Theoretical search for heterogeneously architected 2D structures

Design Criteria for Architected Materials with Programmable Mechanical Properties Within Theoretical Limit Ranges

Architected materials comprising periodic arrangements of cells have attracted considerable interest in various fields because of their unconventional properties and versatile functionality. Although some better properties may be exhibited when this homogeneous layout is broken, most such studies rely on a fixed material geometry, which limits the design space for material properties. Here, combining heterogeneous and homogeneous assembly of cells to generate tunable geometries, a hierarchically architected material (HAM) capable of significantly enhancing mechanical properties is proposed. Guided by the theoretical model and 745 752 simulation cases, generic design criteria are introduced, including dual screening for unique mechanical properties and careful assembly of specific spatial layouts, to identify the geometry of materials with extreme properties. Such criteria facilitate the potential for unprecedented properties such as Young's modulus at the theoretical limit and tunable positive and negative Poisson's ratios in an ultra-large range. Therefore, this study opens a new paradigm for materials with extreme mechanical properties.

Unexpected bending behavior of architected 2D lattice materials

Architected two-dimensional (2D) lattice materials consisting of elastic beams are appealing because of their tunable sign of Poisson's ratio. A common belief is that such materials with positive and negative Poisson's ratios display anticlastic and synclastic curvatures, respectively, when bent in one direction. Here, we show theoretically and demonstrate experimentally that this is not true. For 2D lattices with star-shaped unit cells, we find a transition between anticlastic and synclastic bending curvatures controlled by the beam's cross-sectional aspect ratio even at a fixed Poisson's ratio. The mechanisms lay in the competitive interaction between axial torsion and out-of-plane bending of the beams and can be well captured by a Cosserat continuum model. Our result may provide unprecedented insights to the design of 2D lattice systems for shape-shifting applications.

Bounded Wang tilings with integer programming and graph-based heuristics

Wang tiles enable efficient pattern compression while avoiding the periodicity in tile distribution via programmable matching rules. However, most research in Wang tilings has considered tiling the infinite plane. Motivated by emerging applications in materials engineering, we consider the bounded version of the tiling problem and offer four integer programming formulations to construct valid or nearly-valid Wang tilings: a decision, maximum-rectangular tiling, maximum cover, and maximum adjacency constraint satisfaction formulations. To facilitate a finer control over the resulting tilings, we extend these programs with tile-based, color-based, packing, and variable-sized periodic constraints. Furthermore, we introduce an efficient heuristic algorithm for the maximum-cover variant based on the shortest path search in directed acyclic graphs and derive simple modifications to provide a 1/2 approximation guarantee for arbitrary tile sets, and a 2/3 guarantee for tile sets with cyclic transducers. Finally, we benchmark the performance of the integer programming formulations and of the heuristic algorithms showing that the heuristics provide very competitive outputs in a fraction of time. As a by-product, we reveal errors in two well-known aperiodic tile sets: the Knuth tile set contains a tile unusable in two-way infinite tilings, and the Lagae corner tile set is not aperiodic.

Designing Hierarchical Soft Network Materials with Developable Lattice Nodes for High Stretchability

Soft network materials (SNMs) represent one of the best candidates for the substrates and the encapsulation layers of stretchable inorganic electronics, because they are capable of precisely customizing the J-shaped stress-strain curves of biological tissues. Although a variety of microstructures and topologies have been exploited to adjust the nonlinear stress-strain responses of SNMs, the stretchability of most SNMs is hard to exceed 100%. Designing novel high-strength SNMs with much larger stretchability (e.g., >200%) than existing SNMs and conventional elastomers remains a challenge. This paper develops a class of hierarchical soft network materials (HSNMs) with developable lattice nodes, which can significantly improve the stretchability of SNMs without any loss of strength. The effects of geometric parameters, lattice topologies, and loading directions on the mechanical properties of HSNMs are systematically discussed by experiments and numerical simulations. The proposed node design strategy for SNMs is also proved to be widely applicable to different constituent materials, including polymers and metals.

