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When a soft mechanical metamaterial, consisting of a regular array of representative volume elements (RVEs), is stressed up to a large strain, the delicately tailored behavior of the RVE does not prevail in the metamaterial due to the boundary effect and manufacturing imperfections. A metamaterial sheet comprising RVEs designed for snapping-back behavior exhibits random snapping-through instability when uniaxially stretched. We conceptualize that loss of representativeness of RVE can be avoided by introducing fiber reinforcement to regulate boundary conditions. Through a combination of experiments and numerical simulation, we demonstrate that fiber reinforcements tune behavior of a metamaterial sheet from random snapping-through to sequential and even selective snapping-back instability by introducing small structural variations. Ideal snapping-back instability, characterized by sharp variations of forces in both loading and unloading processes, is captured, while the latter is typically hard to observe in real experiments. Enhanced energy dissipation rate from 25.3% for the case without fiber to 46.4% for the case with fiber-reinforcement is recorded in experiments, when the metamaterial sheet is stretched up to 200% and then released to restore its original length. [ABSTRACT FROM AUTHOR]

Bandgaps are intrinsic physical properties of periodic structures, for example, mechanical metamaterials or phononic crystals, which indicate attenuation of wave propagation within a specific frequency range. Bandgap calculation of mechanical metamaterials is realized via discretizing a representative voluame element (RVE) and imposing complex-valued Bloch wave boundary conditions. It is highly desirable to implement Bloch wave analysis in real-valued commercial finite element software. We present and detail an ABAQUS and Python implementation of Bloch wave analysis. Two-dimensional (2D) soft as well three-dimensional (3D) hard mechanical metamaterials are chosen as numerical examples. Material and geometric nonlinearities are tackled properly and the effects of pre-strains are explored. Our numerical results are validated either by similar results reported in the literature or by our experimental measurement. The presented numerical strategy would aid the design, analysis and utilization of mechanical metamaterials for dynamic applications. The codes and data of the paper could be downloaded from https://github.com/XJTU-Zhou-group/Calculating-band-gaps-of-nonlinear-mechanical-metamaterials. [ABSTRACT FROM AUTHOR]

Soft mechanical metamaterials with hinge-like elements can undergo multi-step reconfiguration through folding and contacts, and thus exhibit highly nonlinear responses. Numerical simulation of the nonlinear behaviors is essential for the design and control of the mechanical metamaterials, but it remains a challenge due to complicated nonlinear effects. Here, we report the finite element modeling of multi-step reconfiguration of a shape-changing metamaterial, and elucidate the underlying mechanism of soft elasticity. The predicted stress–strain curve together with the folding angles of hinge elements shows excellent agreement with experimental data reported in the literature. Moreover, we explore the influence of reconfiguration and folding-induced internal stress on the bandgap distribution of the mechanical metamaterials. Our efforts provide useful guidelines for the design and application of mechanical metamaterials for both static and dynamic situations. [ABSTRACT FROM AUTHOR]

We combine experiment and finite element simulation and come up with a design for a mechanical metamaterial which demonstrates snap-back induced hysteresis and energy dissipation. The resultant is an elastic system that can be used reversibly for many times. The underlying mechanism of the existence of hysteresis and the physics of snap-back induced elastic instability is unveiled. Our results open an avenue for the design and implementation of recoverable energy dissipation devices by harnessing mechanical instability. [ABSTRACT FROM AUTHOR]

Mechanical metamaterials have attracted tremendous interests, owing to their fruitfulness of underlying physics and mechanics as well as diverse potential applications. Conventional soft mechanical metamaterials contain periodic distribution of holes having identical sizes, which can only display one mechanical function. Periodically dispersing a regular pattern of through-holes with two sizes into an elastomer results in metamaterials with more mechanical functions and deformation scenarios. We numerically investigate the deformation behaviors of this type of metamaterials. Switching of modes from the buckling-dominated deformation to a loss-of-instability deformation is emphasized. Replacing the pattern of holes with the same sizes by a pattern of holes with two sizes imposes higher compliance and even loss of negative Poisson’s ratio of the material. [ABSTRACT FROM AUTHOR]