Inverse Design of Energy-Absorbing Metamaterials by Topology Optimization

3D-printed programmable bistable mechanisms for customized wearable devices in tremor attenuation

This research proposes a computational framework for designing a compliant bistable mechanism and fabricating it using 3D printing for customized medical applications. The proposed method reduces upper limb tremors, taking advantage of the nonlinear mechanical properties of flexible structures. The model's development and execution on a single platform streamlines integrated inverse design and simulation, simplifying the customization process. A synthetic human arm model, built to imitate a human wrist, was scanned with a light detection and ranging (LiDAR) sensor to customize the 3D model of the bistable structure. Afterwards, the arm model was used to test the bistable mechanism. Automating the inverse design process with a deep neural network (DNN) and evolutionary optimization decides the optimal bistable mechanism configurations for stiffness and vibration attenuation. The pseudo-rigid-body model (PRBM) of the bistable mechanism was developed to train the machine learning (ML) model in the inverse design, making it computationally affordable to find the optimal parameters of bistable structure for a specific mechanical response based on tremor characteristics. Experimental results showing up to 87.11 % reduction in tremor power while weighing only 27 g to reduce vibrations in various situations suggest its use in 4D printing of wearable orthotic devices for Parkinsonian tremors and related diseases.

Extreme nonlinearity by layered materials through inverse design

Biological materials such as seashell nacre exhibit extreme mechanical properties due to their multilayered microstructures. Collaborative interaction among these layers achieves performance beyond the capacity of a single layer. Inspired by these multilayer biological systems, we architect materials with free-form layered microstructures to program multistage snap-buckling and plateau responses-accomplishments challenging with single-layer materials. The developed inverse design paradigm simultaneously optimizes local microstructures within layers and their interconnections, enabling intricate layer interactions. Each layer plays a synergistic role in collectively achieving high-precision control over the desired extreme nonlinear responses. Through high-fidelity simulations, hybrid fabrication, and tailored experiments, we demonstrate complex responses fundamental to various functionalities, including energy dissipation and wearable devices. We orchestrate multisnapping phenomena from complex interactions between heterogeneous local architectures to encode and store information within architected materials, unlocking data encryption possibilities. These layered architected materials offer transformative advancements across diverse fields, including vibration control, wearables, and information encryption.

Customizable wave tailoring nonlinear materials enabled by bilevel inverse design

Passive wave transformation via nonlinearity is ubiquitous in settings from acoustics to optics and electromagnetics. It is well known that different nonlinearities yield different effects on propagating signals, which raises the question of "what precise nonlinearity is the best for a given wave tailoring application?" In this work, considering a one-dimensional spring-mass chain connected by polynomial springs (a variant of the Fermi-Pasta-Ulam-Tsingou system), we introduce a bilevel inverse design method which couples the shape optimization of structures for tailored constitutive responses with reduced-order nonlinear dynamical inverse design. We apply it to two qualitatively distinct problems-minimization of peak transmitted kinetic energy from impact, and pulse shape transformation-demonstrating our method's breadth of applicability. For the impact problem, we obtain two fundamental insights. First, small differences in nonlinearity can drastically change the dynamic response of the system, from severely under- to outperforming a comparative linear system. Second, the oft-used strategy of impact mitigation via "energy locking" bistability can be significantly outperformed by our optimal nonlinearity. We validate this case with impact experiments and find excellent agreement. This study establishes a framework for broader passive nonlinear mechanical wave tailoring material design, with applications to computing, signal processing, shock mitigation, and autonomous materials.

Two-Phase Approach for Fast Topology Optimization of Multi-Resonant MEMS Involving Model Order Reduction

In this work, we propose a two-phase approach for a fast topology optimization of multi-resonant MEMSs. The approach minimizes the computation effort required to achieve an optimal design. In the first step, we perform a pre-optimization using bi-directional evolutionary structural optimization (BESO). We found in previous research that BESO can achieve optimal MEMS designs in a significantly lower number of iterations when compared to classical density-based methods. However, we encountered convergence issues with BESO towards the end of the optimization. Therefore, we introduced a second, density-based optimization phase to circumvent this issue. Finally, we introduced model order reduction to reduce the optimization time further. The novel approach is benchmarked with the design task of two common multi-resonant MEMS devices: a linear gyroscope and a micromirror. We show that the two-phase approach can achieve an optimal design within 200 iterations. With the addition of MOR, the computation of the goal function can be further reduced by 50% in our examples.

