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Most conventional materials expand in transverse directions when they are compressed uniaxially resulting in the familiar positive Poisson’s ratio. Here we develop a new class of two dimensional (2D) metamaterials with negative Poisson’s ratio that contract in transverse directions under uniaxial compressive loads leading to auxeticity. This is achieved through mechanical instabilities (i.e., buckling) introduced by structural hierarchy and retained over a wide range of applied compression. This unusual behavior is demonstrated experimentally and analyzed computationally. The work provides new insights into the role of structural organization and hierarchy in designing 2D auxetic metamaterials, and new opportunities for developing energy absorbing materials, tunable membrane filters, and acoustic dampeners.

We present a novel cellular metamaterial constructed from Origami building blocks based on Miura-ori fold. The proposed cellular metamaterial exhibits unusual properties some of which stemming from the inherent properties of its Origami building blocks, and others manifesting due to its unique geometrical construction and architecture. These properties include foldability with two fully-folded configurations, auxeticity (i.e., negative Poisson’s ratio), bistability, and self-locking of Origami building blocks to construct load-bearing cellular metamaterials. The kinematics and force response of the cellular metamaterial during folding were studied to investigate the underlying mechanisms resulting in its unique properties using analytical modeling and experiments.

An approach to obtain analytical closed-form expressions for the macroscopic ‘buckling strength’ of various two-dimensional cellular structures is presented. The method is based on classical beam-column end-moment behaviour expressed in a matrix form. It is applied to sample honeycombs with square, triangular and hexagonal unit cells to determine their buckling strength under a general macroscopic in-plane stress state. The results were verified using finite-element Eigenvalue analysis.

We highlight the effect of structural hierarchy and deformation on band structure and wave-propagation behavior of two-dimensional phononic crystals. Our results show that the topological hierarchical architecture and instability-induced pattern transformations of the structure under compression can be effectively used to tune the band gaps and directionality of phononic crystals. The work provides insights into the role of structural organization and hierarchy in regulating the dynamic behavior of phononic crystals, and opportunities for developing tunable phononic devices.

This article provides a comprehensive review of recent research efforts on the development and characterization of sandwich structures with corrugated, honeycomb, and foam cores. The topics discussed in this review article include aspects of core-face bonding and reinforcement, enhancement of core mechanical properties and panel performance (including the role of structural hierarchy), and multifunctional advantages offered by different core constructions. In addition, the review discusses potential applications, including in morphing wing design, impact resistance, and ultralightweight applications. Future research directions are discussed.

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We introduce a novel concept for the design of programmable-elasticity metamaterials; materials whose elastic properties can be modified instantaneously and reversibly on demand. Real-time tunable linear and nonlinear elastic moduli are obtained in lattice materials by adjustment of strut connectivity via actuation of embedded electromagnetic locks. The Young's modulus and Poisson's ratio of prototype 2D materials are varied instantaneously by more than 2 orders of magnitude and between 0.15 and 0.9, respectively. The buckling strength of the structure is altered by an order of magnitude between two bifurcation states associated with a centrosymmetric and an anti-chiral buckling pattern.