We designed and fabricated a simple setup for the controlled crumpling of nanopatterned, surface-porous flat metallic sheets for the fabrication of volume-porous biomaterials and showed that crumpling can be considered as an efficient alternative to origami-inspired folding. Before crumpling, laser cutting was used to introduce pores to the sheets. We then fabricated titanium (Ti) nanopatterns through reactive ion etching on the polished Ti sheets. Thereafter, nanopatterned porous Ti sheets were crumpled at two deformation velocities (i.e., 2 and 100 mm/min). The compression tests of the scaffolds indicated that the elastic modulus of the specimens vary in the range of 11.8–13.9 MPa. Micro-computed tomography scans and computational simulations of crumpled scaffolds were performed to study the morphological properties of the resulting meta-biomaterials. The porosity and pore size of the scaffolds remained within the range of those reported for trabecular bone. Finally, the in vitro cell preosteoblasts culture demonstrated the cytocompatibility of the nanopatterned scaffolds. Moreover, the aspect ratio of the cells residing on the nanopatterned surfaces was found to be significantly higher than those cultured on the control scaffolds, indicating that the nanopatterned surface may have a higher potential for inducing the osteogenic differentiation of the preosteoblasts.

The design of advanced functional devices often requires the use of intrinsically curved geometries that belong to the realm of non-Euclidean geometry and remain a challenge for traditional engineering approaches. Here, it is shown how the simple deflection of thick meta-plates based on hexagonal cellular mesostructures can be used to achieve a wide range of intrinsic (i.e., Gaussian) curvatures, including dome-like and saddle-like shapes. Depending on the unit cell structure, non-auxetic (i.e., positive Poisson ratio) or auxetic (i.e., negative Poisson ratio) plates can be obtained, leading to a negative or positive value of the Gaussian curvature upon bending, respectively. It is found that bending such meta-plates along their longitudinal direction induces a curvature along their transverse direction. Experimentally and numerically, it is shown how the amplitude of this induced curvature is related to the longitudinal bending and the geometry of the meta-plate. The approach proposed here constitutes a general route for the rational design of advanced functional devices with intrinsically curved geometries. To demonstrate the merits of this approach, a scaling relationship is presented, and its validity is demonstrated by applying it to 3D-printed microscale meta-plates. Several applications for adaptive optical devices with adjustable focal length and soft wearable robotics are presented.

Mechanical metamaterials are usually designed to exhibit novel properties and functionalities that are rare or even unprecedented. What is common among most previous designs is the quasi-static nature of their mechanical behavior. Here, we introduce a previously unidentified class of strain rate-dependent mechanical metamaterials. The principal idea is to laterally attach two beams with very different levels of strain rate-dependencies to make them act as a single bi-beam. We use an analytical model and multiple computational models to explore the instability modes of such a bi-beam construct, demonstrating how different combinations of hyperelastic and viscoelastic properties of both beams, as well as purposefully introduced geometric imperfections, could be used to create robust and highly predictable strain rate-dependent behaviors of bi-beams. We then use the bi-beams to design and experimentally realize lattice structures with unique strain rate-dependent properties including switching between auxetic and conventional behaviors and negative viscoelasticity.

Deployable meta-implants aim to minimize the invasiveness of orthopaedic surgeries by allowing for changes in their shape and size that are triggered by an external stimulus. Multi-stability enables deployable implants to transform their shape from some compact retracted state to the deployed state where they take their full sizes and are load-bearing. We combined multiple design features to develop a new generation of deployable orthopaedic implants. Kirigami cut patterns were used to create bi-stability in flat sheets which can be folded into deployable implants using origami techniques. Inspired by Russian dolls, we designed multi-layered specimens that allow for adjusting the mechanical properties and the geometrical features of the implants through the number of the layers. Because all layers are folded from a flat state, surface-related functionalities could be applied to our deployable implants. We fabricated specimens from polylactic acid, titanium sheets, and aluminum sheets, and demonstrated that a deployment ratio of up to ≈2 is possible. We performed experiments to characterize the deployment and load-bearing behavior of the specimens and found that the above-mentioned design variables allow for adjustments in the deployment force and the maximum force before failure. Finally, we demonstrate the possibility of decorating the specimens with micropatterns.

