Mechanical metamaterials with programmable compression-twist coupling

Purpose Mechanical meta-materials have aroused great interest during the past few decades. Unique or even unprecedented mechanical behaviors and functionalities have been created through the rational design of the micro-structure of mechanical meta-materials. Moreover, the development of additive manufacturing (AM) techniques further promotes their applications in various fields like aerospace, automobile, tissue engineering, etc. In recent years, mechanical meta-materials have also been applied to the design of aeroengine structures due to their superior performance and lightweight features. This paper aims to give a comprehensive review of the design of mechanical meta-materials and show their recent applications to aeroengine structures. Design/methodology/approach This paper presents a state-of-the-art review on the design of mechanical meta-materials and their applications to the rotating and stationary components in aeroengine structures. Findings Mechanical meta-materials are categorized into two kinds, including homogeneously architected meta-materials that have one unique unit cell periodically arranged to fill the space and heterogeneously architected meta-materials that may integrate different unit cell designs or introduce gradient changes to the whole structure. A promising design strategy, i.e. “the right micro-structure deployed to the right position,” is proposed for heterogeneous meta-materials, and it is concluded that the design methods for mechanical meta-materials are moving from simple cell design to the direction of customized and optimized design enabled by artificial intelligence. Besides, the integration of metal AM and mechanical meta-materials paved a novel path for the design of lightweight high-performance engine structures. Originality/value The present paper systematically reviews the design of mechanical meta-materials, and for the first time summarizes the application of mechanical meta-materials to aeroengine structures.

Mechanical and phononic metamaterials exhibiting negative elastic moduli, gapped vibrational spectra, or topologically protected modes enable precise control of structural and acoustic functionalities. While much progress has been made in their experimental and theoretical characterization, the inverse design of mechanical metamaterials with arbitrarily programmable spectral properties and mode localization remains an unsolved problem. Here, we present a flexible computational inverse-design framework that allows the efficient tuning of one or more gaps at nearly arbitrary positions in the spectrum of discrete phononic metamaterial structures. The underlying algorithm optimizes the linear response of elastic networks directly, is applicable to ordered and disordered structures, scales efficiently in 2D and 3D, and can be combined with a wide range of numerical optimization schemes. We illustrate the broad practical potential of this approach by designing mechanical bandgap switches that open and close pre-programmed spectral gaps in response to an externally applied stimulus such as shear or compression. We further show that the designed structures can host topologically protected edge modes, and validate the numerical predictions through explicit 3D finite element simulations of continuum elastica with experimentally relevant material parameters. Generally, this network-based inverse design paradigm offers a direct pathway towards manufacturing phononic metamaterials, DNA origami structures and topolectric circuits that can realize a wide range of static and dynamic target functionalities.

A deep learning approach for inverse design of gradient mechanical metamaterials

Mechanical metamaterials - engineered materials whose behavior is defined by their internal structure rather than their base material - have received great at- tention for the unusual properties they can exhibit. However, while the forward problem of predicting the mechanical behavior of a given metamaterial can be reliably done through simulation or experiments, the inverse problem - designing metamaterials with specific properties - remains difficult, especially for heteroge- neous metamaterials composed of multiple unit cells. This dissertation explores the use of generative machine learning to address this inverse design problem. The first part of the work investigates how inverse and generative models can be conditioned to produce unit cells with prescribed mechanical properties and how they can be used to generate multiple valid solutions for the same target. This is examined using a curved-beam metamaterial, which allows a compact geometric representation without complex design restrictions. The effect these restrictions have on the generative models is investigated in the second part. For this, a number of generative models—Variational Autoencoders, Generative Adversarial Networks, and Diffusion Models—are evaluated on a kirigami metamaterial where dependencies between the cuts cause intricate design constraints. The final part covers the challenges that arise when generative models are applied to heteroge- neous metamaterials, in which multiple unit cells are combined to create spatially varying mechanical properties. The results show that the applicability of generative models for the design of metamaterials strongly depends on the choice of geometric parameterization. Generative models make assumptions about their input data that generally hold for images, but can be invalid for metamaterials when complex dependencies be- tween the input parameters exist. B-splines can provide a representation without those dependencies and are therefore well suited to be paired up with generative models. Furthermore, it is also important how these geometrical parameters are sampled to create the training data for the generative models, as this sampling also affects the distribution of the properties in the training data. Overall, while generative machine learning models prove effective for the inverse design of mechanical metamaterials their successful application requires careful parameterization and selection of the training data.