Hierarchical mechanical metamaterials built with scalable tristable elements for ternary logic operation and amplitude modulation

Multistable mechanical metamaterials are artificial materials whose microarchitectures offer more than two different stable configurations. Existing multistable mechanical metamaterials mainly rely on origami/kirigami-inspired designs, snap-through instability, and microstructured soft mechanisms, with mostly bistable fundamental unit cells. Scalable, tristable structural elements that can be built up to form mechanical metamaterials with an extremely large number of programmable stable configurations remains illusive. Here, we harness the elastic tensile/compressive asymmetry of kirigami microstructures to design a class of scalable X-shaped tristable structures. Using these structure as building block elements, hierarchical mechanical metamaterials with one-dimensional (1D) cylindrical geometries, 2D square lattices, and 3D cubic/octahedral lattices are designed and demonstrated, with capabilities of torsional multistability or independent controlled multidirectional multistability. The number of stable states increases exponentially with the cell number of mechanical metamaterials. The versatile multistability and structural diversity allow demonstrative applications in mechanical ternary logic operators and amplitude modulators with unusual functionalities.

Automatic design of mechanical metamaterial actuators

Mechanical metamaterial actuators achieve pre-determined input–output operations exploiting architectural features encoded within a single 3D printed element, thus removing the need for assembling different structural components. Despite the rapid progress in the field, there is still a need for efficient strategies to optimize metamaterial design for a variety of functions. We present a computational method for the automatic design of mechanical metamaterial actuators that combines a reinforced Monte Carlo method with discrete element simulations. 3D printing of selected mechanical metamaterial actuators shows that the machine-generated structures can reach high efficiency, exceeding human-designed structures. We also show that it is possible to design efficient actuators by training a deep neural network which is then able to predict the efficiency from the image of a structure and to identify its functional regions. The elementary actuators devised here can be combined to produce metamaterial machines of arbitrary complexity for countless engineering applications.

Efficient strategies to optimize metamaterial design for specific applications are urgently needed despite the rapid progress in this area. Here the authors propose a computational method combining an optimization algorithm with discrete element simulations for the automatic design of mechanical metamaterial actuators.

Soft three-dimensional network materials with rational bio-mimetic designs

Many biological tissues offer J-shaped stress–strain responses, since their microstructures exhibit a three-dimensional (3D) network construction of curvy filamentary structures that lead to a bending-to-stretching transition of the deformation mode under an external tension. The development of artificial 3D soft materials and device systems that can reproduce the nonlinear, anisotropic mechanical properties of biological tissues remains challenging. Here we report a class of soft 3D network materials that can offer defect-insensitive, nonlinear mechanical responses closely matched with those of biological tissues. This material system exploits a lattice configuration with different 3D topologies, where 3D helical microstructures that connect the lattice nodes serve as building blocks of the network. By tailoring geometries of helical microstructures or lattice topologies, a wide range of desired anisotropic J-shaped stress–strain curves can be achieved. Demonstrative applications of the developed conducting 3D network materials with bio-mimetic mechanical properties suggest potential uses in flexible bio-integrated devices.

The development of artificial 3D soft materials and device systems that can reproduce the nonlinear, anisotropic mechanical properties of biological tissues remains challenging. Here, the authors design a class of soft 3D network materials that can offer defect-insensitive, nonlinear mechanical responses closely matched with those of biological tissues.

Toward Imperfection-Insensitive Soft Network Materials for Applications in Stretchable Electronics

