Shape-morphing structures are at the core of future applications in aeronautics1, minimally invasive surgery2, tissue engineering3 and smart materials4. However, current engineering technologies, based on inhomogeneous actuation across the thickness of slender structures, are intrinsically limited to one-directional bending5. Here, we describe a strategy where mesostructured elastomer plates undergo fast, controllable and complex shape transformations under applied pressure. Similar to pioneering techniques based on soft hydrogel swelling6–10, these pneumatic shape-morphing elastomers, termed here as ‘baromorphs’, are inspired by the morphogenesis of biological structures11–15. Geometric restrictions are overcome by controlling precisely the local growth rate and direction through a specific network of airways embedded inside the rubber plate. We show how arbitrary three-dimensional shapes can be programmed using an analytic theoretical model, propose a direct geometric solution to the inverse problem, and illustrate the versatility of the technique with a collection of configurations. Elastomer sheets with programmable air channel organization swiftly shape into complex three-dimensional structures upon the application of pressure.

/pdf/bio-inspired-pneumatic-shape-morphing-elastomers-20356e2h6q.pdf

Bio-inspired pneumatic shape-morphing elastomers.

We investigate the mechanical response of thin sheets perforated with a square array of mutually orthogonal cuts, which leaves a network of squares connected by small ligaments. Our combined analytical, experimental and numerical results indicate that under uniaxial tension the ligaments buckle out of plane, inducing the formation of 3D patterns whose morphology is controlled by the load direction. We also find that by largely stretching the buckled perforated sheets, plastic strains develop in the ligaments. This gives rise to the formation of kirigami sheets comprising periodic distribution of cuts and permanent folds. As such, the proposed buckling-induced pop-up strategy points to a simple route for manufacturing complex morphable structures out of flat perforated sheets.

Buckling-induced kirigami

The emerging capability to 3D print a diverse palette of functional inks will enable the mass democratization of patient-specific wearable devices and smart biomedical implants for applications such as health monitoring and regenerative biomedicines. These personalized wearables could be fabricated via ex situ printing, which involves first printing a design on a planar substrate and then deploying it to the target surface. However, this can result in a geometrically and dynamically mismatched interface between printed materials and target surfaces. In situ printing provides a potential remedy by directly printing 3D constructs on the target surfaces. This new manufacturing procedure requires the assistance of artificial intelligence (AI) to sense, adapt and predict the state of the printing environment, such as a dynamically morphing organ. In this Review, we discuss electronic and biological inks for in situ 3D printing, AI-empowered 3D-printing approaches with open-loop, closed-loop and predictive control, and recent developments in surgical robotics and AI that could be integrated in future 3D-printing approaches. We anticipate that this convergence of AI, 3D printing, functional materials and personalized biomedical devices will lead to a compelling future for smart manufacturing. Artificial intelligence can be used to facilitate the 3D printing of functional materials and devices directly on target surfaces, such as human bodies. This Review surveys ex situ and in situ artificial-intelligence-assisted 3D printing of multifunctional materials and its combination with surgical robots to enable autonomous medical care and smart biomanufacturing.

3D-printed multifunctional materials enabled by artificial-intelligence-assisted fabrication technologies

Kirigami, the Japanese art of paper cutting, has recently enabled the design of stretchable mechanical metamaterials that can be easily realized by embedding arrays of periodic cuts into an elastic sheet Here, kirigami principles are exploited to design inflatables that can mimic target shapes upon pressurization The system comprises a kirigami sheet embedded into an unstructured elastomeric membrane First, it is shown that the inflated shape can be controlled by tuning the geometric parameters of the kirigami pattern Then, by applying a simple optimization algorithm, the best parameters that enable the kirigami inflatables to transform into a family of target shapes at a given pressure are identified Furthermore, thanks to the tessellated nature of the kirigami, it is shown that we can selectively manipulate the parameters of the single units to allow the reproduction of features at different scales and ultimately enable a more accurate mimicking of the target

Kirigami-Inspired Inflatables with Programmable Shapes

Kirigami tessellations, regular planar patterns formed by cutting flat, thin sheets, have attracted recent scientific interest for their rich geometries, surprising material properties and promise for technologies. Here we pose and solve the inverse problem of designing the number, size, and orientation of cuts that allows us to convert a closed, compact regular kirigami tessellation of the plane into a deployment that conforms approximately to any prescribed target shape in two and three dimensions. We do this by first identifying the constraints on the lengths and angles of generalized kirigami tessellations which guarantee that their reconfigured face geometries can be contracted from a non-trivial deployed shape to a novel planar cut pattern. We encode these conditions in a flexible constrained optimization framework which allows us to deform the geometry of periodic kirigami tesselations with three, four, and sixfold symmetry, among others, into generalized kirigami patterns that deploy to a wide variety of prescribed boundary target shapes. Physically fabricated models verify our inverse design approach and allow us to determine the tunable material response of the resulting structures. We then extend our framework to create generalized kirigami patterns that deploy to approximate curved surfaces in $\mathbb{R}^3$. Altogether, this work illustrates a novel framework for designing complex, shape-changing sheets from simple cuts showing the power of kirigami tessellations as flexible mechanical metamaterials.

