Emerging 4D printing techniques have enabled the realization of smart materials whose shape or properties can change with time. Two important phenomena play important roles in the 4D printing of shape memory polymeric materials. First, the anisotropic deformation of the printed filaments due to residual stresses can be harnessed to create out-of-plane shape transformations. Second, the unavoidable formation of micro-defects during the printing processes often affects the programmability of the printed object. Here, we propose a design approach that harnesses these two effects occurring during fused deposition modeling to create tailor-made curved geometries from initially 2D flat disks. We first determined the size and distribution of the imperfections formed within printed structures by varying two printing parameters namely the printing speed and the number of printed materials. Spatially varying the printing speed and combining polylactic acid filaments with a softer material without shape memory properties allowed us to cover a variety of shapes from negative to positive values of the mean and Gaussian curvature. We propose an analytical model to calculate the magnitude of the maximum out-of-plane deformation from the anisotropic expansion factor of the constituting microstructures. Furthermore, we develop computational models to predict the complex shape-changing of thermally actuated 4D printed structures given the distribution of rationally introduced imperfections and we demonstrate the potential applications of such defect-based metamaterials in drug delivery systems.

Folding nanopatterned flat sheets into complex 3D structures enables the fabrication of meta-biomaterials that combine a rationally designed 3D architecture with nanoscale surface features. Self-folding is an attractive approach for realizing such materials. However, self-folded lattices are generally too compliant as there is an inherent competition between ease-of-folding requirements and final load-bearing characteristics. Inspired by sheet metal forming, an alternative route is proposed for the fabrication of origamilattices. This ‘automated-folding’ approach allows for the introduction of sharp folds into thick metal sheets, thereby enhancing their stiffness. The first time realization of automatically folded origami lattices with bone-mimicking mechanical properties is demonstrated. The proposed approach is highly scalable given that the unit cells making up the meta-biomaterial can be arbitrarily large in number and small in dimensions. To demonstrate the scalability and versatility of the proposed approach, it is fabricated origamilattices with > 100 unit cells, lattices with unit cells as small as 1.25 mm, and auxetic lattices. The nanopatterned the surface of the sheets prior to folding. Protected by a thin coating layer, these nanoscale features remained intact during the folding process. It is found that the nanopatterned folded specimens exhibits significantly increased mineralization as compared to their non-patterned counterparts.

4D printing of flat sheets that self-fold into architected 3D structures is a powerful origami-inspired approach for the fabrication of multi-functional devices and metamaterials. However, the opposite stiffness requirements for the folding process and the subsequent loadbearing of 3D structures impose an intrinsic limitation in designing self-folding metamaterials: while a low stiffness is required for the successful completion of the self-folding step, a high stiffness is needed for utilizing the folded structure as a load-bearing mechanical metamaterial. Here, we present a nonlinear analytical model of self-folding bilayer constructs composed of an active and passive layer. This finite-deformation theoretical model predicts the curvature of activated bilayers, establishes their stability limits, and estimates the stiffness of folded bilayers, yielding the theoretical stiffness limits of self-folding bilayers. We use our model to identify the optimal combinations of geometrical and mechanical properties that result in the highest possible stiffness of folded constructs. We then compare the predictions of our analytical model with computational results, and validate our theory with experimental realizations of 4D printed structures. Finally, we evaluate the theoretical stiffness limits of bilayer constructs made using the most common types of stimuli-responsive materials. Our analysis shows that a maximum effective modulus of ≈ 1.5 GPa can be achieved using the currently available shape-memory polymers.

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.

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.

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.