Multi-target inverse design, which involves designing multiple targets with different optimization objectives, becomes a key focus in mechanical metamaterials (MMs) design. Specifically, many practical applications impose varying requirements for different sections. For instance, the heel of a sole demands to provide support, while the arch should be comfortable, adequately supportive, and lightweight. However, existing approaches, such as topology optimization, typically focus on optimizing MMs for specific objectives, e.g., high strength. Worse, these approaches are often inaccurate and time-consuming, even just for a single target. In this work, based on graded triply periodic minimal surface (TPMS) architectures, a machine-learning-powered approach is proposed for rapid, accurate, and multi-target MM inverse design by employing a six-parallel pipeline network architecture and utilizing deep networks to map structural parameters to mechanical curves. The most suitable results are selected based on the target curves and other performance requirements, which can be derived from the structural parameters. The approach achieves a normalized root-mean-square error (NRMSE) of 2.49% on the test dataset and outputs corresponding design parameters within seconds, simultaneously meeting multiple targets. Finally, such an approach is demonstrated in designing soles suitable for various gait scenarios and foot deformity treatments.

Advances in 3D/4D printing of mechanical metamaterials: From manufacturing to applications

Through finite element analysis and a 3D printing assisted experimental study, we demonstrate a design of mechanical metamaterials for simultaneous mechanical wave filtering and energy harvesting. The mechanical metamaterials compromise a square array of free-standing cantilevers featuring piezoelectric properties being attached to a primary structural frame. A complete bandgap has thus been created via the strong coupling of the bulk elastic wave propagating along the structural frame and the distributed local resonance associated with the square array of piezoelectrically active cantilevers. Operating within the stop-band, external vibration energy has been trapped and transferred into the kinetic energy of the cantilevers, which is further converted into electric energy through mechano-electrical conversion of its integrated piezoelectric elements. Therefore, two distinct functions, vibration isolation and energy harvesting, are achieved simultaneously through the designed mechanical metamaterials.

Continuous carbon fiber reinforced composite negative stiffness mechanical metamaterial for recoverable energy absorption

We report on a Digital Image Correlation-based technique for the detection of in-plane elastic waves propagating in structural lattices. The experimental characterization of wave motion in lattice structures is currently of great interest due its relevance to the design of novel mechanical metamaterials with unique/unusual properties such as strongly directional behaviour, negative refractive indexes and topologically protected wave motion. Assessment of these functionalities often requires the detection of highly spatially resolved in-plane wavefields, which for reticulated or porous structural assemblies is an open challenge. A Digital Image Correlation approach is implemented that tracks small displacements of the lattice nodes by centring image subsets about the lattice intersections. A high speed camera records the motion of the points by properly interleaving subse- quent frames thus artificially enhancing the available sampling rate. This, along with an imaging stitching procedure, enables the capturing of a field of view that is sufficiently large for subsequent processing. The transient response is recorded in the form of the full wavefields, which are processed to unveil features of wave motion in a hexagonal lattice. Time snapshots and frequency contours in the spatial Fourier domain are compared with numerical predictions to illustrate the accuracy of the recorded wavefields.

