of modes, membrane and bending combined, can never exceed 3. Various examples, inspired from curved-crease origami tessellations, illustrate the results.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Origami metamaterials have gained significant attention in recent years, with extensive analysis conducted on their mechanical properties. Previous studies have primarily focused on the effects of design angles, panel side lengths, folding angles or other geometric and material parameters. However, mountain-valley crease assignments of origami patterns, which significantly effect both the geometric and mechanical properties, have yet to be studied in depth. In this article, we create a series of double-corrugated metamaterials with diverse mountain-valley assignments and analyse their Poisson's ratios and mechanical properties under compression loading. The findings of our study demonstrate that varying the mountain-valley assignments allows for the construction of metamaterials with consistent or distinct Poisson's ratios. These assignments have the capability to program the magnitude and to vary the rate of the folding angles. Furthermore, the mechanical properties of the corresponding metamaterials, in particular the specific energy absorption (SEA) and normalized stiffness, exhibit positive correlations with the respective folding angles. Our study highlights the significance of varying mountain-valley assignments as a promising approach for designing origami metamaterials and programming their mechanical properties.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

With its compactness and foldability, origami has recently been applied to robotic systems to enable versatile robots and mechanisms while maintaining a low weight and compact form. This work investigates how to generate different motions and shapes for origami by tuning its creases' stiffness on the fly. The stiffness tuning is realized by a composite material made by sandwiching a thermoplastic layer between two shape memory polymer layers. This enables the composite to act as a living hinge, whose stiffness can be actively controlled through Joule heating. To demonstrate our concept, we fabricate an origami module with four variable stiffness joints (VSJs), allowing it to have freely controlled crease stiffnesses across its surface. We characterize the origami module's versatile motion when heating different VSJs with different temperatures. We further use two origami modules to build a two-legged robot that can locomote on the ground with different locomotion gaits. The same robot is also used as an adaptive gripper for grasping tasks. Our work can potentially enable more versatile robotic systems made from origami as well as other mechanical systems with programmable properties (e.g. mechanical metamaterials).This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

The use of origami in engineering has significantly expanded in recent years, spanning deployable structures across scales, folding robotics and mechanical metamaterials. However, finding foldable paths can be a formidable task as the kinematics are determined by a nonlinear system of equations, often with several degrees of freedom. In this article, we leverage a Lagrangian approach to derive reduced-order compatibility conditions for rigid-facet origami vertices with reflection and rotational symmetries. Then, using the reduced-order conditions, we derive exact, multi-degree of freedom solutions for degree 6 and degree 8 vertices with prescribed symmetries. The exact kinematic solutions allow us to efficiently investigate the topology of allowable kinematics, including the consideration of a self-contact constraint, and then visually interpret the role of geometric design parameters on these admissible fold paths by monitoring the change in the kinematic topology. We then introduce a procedure to construct lower-symmetry kinematic solutions by breaking symmetry of higher-order kinematic solutions in a systematic way that preserves compatibility. The multi-degree of freedom solutions discovered here should assist with building intuition of the kinematic feasibility of higher-degree origami vertices and also facilitate the development of new algorithmic procedures for origami-engineering design.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

The present research focuses on a continuum description of stratified metamaterials achieved through the superposition of layers with alternating chirality. Each layer is constructed as a periodic assembly of centre-symmetric periodic cells, formed by a recurring arrangement of rigid circular discs connected by elastic ligaments. The layers are interconnected through elastic pins passing through the centres of aligned discs, allowing for either restrained or free relative rotation. A micropolar continuum model is used to describe each individual layer. The overall response of the metamaterials to in-plane forces is derived using a multi-field non-local model, expressed in terms of the average and difference of displacement and rotational fields. The overall micropolar and standard (Cauchy) constitutive tensors have been determined in closed form. The validity of the equivalent generalized micropolar model has been confirmed through comparison with discrete Lagrangian solutions of representative examples. In addition, a detailed analysis of a pseudo-indentation test has been carried out. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.