Lattice Metamaterials Research Articles

Nonlinear plane-wave expansion method for analyzing dispersion properties of piezoelectric metamaterial lattices with encapsulated resonators

Nonlinear plane-wave expansion method for analyzing dispersion properties of piezoelectric metamaterial lattices with encapsulated resonators

Machine learning – enabled inverse design of shell-based lattice metamaterials with optimal sound and energy absorption

ABSTRACT Currently, the development in shell-based lattice, is increasingly focused on multifunctionality, with growing interest in combining sound and energy absorption. However, few studies have explored the multi-objective inverse design process. Herein, we propose a new approach using machine learning (ML) to optimise both the mechanical and acoustic performances of shell-based lattices. Firstly, the K-Nearest Neighbour and Artificial Neural Network are employed to predict the properties of different configurations. Then the non-dominated sorting genetic algorithm is employed to generate the desired structures. Finally, the lightweight metamaterials generated achieve optimal multifunctional performances (an energy absorption capacity of 50% higher than typical Gyroid structure and a sound absorption coefficient near 1 at specific frequency band). Besides, the potential trade-off phenomenon of mechanical and acoustic properties is also presented by our work. Overall, this work presents a new concept to use ML and genetic algorithm for multi-functional inverse design for shell lattice metamaterials.

Lattice metamaterials with controllable mechanical properties inspired by projection of four-dimensional hypercubes

There has been an increasing interest among the material research community in the pursuit of enhancing the designability of mechanical properties. The existing approaches usually resorted to sophisticated algorithms (such as machine learning) for the reverse design of materials with specific properties. Different from these existing approaches, here we propose a new approach to create lattice metamaterials with continuously controllable mechanical properties by continuously adjusting the geometric parameters of a unique cell topology originated from the projection of four-dimensional hypercubes. The cells contain an inner region and an outer region, each with different deformation characteristics. For example, the inner region is a stretching-dominated simple cubic (SC) unit cell, while the outer region is a bending-dominated body-centered cubic (BCC) unit cell. Specifically, both stiffness and strength isotropy can be simultaneously realized. The proposed lattice metamaterial exhibits intriguing feature of dual stress plateaus. These plateaus can be effectively controlled by adjusting the geometric parameters of inner and outer regions, which enables these lattice metamaterials to hold promising application prospects in the energy absorption scenarios, such as vehicle and pedestrian protection. Such lattice metamaterial design can be used to realize the gradient distribution of mechanical properties through continuous transition of cell topology without introduction of inefficient interfaces, providing a new approach for the design of heterogeneous metamaterials used in the scenarios involving non-uniform stress distribution.

Design optimization of phononic-fluidic resonator systems

Phononic-fluidic resonators utilize an acoustic fluid domain as a defect inside a solid metamaterial lattice, which can be used used to precisely measure acoustic properties of liquids. The design goal is to offer ideal boundary conditions for the acoustic resonator by matching defect resonance with phononic band gap. The design space of metamaterial or phononic crystal and fluidic resonator is nearly unlimited, especially when utilizing fully three-dimensional structures. In this work, we explore numerical shape and topology optimization to focus acoustic energy into the fluid domain and maximize the quality factor of the defect resonance. This requires the use of complex multi-frequency objective functions, while taking into account practical limits such as finite size and losses in the fluid and solid domains. Results highlight notable but limited improvements of quality factor with shape optimization starting from an initial design constrained by the maximum deformation possible. On the other hand, topology optimization results offer unique and unexpected ideas, and thus a deeper dive into the design space.

A review of structural diversity design and optimization for lattice metamaterials

Metamaterials are a type of groundbreaking engineered materials with unique properties not found in natural substances. Lattice metamaterials, which have a periodic lattice cell structure, possess exceptional attributes such as a negative Poisson’s ratio, high stiffness-to-weight ratios, and outstanding energy dissipation capabilities. This review provides a comprehensive examination of lattice metamaterials. It covers their various structures and fabrication methods. The review emphasizes the crucial role of homogenization methods and multi-scale modeling in assessing metamaterial properties. It also highlights the advancement of topology optimization through advanced computational techniques, such as finite element analysis simulations and machine learning algorithms.

