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1. Diffusive buckling fronts in lattice-based metamaterials

   https://doi.org/10.1093/pnasnexus/pgag272  

   Meijer, Jochem G; Shaik, Faadil H; McDermott, Victoria V; Jaeger, Heinrich M (August 2026, PNAS Nexus)

   Behkam, Bahareh (Ed.)

   Abstract Mechanical metamaterials can be designed to exhibit unique mechanical properties, including tunable auxetic behavior as well as multistability, which arise from the geometry and configuration of the constituent building blocks. Lattice-based metamaterials, in particular, provide lightweight platforms where local instabilities can dictate the global response, with applications in energy routing and vibration isolation. In underdamped structures, perturbations have been found to propagate as nonlinear waves, e.g. transition waves or solitons. Here we investigate the opposite limit of overdamped, highly dissipative lattice metamaterials. Focusing on 3D structures, we uncover how buckling instabilities, triggered by compression, propagate as fronts that shape the macroscopic behavior. We demonstrate in experiments on 3D-printed simple cubic lattices how global and local buckling modes can be controlled via the lattice geometry. By incorporating viscoelastic dissipation into a 3D-continuum model, we show that strain-driven buckling fronts obey coupled reaction–diffusion equations. The diffusion and reaction coefficients, determined by local geometry, material properties, and strain, select the propagation direction and enable steering of the fronts. This establishes a predictive and experimentally validated framework for the control of cascading mechanical instabilities in lattice-based metamaterials. 

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2. Encoding reprogrammable properties into magneto-mechanical materials via topology optimization

   https://doi.org/10.1038/s41524-023-00980-2  

   Zhao, Zhi; Zhang, Xiaojia Shelly (December 2023, npj Computational Materials)

   Abstract The properties of materials and structures typically remain fixed after being designed and manufactured. There is a growing interest in systems with the capability of altering their behaviors without changing geometries or material constitutions, because such reprogrammable behaviors could unlock multiple functionalities within a single design. We introduce an optimization-driven approach, based on multi-objective magneto-mechanical topology optimization, to design magneto-active metamaterials and structures whose properties can be seamlessly reprogrammed by switching on and off the external stimuli fields. This optimized material system exhibits one response under pure mechanical loading, and switches to a distinct response under joint mechanical and magnetic stimuli. We discover and experimentally demonstrate magneto-mechanical metamaterials and metastructures that realize a wide range of reprogrammable responses, including multi-functional actuation responses, adaptable snap-buckling behaviors, switchable deformation modes, and tunable bistability. The proposed approach paves the way for promising applications such as magnetic actuators, soft robots, and energy harvesters. 

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3. Rod Origami (RodOri) Spring Metamaterials for Tunable Vibration Control via Tailored Structural Instabilities

   https://doi.org/10.1002/advs.76120  

   Lee, Jeseung; Leanza, Sophie; Zhao, Ruike Renee (June 2026, Advanced Science)

   ABSTRACT Modern engineering systems increasingly operate under varying vibrational environments, necessitating structural components capable of adapting their dynamic responses on demand. While springs have long served as the core of vibration control systems, their fixed stiffness fundamentally limits adaptability. Here, we introduce reconfigurable springs based on the structural instability of rod origami (RodOri), constructed from pre‐stressed, naturally curved elastic rods. By tailoring the natural curvature and cross‐sectional aspect ratio of the constituent rods, both the onset of snap‐through buckling and the post‐buckling response of individual RodOri springs can be systematically programmed. Leveraging this geometric programmability, we establish a system‐level design principle in which multiple RodOri springs of identical length but distinct buckling behaviors are assembled into a multistable metamaterial. Differences in snapping displacements enable stepwise structural reconfiguration via sequential snap‐through transitions, while variations in post‐snapping stiffness govern the mechanical response of each configuration. This hierarchical tunability enables both broad and fine control of resonance frequencies and dynamic responses across stable states. Numerical simulations and experiments demonstrate on‐demand modulation of vibration amplification, isolation, and impact mitigation within a single metamaterial, establishing RodOri springs as reconfigurable, programmable building blocks for adaptive structural and wave dynamics. 

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4. Fictitious Magnetic Charge Model for Magneto-Mechanical Metamaterials

   https://doi.org/10.1115/1.4070273  

   Zhang, Yuying; Alkuino, Gabriel; Zhang, Teng (January 2026, Journal of Applied Mechanics)

   Abstract Magnetically actuated intelligent structures have shown great promise in various applications ranging from soft robotics to biomedical devices. One important type of structure involves embedding rigid magnets in polymer matrices, thanks to their simplicity in manufacturing and flexibility in structure design. However, accurately modeling their behavior remains challenging due to the strong nonlinear coupling between large deformation and spatially varying magnetic fields. To address this, we employ a fictitious magnetic charge method to transfer the magnetic forces and torques into surface traction under both uniform and nonuniform external magnetic actuation. We implement the proposed method in the commercial finite element software abaqus and validate it through a series of benchmark examples, which cover tuning the area of magneto-mechanical metamaterials, the shape changing of magnetic lattice structures, and the magnetic-field-driven buckling of cellular structures. Our approach enables accurate prediction of shape transformations in magnetically responsive structures, offering a practical tool for the design and optimization of future magneto-mechanical metamaterials and devices. 

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5. Algorithmic encoding of adaptive responses in temperature-sensing multimaterial architectures

   https://doi.org/10.1126/sciadv.adk0620  

   Li, Weichen; Wang, Yue; Chen, Tian; Zhang, Xiaojia Shelly (November 2023, Science Advances)

   We envision programmable matters that can alter their physical properties in desirable manners based on user input or autonomous sensing. This vision motivates the pursuit of mechanical metamaterials that interact with the environment in a programmable fashion. However, this has not been systematically achieved for soft metamaterials because of the highly nonlinear deformation and underdevelopment of rational design strategies. Here, we use computational morphogenesis and multimaterial polymer 3D printing to systematically create soft metamaterials with arbitrarily programmable temperature-switchable nonlinear mechanical responses under large deformations. This is made possible by harnessing the distinct glass transition temperatures of different polymers, which, when optimally synthesized, produce local and giant stiffness changes in a controllable manner. Featuring complex geometries, the generated structures and metamaterials exhibit fundamentally different yet programmable nonlinear force-displacement relations and deformation patterns as temperature varies. The rational design and fabrication establish an objective-oriented synthesis of metamaterials with freely tunable thermally adaptive behaviors. This imbues structures and materials with environment-aware intelligence. 

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