This paper describes two folded metamaterials based on the Miura-ori fold pattern. The structural mechanics of these metamaterials are dominated by the kinematics of the folding, which only depends on the geometry and therefore is scale-independent. First, a folded shell structure is introduced, where the fold pattern provides a negative Poisson's ratio for in-plane deformations and a positive Poisson's ratio for out-of-plane bending. Second, a cellular metamaterial is described based on a stacking of individual folded layers, where the folding kinematics are compatible between layers. Additional freedom in the design of the metamaterial can be achieved by varying the fold pattern within each layer.I n this paper, we describe the use of origami for mechanical metamaterials, where the fold patterns introduce kinematic deformation modes that dominate the overall structural response. The geometry and kinematics of two types of folded metamaterial are described: a folded shell structure and a folded cellular metamaterial. The examples presented here are both based on a particular fold geometry: the classic Miura-ori pattern. This pattern has previously been considered for applications, such as deployable solar panels (1), and was observed in the biaxial compression of stiff thin membranes on a soft elastic substrate (2, 3).In recent years, origami has seen a surge in research interest from engineers and physicists. Developments include folded sandwich panel cores (4, 5), origami-inspired stents (6), selffolding membranes (7), and cellular materials made from folded cylinders (8). An important concept is rigid origami, where the fold pattern is modeled as rigid panels connected through frictionless hinges. These assumptions make the study of origami folding a matter of kinematics. Of particular interest here are fold patterns where four fold lines meet at each vertex (so-called degree-4 vertices). Each such vertex has one degree of freedom, a tessellated fold pattern is overconstrained, and folding is only possible under strict geometric conditions. In a landmark paper, Huffman (9) studied rigid folding using spherical geometry; recent work includes the modeling of crease patterns using quaternions (10) and an increased understanding of the foldability conditions for partly folded quadrilateral surfaces (11,12).In describing the properties of the folded metamaterials, we are here primarily concerned with the deformation kinematics. If required, these models can straightforwardly be extended to include simple constitutive behavior at the fold lines [for instance, elastic (13) or plastic (14) behavior].The paper is structured as follows. First, the Miura-ori unit cell is introduced, because its geometry plays a key role in the mechanical properties of the folded metamaterials. The first such metamaterial is based on a single planar Miura-ori sheet: a folded shell structure. Of particular interest are the shell's outof-plane kinematics. Second, a bulk metamaterial is proposed based on the stacking of individual Miura-or...

Powering electronics without depending on batteries is an open research field. Mechanical vibrations prove to be a reliable energy source, but low-frequency broadband vibrations cannot be harvested effectively using linear oscillators. This article discusses an alternative for harvesting such vibrations, with energy harvesters with two stable configurations. The challenges related to nonlinear dynamics are briefly discussed. Different existing designs of bistable energy harvesters are presented and classified, according to their feasibility for miniaturization. A general dynamic model for those designs is described. Finally, an extensive discussion on quantitative measures of evaluating the effectiveness of energy harvesters is accomplished, resulting in the proposition of a new dimensionless metric suited for a broadband analysis.

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Tension members with a zero rest length allow the construction of tensegrity structures that are in equilibrium along a continuous path of configurations, and thus exhibit mechanism-like properties; equivalently, they have zero stiffness. The zero-stiffness modes are not internal mechanisms, as they involve first-order changes in member length, but are a direct result of the use of the special tension members. These modes correspond to an infinitesimal affine transformation of the structure that preserves the length of conventional members, they hold over finite displacements and are present if and only if the directional vectors of those members lie on a projective conic. This geometric interpretation provides several interesting observations regarding zero stiffness tensegrity structures.

Zero-stiffness structures have the remarkable ability to undergo large elastic deformations without requiring external work. Several equivalent descriptions exist, such as (i) continuous equilibrium, (ii) constant potential energy, (iii) neutral stability and (iv) zero stiffness. Each perspective on zero stiffness provides different methods of analysis and design. This paper reviews the concept of zero stiffness and categorises examples from the literature by the interpretation that best describes their working principle. Lastly, a basic spring-to-spring balancer is analysed to demonstrate the equivalence of the four different interpretations, and illustrate the different insights that each approach brings.

a b s t r a c tRecent research has established the effectiveness of sandwich structures with metallic cellular cores for blast mitigation. The choice of core architecture can enhance sandwich performance, dissipating energy through plastic core compression and exploiting fluid-structure interaction effects to reduce the momentum imparted to the structure by the blast. In this paper we describe the first analysis of a novel sandwich core concept for blast mitigation: the stacked folded core. The core consists of an alternating stacked sequence of folded sheets in the Miura (double-corrugated) pattern, with the stack oriented such that the folding kinematics define the out-of plane compressive strength of the core. It offers a number of distinct characteristics compared to existing cellular cores. (i) The kinematics of collapse of the core by a distinctive folding mechanism give it unique mechanical properties, including strong anisotropy. (ii) The fold pattern and stacking arrangement is extremely versatile, offering exceptional freedom to tailor the mechanical properties of the core. This includes freedom to grade the core properties through progressive changes in the fold pattern. (iii) Continuous manufacturing processes have been established for the Miura folded sheets which make up the core. The design is therefore potentially more straightforward and economical to manufacture than other metallic cellular materials. In this first investigation of the stacked folded core, finite element analysis is used to investigate its characteristics under both quasistatic and dynamic loading. A dynamic analysis of an impulsively loaded sandwich beam with a stacked folded core reveals the versatility of the concept for blast mitigation. By altering the fold pattern alone, the durations of key phases of the dynamic sandwich response (core compression, beam bending) can be controlled. By altering both fold pattern and sheet thickness in the core, the same is achieved without altering the density of the core or the mass distribution of the sandwich beam.

Generally, adjustment of gravity equilibrators to a new payload requires energy, e.g., to increase the preload of the balancing spring. A novel way of energy-free adjustment of gravity equilibrators is possible by introducing the concept of a storage spring. The storage spring supplies or stores the energy necessary to adjust the balancer spring of the gravity equilibrator. In essence, the storage spring mechanism maintains a constant potential energy within the spring mechanism; energy is exchanged between the storage and the balancer spring when needed. Various conceptual designs using both zero-free-length springs and regular extension springs are proposed. Two models were manufactured demonstrating the practical embodiments and functionality.