Ultra‐wide Band Antipodal Vivaldi Antenna Using Metasurface Lens for Gain and Front‐To‐Back Ratio (FBR) Improvement

AbstractThis paper addresses the limited gain of conventional Antipodal Vivaldi Antenna (AVA) at higher frequencies. We propose a novel Metamaterial Lens Vivaldi Antenna (MLVA) design that overcomes this limitation by integrating an exponentially tapered antenna lens and a strategically placed Near Zero Refractive Index (NRZI) metamaterial lattice. The MLVA achieves exceptional wideband performance with a −3 dB gain bandwidth exceeding 148.6% from 3.7 to 25 GHz. The result demonstrates a peak realized gain of 11.8 dBi at 11.2 GHz, compared to 9.1 dBi conventional AVA, especially beyond 5 GHz. The compact MLVA design measures only 120 × 78 × 1.524 mm3 (1.48 × 0.96 × 0.0188λ03) λ0 where free‐space wavelength is the lowest frequency and is fabricated on RO4350 B substrate with a 50‐Ω SMA connector. Key features of the design include exponential flaring, and trapezoidal lens geometries chosen for their inherent ability to effectively collimate and direct the spherical wavefront. The incorporation of a dielectric lens and metasurface further enhances gain and Front‐to‐Back Ratio (FBR) by directing the majority of energy in the end‐fire direction. Experimental results validate the effectiveness of the proposed design, confirming simulation predictions. These outstanding characteristics make the MLVA a promising candidate for diverse wireless communication and radar applications demanding high data rates across a broad frequency range.

Nonlinear elasticity tailoring and failure mode manipulation of functionally graded honeycombs under large deformation

Design of lattice metamaterials with tailored mechanical properties at a relatively higher (macro) length scale by architecting lower (micro) length scale geometric and material configurations leads to achieving unprecedented mechanical properties for fulfilling advanced multi-functional structural demands. In the design space of innovative microstructural configurations, we propose a novel class of lattice metamaterials with cell walls made of optimally designed functionally graded intrinsic materials. Under different modes of remotely applied mechanical stresses, two different intuitive architectures of functional gradations for the intrinsic cell wall materials are proposed. The large-deformation nonlinear lattices result in broadband modulation of effective stiffness, and an unprecedented manipulation capability of failure modes and corresponding strengths covering ductile and brittle types depending on architected material gradation. For estimating the nonlinear elasticity and microstructural stresses as a measure of failure mode for the proposed functionally graded lattices undergoing large deformation, a multi-scale mechanics-based semi-analytical framework is developed. Geometrically nonlinear functionally graded beams with generalized material gradation, integrated with unit cell architectures, are analyzed through iterative variational energy principle-based Ritz approach. Based on the developed physically insightful computational framework, effective nonlinear elastic properties and failure modes of the functionally graded honeycomb lattices are tailored as a function of the intrinsic material gradation at the lower length scale. The proposed novel class of lattices with optimally designed functionally graded intrinsic materials and coupled unit cell architectures would open up innovative avenues for designing advanced multi-functional engineering structures and mechanical systems.

Longitudinal wave propagation in a practical metamaterial lattice

A practical metamaterial lattice is constructed by integrating curved beams, four-link mechanisms, and cantilever beams with lumped masses. It can generate two complete low-frequency bandgaps due to the lateral local resonance, inertia mass, and the main chain. The effective mass density and stiffness are obtained using different effective models, which show negative within the bandgaps. The analysis of the energy distribution and the space wave attenuation reveals that the metamaterial can attenuate the elastic waves in an exponential form within the bandgaps along the lattice. The finite element model is established to show the dynamic behaviour of the elastic wave propagation in the frequency domain and transient domain. Both results show that waves can be efficiently blocked within the bandgaps, while outside the bandgaps, waves can propagate without any attenuation. Finally, the experimental model of practical metamaterial is constructed, and the test piece is excited by a force hammer. Experimental results verify that the practical metamaterial can efficiently suppress the vibration within the bandgap frequency and validate the accuracy of the theoretical prediction.

Novel pre-folded lattice metamaterial for two-stage deformation and variable Poisson’s ratio properties under quasi-static compression

When honeycomb structures are compressed in the axial direction, they are prone to high crushing loads and structural instability. Folded structures with origami ideas can overcome this defect. In this work, a novel pre-folded lattice metamaterial is proposed, with notable energy absorption capacity and vibration isolation properties. The geometry of the structure is described, and a theoretical model of the deformation platform at various stages is established. The compression and energy absorption properties of the structure are evaluated by compression experiments and finite element simulations. The findings indicate that the structure has two smooth and stable platform stages under quasi-static compression. This feature effectively avoids the initial crushing force of compression energy. It possesses a bistable property during the structural deformation process in the first stage. In the meantime, the compression deformation has the characteristic of variable Poisson’s ratio. Furthermore, the vibration modes and vibration isolation capacity of the variable folding angle are investigated as well. Pre-folded lattice metamaterial with 49.1° exhibits the broadest vibration isolation region across the 0–500 Hz spectrum. This work can provide a novel perspective for the integrated design of structural load-bearing and vibration isolation functions.

