Self-Foldable Origami-Architected Metamaterials

Projektinformationen

S-FOAM

ID Finanzhilfevereinbarung: 101086644

DOI

10.3030/101086644

EK-Unterschriftsdatum 7 März 2023

Startdatum 1 Januar 2024

Enddatum 31 Dezember 2028

Finanziert unter

• European Research Council (ERC)

Gesamtkosten

€ 1 930 096,00

EU-Beitrag

€ 1 930 096,00

Koordiniert durch

UNIVERSITA DEGLI STUDI DI TRENTO
Italy

Periodic Reporting for period 1 - S-FOAM (Self-Foldable Origami-Architected Metamaterials)

Berichtszeitraum: 2024-01-01 bis 2026-06-30

Zusammenfassung vom Kontext und den Gesamtzielen des Projekts

Modern technological progress and growing environmental challenges demand materials that are not only stronger and lighter, but also adaptive and resilient. S-FOAM addresses this need by rethinking how materials are designed. Instead of relying on conventional structures, the project embeds origami design into architected cellular materials, enabling active shape change and mechanical reconfiguration. The central idea of S-FOAM is to create metamaterials that can self-fold and morph when stimulated by their environment. Rather than prescribing deformation solely through predefined crease patterns, S-FOAM exploits mechanical instabilities within the material to guide controlled folding and shape transformation. These deformations are influenced by geometric frustration and carefully engineered microstructural features. In this way, the material can reconfigure its shape in response to external actions, adapting its stiffness, strength, and overall mechanical performance. To achieve this, S-FOAM pursues three interconnected objectives. First, it develops analytical models to design origami unit cells combined with micro-lattice architectures. Second, it creates advanced computational tools to simulate and optimize folding behaviour. Third, it fabricates and experimentally tests proof-of-concept prototypes to validate the theoretical predictions. By integrating solid mechanics theory, simulations, and experiments, S-FOAM establishes a predictive framework for programmable metamaterials. Applications include soft robotic grippers, wearable devices, and adaptive medical tools. Through this approach, S-FOAM advances a new direction in material design, where geometry enables controlled and programmable mechanical response.

Arbeit, die ab Beginn des Projekts bis zum Ende des durch den Bericht erfassten Berichtszeitraums geleistet wurde, und die wichtigsten bis dahin erzielten Ergebnisse

S-FOAM aims to establish a predictive, mechanics-based design paradigm for self-foldable architected metamaterials. During the reporting period, substantial progress has been achieved through coordinated analytical development, computational implementation, and experimental validation. The research performed first focused on building a rigorous nonlinear framework for origami-based metamaterials exhibiting programmable multistability and geometric frustration. The mechanics of Kresling-type architectures were formulated within finite-strain elasticity and bifurcation theory, integrating reduced-order energetic models with three-dimensional finite element simulations and experimental calibration. This systematic approach enabled the identification of quantitative bistability thresholds and stiffness ratios governing mono–bistable transitions, producing reproducible engineering design maps. The analytical work was extended through the derivation of coarse-grained fundamental forms for trapezoid-based tessellations, establishing a discrete-to-continuum mapping between fold kinematics and macroscopic curvature, and enabling controlled curvature programming. In parallel, advanced computational tools were developed and deployed to validate and optimize programmable morphing responses. Nonlinear simulations incorporating visco-hyperelastic crease behaviour were coupled with energetic formulations to predict instability thresholds, snap-through dynamics, and energy barrier modulation. The programmable role of geometric frustration was demonstrated in multi-cell assemblies, where controlled prestress was shown to reshape energy landscapes and enable sequence-dependent morphing. Furthermore, the spectro-hierarchical homogenization framework was implemented to provide rigorous multiscale upscaling from microstructure to macroscopic dynamic response. All major theoretical and computational developments were systematically validated through fabrication and testing of multi-material 3D-printed prototypes. Mechanical characterization confirmed predicted bistability thresholds, energy barriers, and morphing pathways, demonstrating strong quantitative agreement between modelling and experiment. In addition, the work performed directly enabled translational progress. The continuum curvature mapping and programmable multistability principles developed within S-FOAM formed the scientific basis for the ERC Proof of Concept project FLEXGRIP, aimed at developing rigid/hybrid robotic grippers with controllable curvature and adaptive morphologies. Overall, the work performed during the reporting period consolidated an integrated predictive framework for origami-architected metamaterials and established a clear pathway from fundamental mechanics to functional device implementation.

Fortschritte, die über den aktuellen Stand der Technik hinausgehen und voraussichtliche potenzielle Auswirkungen (einschließlich der bis dato erzielten sozioökonomischen Auswirkungen und weiter gefassten gesellschaftlichen Auswirkungen des Projekts)

S-FOAM has produced advances that significantly reshape the way origami-inspired metamaterials are conceived, modelled, and engineered. Several of these outcomes represent genuine conceptual breakthroughs in programmable instability and architected materials design. A first major advance concerns the transition from fixed to programmable energy landscapes. Conventional origami assemblies possess intrinsic energy barriers fully determined at fabrication, meaning that their multistability is static and cannot be modified afterward. S-FOAM overturns this limitation by introducing geometrical frustration as a continuously tunable energetic control parameter. Through controlled prestress mechanisms—global stretch, global rotation, and localized crease actuation—the total potential energy of the system becomes externally reconfigurable. Instability is therefore elevated from a passive geometric consequence to an active design variable. Origami assemblies evolve from static multistable mechanisms into reprogrammable mechanical systems capable of deterministic folding sequences and non-commutative state transitions. A second breakthrough lies in the generalization of continuum origami theory. Previous continuum descriptions were largely confined to parallelogram-based tessellations, whose quasi-planar symmetry restricts admissible deformation modes. S-FOAM extends this framework to trapezoid-based architectures by deriving coarse-grained fundamental forms directly from discrete fold kinematics. This establishes an explicit mapping between micro-scale topology and macroscopic curvature and identifies independent breathing and shearing modes at the continuum level. The result broadens the design space beyond quasi-planar folding toward systematic curvature programming in cylindrical and quasi-cylindrical structures. Another conceptual advance concerns the integration of viscosity into multistability design. Multistable origami systems have traditionally been analysed under purely elastic assumptions. By incorporating viscoelastic constitutive behaviour and validating it experimentally, S-FOAM demonstrates how stress relaxation reshapes energy landscapes and modifies stability retention over time. Viscosity thus becomes a primary design parameter in programmable energy envelopes, extending multistability theory into time-dependent regimes. Finally, these theoretical advances have demonstrated immediate technological transferability. The curvature mapping and programmable multistability principles developed in S-FOAM directly enable rigid/hybrid robotic grippers with tunable morphologies and controllable force–displacement behaviour. This confirms that the advances achieved are not only conceptually transformative but also structurally transferable to deployable engineering systems.