Programming shape using kirigami tessellations

We present a computational method for interactive 3D design and rationalization of surfaces via auxetic materials, i.e., flat flexible material that can stretch uniformly up to a certain extent. A key motivation for studying such material is that one can approximate doubly-curved surfaces (such as the sphere) using only flat pieces, making it attractive for fabrication. We physically realize surfaces by introducing cuts into approximately inextensible material such as sheet metal, plastic, or leather. The cutting pattern is modeled as a regular triangular linkage that yields hexagonal openings of spatially-varying radius when stretched. In the same way that isometry is fundamental to modeling developable surfaces, we leverage conformal geometry to understand auxetic design. In particular, we compute a global conformal map with bounded scale factor to initialize an otherwise intractable non-linear optimization. We demonstrate that this global approach can handle non-trivial topology and non-local dependencies inherent in auxetic material. Design studies and physical prototypes are used to illustrate a wide range of possible applications.

/pdf/beyond-developable-computational-design-and-fabrication-with-2ogs6dsq70.pdf

Beyond developable: computational design and fabrication with auxetic materials

Form-active hybrid structures (FAHS) couple two or more different structural elements of low self weight and low or negligible bending flexural stiffness (such as slender beams, cables and membranes) into one structural assembly of high global stiffness. They offer high load-bearing capacity at a fraction of the weight of traditional building elements and do so with a clear aesthetic expression of force flow and equilibrium. The design of FAHS is limited by one significant restriction: the geometry definition, form-finding and structural analysis are typically performed in separate and bespoke software packages which introduce interruptions and data exchange issues in the modelling pipeline. The mechanical precision, stability and open software architecture of Kangaroo has facilitated the development of proof-of-concept modelling pipelines which tackle this challenge and enable powerful materially-informed sketching. Making use of a projection-based dynamic relaxation solver for structural analysis, explorative design has proven to be highly effective.

/pdf/calibrated-and-interactive-modelling-of-form-active-hybrid-3ucqmb7l9k.pdf

Calibrated and Interactive Modelling of Form-Active Hybrid Structures

Emerging directly from a masterclass held by the authors at IASS 2017, this paper presents a quantitative and qualitative benchmark comparison between three distinct software environments, namely SOFiSTiK, Kangaroo and Kiwi3d, framed specifically within the context of designing and simulating bending-active structures. The three environments differ significantly not only in their numerical methods and implementation but also in their stages of software development, licensing structure and design intent and so their comparison represents a timely and valuable insight into the status quo for the design of bending-active hybrid structures.

Exploring Software Approaches for the Design and Simulation of Bending Active Systems

Extra-terrestrial infrastructure design and architecture are experiencing a resurgence due to the prospect of permanent human presence on celestial bodies such as our moon and Mars. There, the conditions and constraints within which structural design and assembly should be developed are extreme – for example, scarcity of processed structural material, labour, machinery and imports from Earth. Consequently, the guiding design principles for building off-Earth should include efficient In-Situ Resource Utilisation (ISRU) and reusability. Significantly, these aspects have striking similarities to some characteristics of our vernacular construction history on Earth, such as inherent material efficiency and use of local materials. The majority of contemporary proposals for off-Earth design concern 3D-printed monolithic structures which are not reusable nor reconfigurable. As a result, there is scope for developing component-based, recyclable infrastructure which is based on efficient ISRU. In this research paper, we propose a two-fold assembly and structural design methodology which synthesises three-dimensional geometries in static equilibrium and vernacular construction techniques for deriving scaffoldless, component-based structures. This framework is underpinned by the development of a bespoke mechanically interlocking system which enables mortarless construction. This minimises the need for importing material binders and maximises the reconfigurability and reusability of off-Earth infrastructure.

Off-Earth infrastructure assembly: A conceptual method for scaffoldless and mortarless component-based structures in static equilibrium

We present ShapeOp, a robust and extensible geometric modelling paradigm. ShapeOp builds on top of the state-of-the-art physics solver (Bouaziz et al. in ACM Trans Graph 33:154:1–154:11, 2014). We discuss the main theoretical advantages of the underlying solver and how this influences our modelling paradigm. We provide an efficient open-source C++ implementation (www.shapeop.org) together with scripting interfaces to enable ShapeOp in Rhino/Grasshopper and potentially other tools. This implementation can also act as a template for future integration of computer graphics research. To evaluate the potential of ShapeOp we present various examples using our implementation and discuss potential implications on the design process.

ShapeOp—A robust and extensible geometric modelling paradigm

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