Assembled mechanical metamaterials with integrated functionalities of programmable multistability and multitransition behaviors

Mechanical metamaterials with integrated functionalities can simultaneously fulfill multiple design requirements through design consolidation, which is highly desirable for weight-sensitive and space-constrained applications. Despite the extensive research on multistable metamaterials, their integration with other functionalities, such as vibration isolation, sensing, and hierarchical energy absorption, remains largely untapped. Here, we report a novel class of mechanical metamaterial featuring programmable multistability and function-oriented multitransition behaviors. This integration is realized through a novel assembly-based design concept that incorporates interchangeable contact block (CB) units into a classical bistable structure. By varying the position, number, and shape of CB units, we can obtain a spectrum of function-oriented transition behaviors, offering reconfigurability through unit replacement. To ensure the rational design of CB, we employ a comprehensive approach that combines theoretical analysis, numerical simulations, and experimental validation to investigate the nonlinear behaviors of these assembled metamaterials, including snap-through instability and contact behaviors. Additionally, we explore design strategies such as 2D arraying and 3D extension to achieve programmable multistability. Furthermore, we demonstrate the versatility of these assembled mechanical metamaterials by constructing digital materials with scalability, reconfigurability, and multidirectionality. The proposed assembly-based design concept breaks new ground in engineering multistable structures with integrated functionalities for deployable structures, robotics, and beyond.

Temperature-responsive metamaterials made of highly sensitive thermostat metal strips

Temperature-responsive metamaterials have remarkable shape-morphing ability during thermal energy conversion. However, integrating the thermal shape programmability, wide-working temperature range, fast temperature response, and actuation into metamaterials remains challenging. Here, we introduce using thermostat metal strips to assemble metamaterials with desirable and balanced temperature-responsive properties, and we systematically investigate the thermal deformation performance. Achieving 70 to 80% of the designed strain requires only 5 seconds of heating. A thermal strain of around 30% is achieved for the assembled metamaterials, surpassing other bimetallic metamaterials by a magnitude of 100 to 200. The actuation capacity of thermostat metal strips exceeds 26 times their weight. Further, by leveraging the highly programmable thermal deformation, the tuneable bandgap range is 3847 to 40,000 hertz. These fully integrated mechanical performances in the multiphysics have great application potential, for example, as soft actuators and soft robots in intelligent structure systems, vibration isolation and noise reduction in hypersonic vehicles, and unique thermal deformation in precision instruments.

Soft Magnetoelastic Tactile Multi-Sensors with Energy-Absorbing Properties for Self-Powered Human-Machine Interfaces

Tactile sensors play a key role in human-machine interfaces (HMIs) for augmented and virtual reality, point-of-care devices, and human-robot collaboration, which show the promise of revolutionizing our ways of life. Here, we present a sensor (EMTS) that utilizes the magnetoelastic effect in a soft metamaterial to convert mechanical pressure into electrical signals. With this unique mechanism, the proposed EMTS simultaneously possesses self-powering, waterproof, and compliant features. The soft metamaterial is essentially a porous magnetoelastomer structure designed based on the Fourier series expansion, which allows for programmable mechanical response and sensing performance of the EMTS. Fabricated by simple 3D-printed molds, the EMTS also holds potential for low-cost production. Particularly, the porous magnetoelastomer structure comes with selectable buckling instabilities that can significantly enhance biomechanical-to-electrical energy conversion. Also, with the embedded magnetic microparticles, the energy-absorbing performance of the sensor is greatly improved, which is highly beneficial to HMIs. To pursue practical applications, the EMTSs are further integrated with two systems as control and perception modules. It is demonstrated that the EMTS is able to identify different hand gestures to control a lighting system even in a high-humidity environment. Also, the EMTS stands out for its superior capability of simultaneous impact perception and energy absorption in drop tests. Overall, with its compelling array of features, the presented EMTS gives impetus to multi-sensing technology and practically enables a variety of HMI applications.

Tailoring Stress-Strain Curves of Flexible Snapping Mechanical Metamaterial for On-Demand Mechanical Responses via Data-Driven Inverse Design

By incorporating soft materials into the architecture, flexible mechanical metamaterials enable promising applications, e.g., energy modulation, and shape morphing, with a well-controllable mechanical response, but suffer from spatial and temporal programmability towards higher-level mechanical intelligence. One feasible solution is to introduce snapping structures and then tune their responses by accurately tailoring the stress-strain curves. However, owing to the strongly coupled nonlinearity of structural deformation and material constitutive model, it is difficult to deduce their stress-strain curves using conventional ways. Here, a machine learning pipeline is trained with the finite element analysis data that considers those strongly coupled nonlinearities to accurately tailor the stress-strain curves of snapping metamaterialfor on-demand mechanical response with an accuracy of 97.41%, conforming well to experiment. Utilizing the established approach, the energy absorption efficiency of the snapping-metamaterial-based device can be tuned within the accessible range to realize different rebound heights of a falling ball, and soft actuators can be spatially and temporally programmed to achieve synchronous and sequential actuation with a single energy input. Purely relying on structure designs, the accurately tailored metamaterials increase the devices' tunability/programmability. Such an approach can potentially extend to similar nonlinear scenarios towards predictable or intelligent mechanical responses.

