Up until recently, the rational design of mechanical metamaterials has usually involved devising geometrical arrangements of micro-architectures that deliver unusual properties on the macro-scale. A less explored route to rational design is spatially distributing materials with different properties within lattice structures to achieve the desired mechanical properties. Here, we used computational models and advanced multi-material 3D printing techniques to rationally design and additively manufacture multi-material cellular solids for which the elastic modulus and Poisson's ratio could be independently tailored in different (anisotropic) directions. The random assignment of a hard phase to originally soft cellular structures with an auxetic, zero Poisson's ratio, and conventional designs allowed us to cover broad regions of the elastic modulus-Poisson's ratio plane. Patterned designs of the hard phase were also used and were found to be effective in the independent tuning of the elastic properties. Close inspection of the strain distributions associated with the different types of material distributions suggests that locally deflected patterns of deformation flow and strain localizations are the main underlying mechanisms driving the above-mentioned adjustments in the mechanical properties.

Mechanical metamaterials are a sub-category of designer materials where the geometry of the material at the small-scale is rationally designed to give rise to unusual properties and functionalities. Here, we propose the concept of "action-at-a-distance" metamaterials where a specific pattern of local deformation is programmed into the fabric of (cellular) materials. The desired pattern of local actuation could then be achieved simply through the application of one single global and far-field force. We proposed graded designs of auxetic and conventional unit cells with changing Poisson's ratios as a way of making "action-at-a-distance" metamaterials. We explored five types of graded designs including linear, two types of radial gradients, checkered, and striped. Specimens were fabricated with indirect additive manufacturing and tested under compression, tension, and shear. Full-field strain maps measured with digital image correlation confirmed different patterns of local actuation under similar far-field strains. These materials have potential applications in soft (wearable) robotics and exosuits.

Architectured materials with rationally designed geometries could be used to create mechanical metamaterials with unprecedented or rare properties and functionalities. Here, we introduce "shape-matching" metamaterials where the geometry of cellular structures comprising auxetic and conventional unit cells is designed so as to achieve a pre-defined shape upon deformation. We used computational models to forward-map the space of planar shapes to the space of geometrical designs. The validity of the underlying computational models was first demonstrated by comparing their predictions with experimental observations on specimens fabricated with indirect additive manufacturing. The forward-maps were then used to devise the geometry of cellular structures that approximate the arbitrary shapes described by random Fourier's series. Finally, we show that the presented metamaterials could match the contours of three real objects including a scapula model, a pumpkin, and a Delft Blue pottery piece. Shape-matching materials have potential applications in soft robotics and wearable (medical) devices.

Crumpled-based materials are relatively easy to fabricate and show robust mechanical properties for practical applications, including meta-biomaterials design aimed for improved tissue regeneration. For such requests, however, the structure needs to be porous. We introduce a crumpled holey thin sheet as a robust bio-metamaterial and measure the mechanical response of a crumpled holey thin Mylar sheet as a function of the hole size and hole area fraction. We also study the formation of patterns of crease lines and ridges. The area fraction largely dominated the crumpling mechanism. We also show, the crumpling exponents slightly increases with increasing the hole area fraction and the total perimeter of the holes. Finally, hole edges were found to limit and guide the propagation of crease lines and ridges.

The elastic properties of mechanical metamaterials are direct functions of their topological designs. Rational design approaches based on computational models could, therefore, be used to devise topological designs that result in the desired properties. It is of particular importance to independently tailor the elastic modulus and Poisson's ratio of metamaterials. Here, we present patterned randomness as a strategy for independent tailoring of both properties. Soft mechanical metamaterials incorporating various types of patterned randomness were fabricated using an indirect additive manufacturing technique and mechanically tested. Computational models were also developed to predict the topology-property relationship in a wide range of proposed topologies. The results of this study show that patterned randomness allows for independent tailoring of the elastic properties and covering a broad area of the elastic modulus-Poisson's ratio plane. The uniform and homogenous topologies constitute the boundaries of the covered area, while topological designs with patterned randomness fill the enclosed area.