4D printing of reconfigurable metamaterials and devices

The study addresses the challenge of realizing 3D-to-3D (reconfigurable) shape-shifting using accessible 4D printing methods. While 2D-to-3D self-folding from planar precursors is well-developed and leverages in-plane anisotropy, achieving reconfiguration between distinct 3D states is limited by the inherently planar, layer-by-layer nature of common additive manufacturing processes. The authors propose modifying a standard FDM printer to print on curved substrates, thereby embedding anisotropy both along and around curved geometries. The purpose is to enable single-step fabrication and programming of complex reconfigurable metamaterials and devices, with potential impact in areas such as adaptive mechanical properties and deployable medical devices (e.g., stents). This work aims to democratize 4D printing by using low-cost hardware and widely available materials while expanding the design space for 3D-to-3D transformations.

Prior works demonstrate shape-shifting via active materials (e.g., hydrogels swelling, pre-strained shape-memory polymers) and various 4D printing approaches that program anisotropy during fabrication to drive complex deformations. Origami/kirigami-inspired metamaterials and self-folding scaffolds illustrate 2D-to-3D transformations with rich functionality. The authors’ earlier work and others’ approaches showed effective 2D-to-3D programming using hobbyist FDM printers by exploiting filament-level memory from extrusion and rapid cooling to induce longitudinal shrinkage above Tg and transverse expansion. However, existing strategies largely impose in-plane anisotropy, limiting 3D-to-3D reconfiguration needed for reconfigurable metamaterials. The study builds on this background by extending printing to curved substrates to overcome in-plane constraints, integrating computational modeling (FEA) and material characterization (DMA) to support design.

Hardware: A simple add-on device with a stepper-motor-driven rotating drum was mounted on a hobbyist FDM printer (Ultimaker 2+). The rotating drum adds a rotational degree of freedom to the printer’s linear axes, enabling printing on curved surfaces and programming anisotropy along longitudinal and circumferential directions. Adhesion sheets ensured part adherence. Printing paths and G-code were generated via custom MATLAB scripts. Materials and characterization: PLA filaments were used. Molded PLA specimens (independent of print-induced effects) were tested by DMA (TA Q-800) to obtain temperature-dependent viscoelastic properties. A Tg of ~70 °C was identified. Time–temperature superposition was applied to construct a master curve, and WLF parameters and a Prony series viscoelastic model were fit for FEA. Process–structure–response studies: The effects of extrusion temperature (180–225 °C) and layer thickness (25–100 µm) on single-filament shrinkage were quantified; lower temperature and smaller layers increased longitudinal shrinkage. 180 °C was the practical lower bound for reliable extrusion. Printing path effects were examined; significant influence occurred only for parallel filaments with lengths <5 mm. Empirical deformation curves derived from experiments were used in simulations. Design of basic elements: In-plane bending elements comprised a shrinking line adjacent to an expanding block-wave pattern; out-of-plane bending elements were formed by orthogonally oriented filament layers (longitudinal over transverse), including printing on curved drums with different initial radii. Element width was varied to study curvature response. Computational modeling: Transient coupled temperature–displacement FEA (Abaqus Standard, C3D8T elements) captured viscoelastic behavior and time-dependent shape-shifting over 2 min simulations. Penalty-based surface-to-surface contact prevented interpenetration where needed. Material models incorporated DMA-derived Prony series; empirical filament deformation curves informed programmed strains. Comparisons between experiments and FEA validated predictive capability. Sample activation and testing: Activation was performed in hot water baths at 90 °C for ≥30 s; hot air tests also conducted to assess medium effects. Digital imaging recorded deformations. Mechanical testing evaluated stiffness changes and Poisson’s ratio switching before/after activation. Designs ranged from simple elements to lattices, tubes, and deployable devices including stents. Design parameters included element width, unit-cell arm length L0, and the fraction of passive layers α. For bifurcation stents, out-of-plane actuation was tuned via β = Nactive,top / Nactive,bottom and selective removal of inter-cell connectors.