Chiral mechanical metamaterials with engineered asymmetric structures have garnered significant interest owing to their potential for manipulating mechanical waves and unconventional mechanical properties. Although several design methodologies have made significant strides in the design and discovery of chiral mechanical metamaterials, 3D designs that incorporate multiple mechanical characteristics remain largely unexplored and the static and dynamic properties of these structures have not received sufficient attention. Here, an innovative approach is introduced for the inverse design of 3D chiral mechanical metamaterials with desired static and dynamic properties, leveraging streamlined shapes to enable a versatile design. By employing conditional generative adversarial networks (c‐GANs), the desired mechanical properties are targeted by focusing on both wave attenuation and stress distribution under compression and shear loading. 3D chiral mechanical metamaterials with additive manufacturing are fabricated to demonstrate the performance of the proposed c‐GAN. Experimental investigations show that the generated structures exhibited a wide range of wave attenuation properties, low stress concentrations, and a variety of stress‐strain curve profiles including nonlinear stiffness, demonstrating their effectiveness in achieving the desired mechanical characteristics. This research offers significant advancements in the on‐demand design capabilities of metamaterials and their applications.

This paper proposes an effective method for the design of mechanical metamaterials by combining the parametric level set method (PLSM) with the energy-based homogenisation method (EBHM), where the topologies and shapes of microstructures periodically distributed in the material with negative Poisson's ratios are optimised simultaneously. Firstly, the effective properties of the materials are calculated by the EBHM under the topologies of microstructures, where the stress and strain theorems work as the basic theoretical framework rather than the asymptotic theory. Secondly, under the definition of the objective function to seek for the negative Poisson's ratio, the PLSM is used to evolve the topological configurations of microstructures until the bulk material is to be featured with a negative Poisson's ratio. Thirdly, the discrete wavelet transform (DWT) is utilised to deal with the full matrix of the globally supported radial basis function (GSRBF) interpolation. The proposed method can efficiently design the microstructure with the negative Poisson's ratio on the premise of ensuring the calculation accuracy. Several numerical examples are provided to illustrate the effectiveness of the proposed method for design of microstructures considering the orthotropy and isotropy. [Submitted 31 August 2019; Accepted 26 November 2019]

Recently, mechanical metamaterials have garnered extensive interests due to their unique properties. By combining hierarchical structures with the concept of size effect, mechanical metamaterials have enabled the creation of a sequence of novel designs. Those new materials allow us to explore new regions in the materials space, including ultrahigh resilience, high strength-to-volume, strong energy absorption, negative thermal expansion and so on. One of the most interesting properties of mechanical metamaterials is the negative Poisson's ratio.Poisson's ratio is the ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching force. In most cases, Poisson's ratio is positive, which means that as a material is stretched along the lateral direction, it becomes thinner along the transverse direction. In contrast, the thickness of a material with a negative Poisson's ratio increases when it is stretched. A range of natural and artificial materials, including certain polymers, metals, and ceramics, exhibit this so-called auxetic characteristic. Materials with negative Poisson's ratio offer special mechanical and thermal characteristics that are advantageous for a variety of applications, such as energy absorption, sensing, and medical implants. Auxetic materials also exhibit mechanical properties that are unique compared to conventional materials including indentation resistance, shear resistance and fracture resistance. In my thesis work, I have explored four kinds of auxetic designs with interesting properties. The designs in my study include re-entrant ribs and a star shape, both of which exhibit good auxetic behaviors. Two of the designs also demonstrate auxetic behaviors in both directions. I have used stereolithography to fabricate the samples and applied tension test to measure their mechanical properties. The experimental results confirm that all four structures exhibit auxetic characteristics, and the re-entrant ribs and star-shape structures can enhance the auxetic behavior. --Author's abstract