Development of stretchable devices with mechanical responses that mimic those of biological tissues/organs is of particular importance for the long-term biointegration, as the discomfort induced by the mechanical mismatch can be minimized. Recent works have established the bioinspired designs of soft network materials that can precisely reproduce the unconventional J-shaped stress-strain curves of human skin at different regions. Existing studies mostly focused on the design, fabrication, and modeling of perfect soft network materials. When utilized as the substrates of biointegrated electronics, the soft network designs, however, often need to incorporate deterministic holes, a type of imperfection, to accommodate hard, inorganic electronic components. Understanding of the effect of hole imperfections on the mechanical properties of soft network materials is thereby essential in practical applications. This paper presents a combined experimental and computational study of the stretchability and elastic modulus of imperfect soft network materials consisting of circular holes with a variety of diameters. Both the size and location of the circular-hole imperfections are shown to have profound influences on the stretchability. Based on these results, design guidelines of imperfection-insensitive network materials are introduced. For the imperfections that result in an evident reduction of stretchability, an effective reinforcement approach is presented by enlarging the width of horseshoe microstructures at strategic locations, which can enhance the stretchability considerably. A stretchable and imperfection-insensitive integrated device with a light-emitting diode embedded in the network material serves a demonstrative application.

Mechanical anisotropy of two-dimensional metamaterials: a computational study

Metamaterials, rationally designed multiscale composite systems, have attracted extensive interest because of their potential for a broad range of applications due to their unique properties such as negative Poisson's ratio, exceptional mechanical performance, tunable photonic and phononic properties, structural reconfiguration, etc. Though they are dominated by an auxetic structure, the constituents of metamaterials also play an indispensable role in determining their unprecedented properties. In this vein, 2D materials such as graphene, silicene, and phosphorene with superior structural tunability are ideal candidates for constituents of metamaterials. However, the nanostructure-property relationship and composition-property relationship of these 2D material-based metamaterials remain largely unexplored. Mechanical anisotropy inherited from the 2D material constituents, for example, may substantially impact the physical stability and robustness of the corresponding metamaterial systems. Herein, classical molecular dynamics simulations are performed using a generic coarse-grained model to explore the deformation mechanism of these 2D material-based metamaterials with sinusoidally curved ligaments and the effect of mechanical anisotropy on mechanical properties, especially the negative Poisson's ratio. The results indicate that deformation under axial tensile load can be divided into two stages: bending-dominated and stretching-dominated, in which the rotation of junctions in the former stage results in auxetic behavior of the proposed metamaterials. In addition, the auxetic behavior depends heavily on both the amplitude/wavelength ratio of the sinusoidal ligament and the stiffness ratio between axial and transverse directions. The magnitude of negative Poisson's ratio increases from 0 to 0.625, with an associated increase of the amplitude/wavelength ratio from 0 to 0.225, and fluctuates at around 0.625, in good agreement with the literature, with amplitude/wavelength ratios greater than 0.225. More interestingly, the magnitude of negative Poisson's ratio increases from 0.47 to 0.87 with the increase of the stiffness ratio from 0.125 to 8, in good agreement with additional all-atom molecular dynamics simulations for phosphorene and molybdenum disulfide. Overall, these research findings shed light on the deformation mechanism of auxetic metamaterials, providing useful guidelines for designing auxetic 2D lattice structures made of 2D materials that can display a tunable negative Poisson's ratio.

Multilayer Polypyrrole Nanosheets with Self-Organized Surface Structures for Flexible and Efficient Solar-Thermal Energy Conversion

Converting solar energy into concentrated heat is very appealing for various applications. Polypyrrole (PPy) is known to possess excellent photothermal property with low thermal conductivity, and thus is an ideal candidate for solar-thermal energy conversion. However, solar-thermal materials based on PPy or other conducting polymers still exhibit limited energy conversion efficiency due to the lack of effective light-trapping schemes. Here, it is demonstrated that multilayer PPy nanosheets with spontaneously formed surface structures such as wrinkles and ridges via sequential polymerization on paper substrates can dramatically enhance broadband and wide-angle light absorption across the full solar spectrum, leading to an impressive solar-thermal conversion efficiency of 95.33%. The intriguing solar-thermal properties and structural features of multilayer PPy nanosheets can be used for solar heating and photoactuators. Meanwhile, when used for solar steam generation, the measured efficiency could achieve ≈92% under one sun irradiation. The hierarchically multilayer structure is mechanically flexible and robust, holding great potential for practical solar energy utilization. This study provides a simple and straightforward approach toward engineering light-weight and thermally insulating polymers into efficient solar-thermal materials for emerging solar energy-related applications.