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1. Transition Wave Interference in Multistable Mechanical Metamaterials

   https://doi.org/10.1115/1.4067856  

   Bonthron, Michael; Tubaldi, Eleonora (May 2025, Journal of Applied Mechanics)

   Mechanical metamaterials with multiple stable configurations offer a promising avenue for the design and development of adaptable materials with unprecedented levels of control over physical properties. Specifically, arrays of bistable beam elements represent a unique metamaterial platform with tunable transition waves offering means of passive control, sensing, and memory effects of environmental conditions. Although previous studies have mainly investigated transition waves triggered by a static input in nonlinear metamaterials, the dynamic properties of these structures and the interference of colliding waves are still unknown. Here, we investigate the dynamic properties of arrays of bistable beam elements which are important keys in the further development of applications of these metastructures. We determine the critical force and the optimal location to apply a force to trigger a transition wave and characterize the natural frequencies of the metamaterial. Moreover, we study the interference between two transition waves simultaneously actuated at both ends of the one-dimensional multistable array. Our new insights on the nonlinear dynamic responses of multistable metamaterials pave the way for the ability to design and program adaptable structures with enhanced energy absorption, vibration isolation, and wave steering capabilities. 

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2. Review of Morphing Laminated Composites

   https://doi.org/10.1115/1.4044269  

   Chillara, V. S.; Dapino, M. J. (January 2020, Applied Mechanics Reviews)

   Abstract Morphing structures, defined as body panels that are capable of a drastic autonomous shape transformation, have gained importance in the aerospace, automotive, and soft robotics industries since they address the need to switch between shapes for optimal performance over the range of operation. Laminated composites are attractive for morphing because multiple laminae, each serving a specific function, can be combined to address multiple functional requirements such as shape transformation, structural integrity, safety, aerodynamic performance, and minimal actuation energy. This paper presents a review of laminated composite designs for morphing structures. The trends in morphing composites research are outlined and the literature on laminated composites is categorized based on deformation modes and multifunctional approaches. Materials commonly used in morphing structures are classified based on their properties. Composite designs for various morphing modes such as stretching, flexure, and folding are summarized and their performance is compared. Based on the literature, the laminae in an n-layered composite are classified based on function into three types: constraining, adaptive, and prestressed. A general analytical modeling framework is presented for composites comprising the three types of functional laminae. Modeling developments for each morphing mode and for actuation using smart material-based active layers are discussed. Results, presented for each deformation mode, indicate that the analytical modeling can not only provide insight into the structure's mechanics but also serve as a guide for geometric design and material selection. 

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3. Level-Set-Based Shape & Topology Optimization of Thermal Cloaks

   Xu, Xiaoqiang; Chen, Shikui (January 2022, ASME Design Engineering Technical Conferences)

   Thermal metamaterials are gaining increasing popularity, especially for heat flux manipulation purposes. However, due to the high anisotropy of the structures resulting from the transformation thermotics or scattering cancellation methods, researchers are resorting to topology optimization as an alternative to find the optimal distribution of constituent bulk materials to realize a specific thermal function. This paper proposes to design a thermal cloak using the level-set-based shape and topology optimization. The thermal cloak design is considered in the context of pure heat conduction. The cloaking effect is achieved by reproducing the reference temperature field through the optimal distribution of two thermally conductive materials. The structural boundary is evolved by solving the Hamilton-Jacobi equation. The feasibility and validity of the proposed method to design thermal meta-devices with cloaking functionality are demonstrated through two numerical examples. The optimized structures have clear boundaries between constituent materials and do not exhibit thermal anisotropy, making it easier for physical realization. The first example deals with a circular cloaking region as a benchmark design. The robustness of the proposed method against various cloaking regions is illustrated by the second example concerning a human-shaped cloaking area. This work can inspire a broader exploration of the thermal meta-device in the heat flux manipulation regime. 

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4. An uncertainty-aware deep learning framework-based robust design optimization of metamaterial units

   https://doi.org/10.1007/s00158-025-03979-z  

   Wang, Zihan; Bhaduri, Anindya; Xu, Hongyi; Wang, Liping (March 2025, Structural and Multidisciplinary Optimization)

   Mechanical metamaterials represent an innovative class of artificial structures, distinguished by their extraordinary mechanical characteristics, which are beyond the scope of traditional natural materials. The use of deep generative models has become increasingly popular in the design of metamaterial units. The effectiveness of using deep generative models lies in their capacity to compress complex input data into a simplified, lower-dimensional latent space, while also enabling the creation of novel optimal designs through sampling within this space. However, the design process does not take into account the effect of model uncertainty due to data sparsity or the effect of input data uncertainty due to inherent randomness in the data. This might lead to the generation of undesirable structures with high sensitivity to the uncertainties in the system. To address this issue, a novel uncertainty-aware deep learning framework-based robust design approach is proposed for the design of metamaterial units with optimal target properties. The proposed approach utilizes the probabilistic nature of the deep learning framework and quantifies both aleatoric and epistemic uncertainties associated with surrogate-based design optimization. We demonstrate that the proposed design approach is capable of designing high-performance metamaterial units with high reliability. To showcase the effectiveness of the proposed design approach, a single-objective design optimization problem and a multi-objective design optimization problem are presented. The optimal robust designs obtained are validated by comparing them to the designs obtained from the topology optimization method as well as the designs obtained from a deterministic deep learning framework-based design optimization where none of the uncertainties in the system are explicitly considered. 

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5. Obtaining auxetic and isotropic metamaterials in counterintuitive design spaces: an automated optimization approach and experimental characterization

   https://doi.org/10.1038/s41524-023-01186-2  

   Meier, Timon; Li, Runxuan; Mavrikos, Stefanos; Blankenship, Brian; Vangelatos, Zacharias; Yildizdag, M. Erden; Grigoropoulos, Costas P. (January 2024, npj Computational Materials)

   Abstract Recent advancements in manufacturing, finite element analysis (FEA), and optimization techniques have expanded the design possibilities for metamaterials, including isotropic and auxetic structures, known for applications like energy absorption due to their unique deformation mechanism and consistent behavior under varying loads. However, achieving simultaneous control of multiple properties, such as optimal isotropic and auxetic characteristics, remains challenging. This paper introduces a systematic design approach that combines modeling, FEA, genetic algorithm, and optimization to create tailored mechanical behavior in metamaterials. Through strategically arranging 8 distinct neither isotropic nor auxetic unit cell states, the stiffness tensor in a 5 × 5 × 5 cubic symmetric lattice structure is controlled. Employing the NSGA-II genetic algorithm and automated modeling, we yield metamaterial lattice structures possessing both desired isotropic and auxetic properties. Multiphoton lithography fabrication and experimental characterization of the optimized metamaterial highlights a practical real-world use and confirms the close correlation between theoretical and experimental data. 

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