The emergence of advanced 3D printing techniques and the recent interest in architected materials have sparked a surge of interest in mechanical metamaterials whose unusual properties are defined by their highly ordered microarchitectures. Mechanical metamaterials with disordered microarchitectures have, however, not received as much attention despite their inherent advantages, such as robustness against the precise arrangement and design parameters of individual unit cells. Here, we computationally studied the elastic properties of two general types of disordered networks, namely, lattice-restricted and unrestricted networks that were made of beamlike elements and possessed mean connectivity values, Z, ranging between 2.5 and 7. We also additively manufactured a number of representative networks using selective laser sintering and showed that their deformations are consistent with our computational predictions. Unrestricted networks exhibited several advantages over the lattice-restricted ones including a broader range of achievable elastic modulus-Poisson's ratio duos as well as a higher probability of exhibiting auxetic and double-auxetic (i.e., auxetic behavior in both orthogonal directions) behaviors. Most interestingly, we could find unrestricted auxetic networks for high connectivity levels of up to 4.5, while no lattice-restricted auxetic networks were found for any connectivity level beyond 3.5. Given the fact that, according to Maxwell's criterion, 3.5 is the highest Z for which both of our lattice-restricted and unrestricted networks are bending-dominated, we concluded that unrestricted networks exhibit auxetic behavior well into their stretch-dominated domain. This is a promising observation that underlines the potential of unrestricted networks for the challenging task of designing stiff auxetic metamaterials in the stretch-dominated domain (i.e., Z = 4–4.5).

The mid to lower cervical spine is a common site for compression related injury. In the present study, we determined the patterns of localized strain distribution in the anterior aspect of the vertebral body and in the lateral masses of lower cervical three-segment units. Miniature strain gages were mounted to human cadaveric vertebrae. Each preparation was line-loaded using a knife-edge oriented in the coronal plane that was moved incrementally from anterior to posterior to induce compression-flexion or compression-extension loading. Uniform compressive loading and failure runs were also conducted. Failure tests indicated strain shifting to "restabilize" the preparation after failure of a component. Under these various compressive loading vectors, the location which resulted in the least amount of deformation for a given force application (i.e., stiffest axis) was quantified to be in the region between 0.5- 1.0 cm anterior to the posterior longitudinal ligament. The location in which line-loading produced no rotation (i.e., balance point) was in this region; it was also close to where the vertebral body strains change from compressive to tensile. Strain values from line loading in this region produced similar strains as recorded under uniform compressive loading, and this was also the region of minimum strain. The region of minimum strain was also more pronounced under higher magnitudes of loading, suggesting that as the maximum load carrying capacity is reached the stiffest axis becomes more well defined.

A shift is occurring from avoiding structural geometric nonlinearities to deliberately exploiting them for new functionalities. Forward design–predicting nonlinear responses from given parameters–is well established, but the inverse problem–identifying parameters that yield a desired nonlinear behaviour–remains a major challenge due to the complexity of the response. Developing an efficient inverse design framework is therefore essential to enable broader application of nonlinear mechanical metamaterials. To address this, we introduce an enhanced conditional generative adversarial network (c-GAN) framework that synergizes three key innovations: (i) surrogate-based physics-informed supervision via a pre-trained simulator network, (ii) residual generator architecture for stable gradient flow, and (iii) structured noise encoding for enhanced diversity and controllability. This c-GAN-Physics-Stochastic architecture generates precise geometric parameters in a single forward pass, bypassing traditional iterative optimization bottlenecks. We demonstrate the framework’s effectiveness through two case studies: mechanical metamaterials designed for recoverable energy dissipation via sequential snap-through instabilities, and auxetic metamaterials maintaining a constant Poisson’s ratio under large deformations. Experimental results validate the physical realisability of the generated designs. Inference with the conditional GAN provides millisecond-level design prediction, while a hybrid c-GAN + genetic algorithm (GA) refinement strategy achieves exceptional agreement with high-fidelity evaluations (up to R 2 > 0.99 ) at increased computational cost. This work demonstrates the potential of data-driven methods, particularly c-GANs, in addressing the inverse design challenge for nonlinear mechanical metamaterials for novel functionalities. By delivering an accessible toolbox, we aim to promote its widespread use and practical implementation by engineers, paving the way for innovative applications.