Self-folding of complex origami-inspired structures from flat states allows for the incorporation of a multitude of surface-related functionalities into the final 3D device. Several self-folding techniques have therefore been developed during the last few years to fabricate such multi-functional devices. The vast majority of such approaches are, however, limited to simple folding sequences, specific materials, or large length scales, rendering them inapplicable to microscale (meta)materials and devices with complex geometries, which are often made from materials other than the ones for which these approaches are developed. Here, we propose a mechanical self-folding technique that only requires global stretching for activation, is applicable to a wide range of materials, allows for sequential self-folding of multi-storey constructs, and can be downscaled to microscale dimensions. We combined two types of permanently deforming kirigami elements, working on the basis of either multi-stability or plastic deformation, with an elastic layer to create self-folding basic elements. The folding angles of these elements could be controlled using the kirigami cut patterns as well as the dimensions of the elastic layer and be accurately predicted using our computational models. We then assembled these basic elements in a modular manner to create multiple complex 3D structures (e.g., multi-storey origami lattices) in different sizes including some with microscale feature sizes. Moreover, starting from a flat state enabled us to incorporate not only precisely controlled, arbitrarily complex, and spatially varied micropatterns but also flexible electronics into the self-folded 3D structures. In all cases, our computational models could capture the self-folding behavior of the assemblies and the strains in the connectors of the flexible electronic devices, thereby guiding the rational design of our specimens. This approach has numerous potential applications including fabrication of multi-functional and instrumented implantable medical devices, steerable medical instruments, and microrobots.

Additive manufacturing (AM) has recently been introduced as a reliable technique for the fabrication of highly complex geometries that were not possible before. Due to the flexibility in the organization of material properties such as responsive elements in space, AM is now a capable technology for the production of smart structures that can transform their geometry, for example, from a compact state to a deployed configuration. Among others, fused deposition modeling (FDM) can reliably be used to manufacture polymeric constructs with high resolution. Polylactide (PLA), the most popular polymer in FDM printing is a shape-memory polymer. Therefore, the manufacturing of shape-transforming constructs can be simplified to the construction of foldable products that can be programmed simply by applying mechanical forces. Origami can then be used as a simple platform in which the shape-transforming of a programmed construct is via the folding of material through the thinner sections (hinges). Herein, PLA and FDM are used to fabricate foldable structures. The effects of different parameters namely total thickness, layer height, nozzle temperature, and activation temperature on the shape recovery of the manually programmed origami structures are then investigated.

Buckling, which was once considered the epitome of design failure, has been harnessed during the last few years to develop mechanical metamaterials with advanced functionalities. Soft robotics in general and soft actuators in particular could greatly benefit from such designer materials. Unlocking the great potential of buckling-driven materials is, however, contingent on resolving the main limitation of the designs presented to date, namely the limited range of their programmability. Here, we present multi-material buckling-driven metamaterials with high levels of programmability. We combined rational design approaches based on predictive computational models with advanced multi-material additive manufacturing techniques to 3D print cellular materials with arbitrary distributions of flexible and stiff materials in the central and corner parts of their unit cells. Using the geometry and spatial distribution of material properties as the main design parameters, we developed soft mechanical metamaterials behaving as mechanisms whose actuation force and actuation amplitude could be adjusted both independently and concomitantly within wide ranges. Our designs also resulted in the emergence of a new lowest instability mode, i.e. double-side buckling, in addition to the already known modes of side-buckling and symmetric compaction. Finally, we proposed a general approach to pre-dispose our soft mechanical metamaterials such that they can reliably actuate their higher instability modes without any need for additional boundary conditions or fixtures. To demonstrate this approach, we created a cellular mechanism with a rotational buckling pattern that clones the functionality of mechanical machines. The potential of the presented designs in robotics is then demonstrated by applying them as a force switch, kinematic controllers, and a pick and place end-effector.

From pottery to clay tablets and building materials, clay easily qualifies as one of the most versatile materials in the history of human civilization. Clay owes this versatility to the distinct properties it exhibits before and after firing. Soft, unfired clay can morph into complex shapes, while fired clay offers a fixed shape and higher stiffness. Despite several potential applications, thus far, no designer materials with similar properties have been demonstrated. Here, we introduce the concept of metallic clay: a designer material that mimics the two-state behavior of clay. Metallic clay could initially morph into arbitrarily complex shapes owing to numerous degrees-of-freedom that its various kinematic (moving) and compliant (deformable) joints afford. Once the desired shape is achieved, shape-locking mechanisms (kinematic or compliant) lock the shape of the metallic clay. The fabrication of metallic clay requires novel designs of joints and locking mechanisms that are compatible with metal 3D printing (additive manufacturing) techniques such that metallic clay can be fabricated through a single-step, non-assembly, and self-supporting 3D printing process. We designed with 3D printing 17 prototypes using selective laser melting from a medical grade high strength titanium alloy (Ti-6Al-4V) to demonstrate the various aspects of metallic clay.