Design of lattice metamaterials under the equal strength concept and research on the mechanical properties of their sandwich structures

This study proposes a novel lattice metamaterial with equal strength struts based on the concept of equal strength of beams, which has been designated the strut-enhanced body-centered cubic lattice structure (EBCC). The structure is capable of effectively reducing the stress concentration of the lattice structure at the nodes and increasing the structural energy absorption. The effective elastic properties of EBCC unit cells are investigated in detail under periodic boundary conditions (PBC), and the results show that the deformation response of the unit cell under compressive loading is dominated by bending. A novel sandwich structure, designated S-EBCC, was developed utilizing EBCC as the core material. The effects of geometrical parameters and relative density on the deformation mechanism and mechanical properties of the sandwich structure were analyzed through experiments, numerical simulations and theoretical predictions. The results show that under compressive loading, the stress concentration at the nodes of the EBCC structure is effectively improved and the peak stress is reduced while the energy absorption is increased compared with the traditional S-BCC structure. Under three-point bending load, the larger the strut angle of the S-EBCC structure, the higher the load capacity. Comparison of experimental and theoretical results shows that the failure modes of the S-EBCC structure under both compressive and three-point bending loads are plastic yield.

Investigation of additively manufactured metamaterials for load-bearing structural applications

The study explores the potential application of Triply Periodic Minimal Surface (TPMS) metamaterials in structural engineering and architecture. It evaluates parametric design possibilities and analysis approaches while examining the mechanical properties of five TPMS structures (Gyroid, Schwarz, Diamond, Split, and Neovius). Comparisons are made between Additively Manufactured (AM) samples and numerical simulations. Gyroid and Diamond structures, which display advantageous properties, undergo further investigation with parametric design for uniform and non-uniform lattices. The study proposes simplified analytical formulations for metamaterial design, along with Homogenization analysis and detailed FEM analysis. Compression tests reveal distinct failure modes and stress-strain behaviors for each TPMS. The research suggests further investigation into the influence of the 3D printing process, void detection, and thermomechanical analysis. Finally, the study provides insights into tailored applications of these lattice metamaterials in structural engineering.

Crack-Deflecting Lattice Metamaterials Inspired by Precipitation Hardening.

Lattice structures, comprising nodes and struts arranged in an array, are renowned for their lightweight and unique mechanical deformation characteristics. Previous studies on lattice structures have revealed that failure often originates from stress concentration points and spreads throughout the material. This results in collapse failure, similar to the accumulation of damage at defects in metallic crystals. Here the precipitation hardening mechanism found in crystalline materials is employed to deflect the initial failure path, through the strategic placement of strengthening units at stress concentration points using the finite element method. Both the mesostructure, inspired by the arrangement of crystals, and the inherent microstructure of the base materials have played crucial roles in shaping the mechanical properties of the macro-lattices. As a result, a groundbreaking multiscale hierarchical design methodology, offering a spectrum of design concepts for engineering materials with desired properties is introduced.

Fracture and size effect in mechanical metamaterials

We resort to variational methods to evaluate the asymptotic behavior of fine metamaterials as a function of cell size. To zeroth order, the metamaterial behaves as a micropolar continuum with both displacement and rotation degrees of freedom, but exhibits linear-elastic fracture mechanics scaling and therefore no size effect. To higher order, the overall energetics of the metastructure can be characterized explicitly in terms of the solution of the zeroth-order continuum problem by the method of Γ-expansion. We present explicit expressions of the second-order correction for octet frames. As an application, we evaluate the compliance of double-cantilever octet specimens to second order and use the result to elucidate the dependence of the apparent toughness of the specimen on cell size. The analysis predicts the discreteness of the metamaterial lattice to effectively shield the crack-tip, a mechanism that we term lattice shielding. The theory specifically predicts anti-shielding, i. e., coarser is weaker, in agreement with recent experimental observations.

TPMS-based strut-shell interpenetrating lattice metamaterial with wide-range customizable mechanical properties and superior energy absorption

Mechanical metamaterials (MMs) are artificially designed structures with superior properties that originate from unit cells. Compared with the widely studied single-morphology MMs, multi-morphology interpenetrating MMs offer, by the virtue of their fused lattice characteristics, the potential for customizable mechanical properties and new application fields. Inspired by the fact that the isosurface of triply periodic minimal surfaces (TPMS) can divide a lattice into two independent regions, this paper proposes a novel TPMS-based strut-shell interpenetrating (TSSI) lattice metamaterial. This study demonstrates that the TSSI lattice has a larger specific surface area than traditional TPMS lattices. Compared with the volume fraction, the fusion proportion parameter is not only more conducive to effectively adjusting the mechanical properties in a wide range and controlling the anisotropy of the lattice metamaterials to achieve elastic isotropy but significantly changes the dominant mechanism of deformation under uniaxial and shear loads. Moreover, the TSSI lattice metamaterial can avoid sharp stress drops due to the mutual support and wrapping of the internal interpenetrating lattices after failure, resulting in a more stable energy absorption efficiency and a maximum increase in energy absorption of 74%. This work provides new opportunities to design lightweight components with a wide range of customizable mechanical properties and superior energy absorption.