Ultrastiff metamaterials generated through a multilayer strategy and topology optimization

Metamaterials composed of different geometrical primitives have different properties. Corresponding to the fundamental geometrical forms of line, plane, and surface, beam-, plate-, and shell-based lattice metamaterials enjoy many advantages in many aspects, respectively. To fully exploit the advantages of each structural archetype, we propose a multilayer strategy and topology optimization technique to design lattice metamaterial in this study. Under the frame of the multilayer strategy, the design space is enlarged and diversified, and the design freedom is increased. Topology optimization is applied to explore better designs in the larger and diverse design space. Beam-plate-shell-combined metamaterials automatically emerge from the optimization to achieve ultrahigh stiffness. Benefiting from high stiffness, energy absorption performances of optimized results also demonstrate substantial improvements under large geometrical deformation. The multilayer strategy and topology optimization can also bring a series of tunable dimensions for lattice design, which helps achieve desired mechanical properties, such as isotropic elasticity and functionally grading material property, and superior performances in acoustic tuning, electrostatic shielding, and fluid field tuning. We envision that a broad array of synthetic and composite metamaterials with unprecedented performance can be designed with the multilayer strategy and topology optimization.

Three-Dimensional Optical Imaging of Internal Deformations in Polymeric Microscale Mechanical Metamaterials

Recent advances in two-photon polymerization fabrication processes are paving the way to creating macroscopic metamaterials with microscale architectures, which exhibit mechanical properties superior to their bulk material counterparts. These metamaterials typically feature lightweight, complex patterns such as lattice or minimal surface structures. Conventional tools for investigating these microscale structures, such as scanning electron microscopy, cannot easily probe the internal features of these structures, which are critical for a comprehensive assessment of their mechanical behavior. In turn, we demonstrate an optical confocal microscopy-based approach that allows for high-resolution optical imaging of internal deformations and fracture processes in microscale metamaterials under mechanical load. We validate this technique by investigating an exemplary metamaterial lattice structure of 80 × 80 × 80 μm3 in size. This technique can be extended to other metamaterial systems and holds significant promise to enhance our understanding of their real-world performance under loading conditions.

Improved mechanical performance of quasi-cubic lattice metamaterials with asymmetric joints

In this paper, we propose a simple method for the modification of the unit cells in the lattice metamaterials that provides an improvement of their impact strength. The idea is based on the introduction of small mutual offsets of the interconnected struts inside the unit cells. In such way, the joints between the struts become asymmetric and the overall geometry of the unit cells can be defined as the quasi-cubic with the axis of chirality. Considering four types of cubic lattices with BCC, BCT, FCC and octahedron structures, we modified their geometry and investigated the influence of the offsets and the unit cell size on the overall performance in static and dynamic tests. From the experiments we found that the small offsets (less than the strut diameter) can allow to increase the impact strength of 3d-printed polymeric specimens in 1.5-3 times remaining almost the same density and static mechanical properties. Based on the numerical simulations, we show that the explanation of the observed phenomena can be related to the increase of plastic deformations and damage accumulation in the unit-cells with asymmetric joints leading to the transition from the quasi-brittle to the ductile type of fracture in tested specimens.

Sb2S3-Based Dynamically Tuned Color Filter Array via Genetic Algorithm

Color displays have become increasingly attractive, with dielectric optical nanoantennas demonstrating especially promising applications due to the high refractive index of the material, enabling devices to support geometry-dependent Mie resonance in the visible band. Although many structural color designs based on dielectric nanoantennas employ the method of artificial positive adjustment, the design cycle is too lengthy and the approach is non-intelligent. The commonly used phase change material Ge₂Sb₂Te₅ (GST) is characterized by high absorption and a small contrast to the real part of the refractive index in the visible light band, thereby restricting its application in this range. The Sb₂S₃ phase change material is endowed with a wide band gap of 1.7 to 2 eV, demonstrating two orders of magnitude lower propagation loss compared to GST, when integrated onto a silicon waveguide, and exhibiting a maximum refractive index contrast close to 1 at 614 nm. Thus, Sb₂S₃ is a more suitable phase change material than GST for tuning visible light. In this paper, genetic algorithms and finite-difference time-domain (FDTD) solutions are combined and introduced as Sb₂S₃ phase change material to design nanoantennas. Structural color is generated in the reflection mode through the Mie resonance inside the structure, and the properties of Sb₂S₃ in different phase states are utilized to achieve tunability. Compared to traditional methods, genetic algorithms are superior-optimization algorithms that require low computational effort and a high population performance. Furthermore, Sb₂S₃ material can be laser-induced to switch the transitions of the crystallized and amorphous states, achieving reversible color. The large chromatic aberration ∆E modulation of 64.8, 28.1, and 44.1 was, respectively, achieved by the Sb₂S₃ phase transition in this paper. Moreover, based on the sensitivity of the structure to the incident angle, it can also be used in fields such as angle-sensitive detectors.