crumpled thin sheets exhibit extraordinary characteristics such as a high strength combined with a low volume ratio. This review focuses on the physics of crumpled thin sheets, including the crumpling mechanics, crumpling methods, and the mechanical behavior of crumpled thin sheets. Most of the physical and mechanical properties of crumpled thin sheets change with the compaction ratio, which creates the opportunity to obtain the properties that are needed for a specific application simply by changing the compaction ratio. This also enables obtaining unusual combinations of material properties, which cannot be easily found in nature. Furthermore, crumpling starts from a flat surface, which could first be decorated with (nano-) patterns or functionalized through other surface treatment techniques, many of which are only applicable to flat surfaces. Ultimately, the crumpling of thin sheets could be used for creating disordered mechanical metamaterials, which are less sensitive to geometric imperfections compared to ordered designs of mechanical metamaterials that are based, for example, on origami or lattice structures.

Shape-shifting of flat materials into the desired 3D configuration is an alternative design route for fabrication of complex 3D shapes, which provides many benefits such as access to the flat material surface and the ability to produce well-described motions. The advanced production techniques that primarily work in 2D could then be used to add complex surface features to the flat material. The combination of complex 3D shapes and surface-related functionalities has a wide range of applications in biotechnology, actuators/sensors, and engineering of complex metamaterials. Here, we categorize the different programming strategies that could be used for planning the shape-shifting of soft matter based on the type of stresses generated inside the flat material and present an overview of the ways those mechanisms could be used to achieve the desired 3D shapes. Stress gradients through the thickness of the material, which generate out-of-plane bending moments, and compressive in-plane stresses that result in out-of-plane buckling constitute the major mechanisms through which shape-shifting of the flat matter could be programmed. We review both programming strategies with a focus on the underlying physical principles, which are highly scalable and could be applied to other structures and materials. The techniques used for programming the time sequence of shape-shifting are discussed as well. Such types of so-called “sequential” shape-shifting enable achieving more complex 3D shapes, as the kinematics of the movements could be planned in time to avoid collisions. Ultimately, we discuss what 3D shapes could be achieved through shape-shifting from flat soft matter and identify multiple areas of application.

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.

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.

Meta-biomaterials exhibit unprecedented or rare combinations of properties not usually found in nature. Such unusual mechanical, mass transport, and biological properties could be used to develop novel categories of orthopedic implants with superior performance, otherwise known as meta-implants. Here, we use bi-stable elements working on the basis of snap-through instability to design deployable meta-implants. Deployable meta-implants are compact in their retracted state, allowing them to be brought to the surgical site with minimum invasiveness. Once in place, they are deployed to take their full-size load-bearing shape. We designed five types of meta-implants by arranging bi-stable elements in such a way to obtain a radially-deployable structure, three types of auxetic structures, and an axially-deployable structure. The intermediate stable conditions (i.e. multi-stability features), deployment force, and stiffness of the meta-implants were found to be strongly dependent on the geometrical parameters of the bi-stable elements as well as on their arrangement.

Soft mechanical metamaterials working on the basis of instability have numerous potential applications in the context of "machine materials." Controlling the onset of instability is usually required when rationally designing such metamaterials. We study the isolated and modulated effects of geometrical design and material distribution on the onset of instability in multimaterial cellular metamaterials. We use multimaterial additive manufacturing to fabricate cellular specimens whose unit cells are divided into void space, a square element, and an intermediate ligament. The ratio of the elastic modulus of the ligament to that of the square element [(EL)/(ES)] is changed by using different material types. Computational models are also developed, validated against experimental observations, and used to study a wide range of possible designs. The critical stress can be adjusted independently from the critical strain by changing the material type while keeping [(EL)/(ES)] constant. The critical strain shows a power-law relationship with [(EL)/(ES)] within the range [(EL)/(ES)]=0.1-10. The void shape design alters the critical strain by up to threefold, while the combined effects of the void shape and material distribution cause up to a ninefold change in the critical strain. Our findings highlight the strong influence of material distribution on the onset of the instability and buckling mode.

Biomimetic composites are usually made by combining hard and soft phases using, for example, multi-material additive manufacturing (AM). Like other fabrication methods, AM techniques are limited by the resolution of the device, hence, setting a minimum length scale. The effects of this length scale on the performance of hard-soft composites are not well understood. Here, we studied how this length scale affects the fracture toughness behavior of single-edge notched specimens made using random, semi-random, and ordered arrangements of the hard and soft phases with five different ratios of hard to soft phases. Increase in the length scale (40 to 960 μm) was found to cause a four-fold drop in the fracture toughness. The effects of the length scale were also modulated by the arrangement and volumetric ratio of both phases. A decreased size of the crack tip plastic zone, a crack path going through the soft phase, and highly strained areas far from the crack tip were the main mechanisms explaining the drop of the fracture toughness with the length scale.

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.