• Curved 4D printing: A low-cost add-on enables FDM printing on curved drums, allowing programming of anisotropy in both longitudinal and circumferential directions and enabling 3D-to-3D reconfiguration.
• Material behavior: PLA Tg ≈ 70 °C (DMA). Heating above Tg triggers longitudinal filament shrinkage and transverse expansion. Lower extrusion temperature and thinner layers increase programmed shrinkage; 180 °C is the lower practical extrusion limit.
• Printing path effects: Significant for parallel filaments shorter than 5 mm; otherwise minor. Empirical deformation curves captured these dependencies and informed FEA.
• Basic elements: In-plane bending elements achieved maximum curvature at ~0.5 mm width; out-of-plane elements printed on curved substrates achieved maximum curvature at ~2.0 mm width. Initial curvature (drum radius) influenced bending via transverse expansion effects. FEA agreed well with experiments; deviations attributed to print porosity and unmodeled imperfections.
• Reconfigurable structures: Three strategies demonstrated: (1) spatially varying filament orientations causing out-of-plane buckling and complex shape changes of cylinders; (2) lattices with in-plane bending elements yielding diverse programmed deformations; (3) tubes composed of out-of-plane elements connected by semi-passive segments yielding axial shrinking, bending, or unfolding behaviors. Experiments matched FEA predictions.
• Adaptive mechanical properties: A ring–flexure architecture switched from highly compliant (≤~1.0 N/mm stiffness) to semi-rigid upon activation via contact-induced change in deformation mode; tensile stiffness increased ~30× and compressive stiffness increased by >100×. A re-entrant honeycomb design exhibited a switch in Poisson’s ratio from negative (auxetic) to positive (conventional) upon activation, confirmed experimentally and by FEA.
• Deployable devices: A programmable unit cell with in-plane bending arms and passive layers characterized by α and arm length L0 enabled tunable lateral expansion vs longitudinal shrinkage; contact between arms limited expansion at higher α and L0. Arrays (5×10 cells) with α-gradients produced distinct deployed cylinder geometries from identical precursors. Self-expandable polymeric stents achieved ~3× diameter increase upon activation; miniaturization achieved using smaller drums. A bifurcation stent, designed by spatial control of α, out-of-plane actuation β, and selective connector removal, deployed successfully in a model artery, opening an anchor for a side-branch stent.
• Activation robustness: Shape-shifting completed typically in <30 s and was largely independent of activation medium (hot water vs hot air).

By enabling printing on curved substrates, the method overcomes the in-plane anisotropy limitation of conventional 4D printing for 3D-to-3D reconfiguration. The integration of empirical filament-level deformation behavior with viscoelastic material modeling allowed accurate FEA predictions of complex shape changes across scales, supporting rational design. The demonstrated repertoire—from basic bending elements to lattices, tubes, and deployable medical devices—shows that accessible hardware and standard PLA can yield reconfigurable metamaterials with programmable functions. Adaptive stiffness and switchable Poisson’s ratio exemplify how geometry and programmed anisotropy can tune effective properties post-activation. The deployable stent demonstrations, including bifurcation architectures, highlight translational potential where minimally invasive delivery and controlled deployment are essential. Overall, the findings validate that low-barrier 4D printing can produce versatile, predictable 3D-to-3D transformations suitable for metamaterials and devices.

The study introduces a simple, broadly accessible modification to FDM printers—printing on a rotating drum—to fabricate and program 3D-to-3D shape-shifting metamaterials and devices in a single step. Using PLA and empirically informed viscoelastic FEA, the authors designed basic bending elements, complex lattices, and curved structures with predictable transformations. They demonstrated adaptive mechanical behavior (large stiffness increase; switch in Poisson’s ratio) and deployable devices, including self-expandable and bifurcation stents with substantial diameter expansion. Activation is rapid and largely medium-independent. Future directions include: expanding material platforms to shape-memory polymers with varied Tg for application-specific activation conditions; refining process control to minimize porosity and variability; incorporating failure and contact mechanics more comprehensively into models; exploring miniaturization and biocompatible materials for medical deployment; and broadening property switching (e.g., acoustic, thermal, or wave-propagation characteristics) in reconfigurable metamaterials.

• Material scope: Experiments used PLA; while concepts are material-agnostic, generalization to other polymers and composites requires characterization and validation.
• Manufacturing imperfections: 3D-printed porosity and variability introduce anisotropy and reduce stiffness, contributing to discrepancies between experiments and FEA; such imperfections were not explicitly modeled.
• Modeling assumptions: FEA used viscoelastic models without local failure and with simplified contacts; local failures observed experimentally can affect constitutive response.
• Process constraints: Reliable extrusion limited below 180 °C; printing path significantly affects deformation only for very short filament segments (<5 mm), constraining certain fine-feature designs.
• Activation conditions: While hot water and hot air both work, practical applications may impose constraints on activation method and thermal exposure; detailed in situ activation strategies were not explored.
• Contact-limited expansion: At higher α and L0, unit-cell expansion is limited by arm contact, setting bounds on achievable deployment without redesign.