Superior fracture resistance and topology-induced intrinsic toughening mechanism in 3D shell-based lattice metamaterials.

Lattice metamaterials have demonstrated remarkable mechanical properties at low densities. As these architected materials advance toward real-world applications, their tolerance for damage and defects becomes a limiting factor. However, a thorough understanding of the fracture resistance and fracture mechanisms in lattice metamaterials, particularly for the emerging shell-based lattices, has remained elusive. Here, using a combination of in situ fracture experiments and finite element simulations, we show that shell-based lattice metamaterials with Schwarz P minimal surface topology exhibit superior fracture resistance compared to conventional octet truss lattices, with average improvements in initiation toughness up to 150%. This superiority is attributed to the unique shell-based architecture that enables more efficient load transfer and higher energy dissipation through material damage, structural plasticity, and material plasticity. Our study reveals a topology-induced intrinsic toughening mechanism in shell-based lattices and highlights these architectures as a superior design route for creating lightweight and high-performance mechanical metamaterials.

Fracture mechanics of bi-material lattice metamaterials

The advent of additive manufacturing technology empowers precise control of multi-material components or specific defects in lightweight lattice metamaterials, however, fracture mechanics and toughening design strategies in such metamaterials remain enigmatic. By incorporating theoretical analysis, numerical simulation, and experimental investigation, our study reveals that stretch-bend synergistic strut deformations caused by bi-material components or topology defects contribute notably tougher lattice structures surpassing its ideal single-material lattices. A peak fracture energy at a critical modulus ratio was found in a designed bi-material lattice composed of triangular soft struts and hexagonal stiff struts, which originates from the shift of fracture modes at crack tip from strut bending to stretching dominated failure modes as the modulus of soft struts increases, where the compromise in competition between bending-enhanced and stretching-weakened energy dissipations of struts deformations results in the maximized fracture energy. A parametric design protocol was proposed to optimize fracture energy of bi-material lattices through tuning the modulus ratio and relative density. Furthermore, the concept of stretch-bend synergistic toughening can also be applied to make tougher single-material lattices with specific topological defects. Our findings not only provide physical insights into directing crack propagation but also provide quantitative guidance to optimize fracture resistance within low-density tough lattice metamaterials.

Effect of sample dimensions on the stiffness of PA12 Lattice materials fabricated using Powder Bed Fusion

Powder Bed Fusion fabrication techniques, including selective laser sintering, have made the fabrication of lattice meta-materials consisting of periodic cells formed by interconnected struts possible. It is generally observed that cell size has a strong influence on the lattice’s effective Young’s modulus, following in the case of typical polymers used for printing a trend of the smaller the softer. However, there is no clear understanding of the origin of the effective elastic modulus reduction with lattice cell size. In this paper, an integrated study is performed to unravel the reasons behind this effect. The analysis performed encompasses mechanical characterization (compression tests and nanoindentation), microstructure characterization (X-ray tomography, DSC, SAXS, and WAXS), and numerical analysis of the effect of defects (FFT and Finite element simulations of cells with roughness and defects) of PA12 printed single cells of different sizes and full lattice specimens containing many cells. It is found that the effect of porosity and roughness is not enough to explain the reduction of the effective elastic modulus with the cell size, suggesting that this effect is necessarily a combination of the defects, incomplete melting of particles and the changes of PA12 nanostructure induced by the different printing conditions as function of full specimen size . The results of the micro- and nanostructure characterization validate this assumption.

Constitutive behavior of asymmetric multi-material honeycombs with bi-level variably-thickened composite architecture

Bi-level tailoring of cellular metamaterials involving a dual design space of unit cell and elementary beam level architectures has recently gained traction for the ability to achieve extreme elastic constitutive properties along with modulating multi-functional mechanical behavior in an unprecedented way. This article proposes an efficient analytical approach for the accurate evaluation of all constitutive elastic constants of asymmetric multi-material variably-thickened hexagonal lattices by considering the combined effect of bending, stretching, and shearing deformations of cell walls along with their rigid rotation. A tri-member unit cell is conceptualized, wherein all nine constitutive constants are obtained through the mechanics under one cell wall direction and subsequent repetitive coordinate transformations. We enhance the design space of lattice metamaterials substantially here by introducing multiple exploitable dimensions such as asymmetric geometry, multi-material unit cells and variably-thickened cell walls, wherein the conventional monomaterial auxetic and non-auxetic hexagonal configurations can be analyzed as special cases along with other symmetric and asymmetric lattices such as a range of rectangular and rhombic geometries. The generic analytical approach along with extensive numerical results presented in this paper opens up new avenues for efficient optimized design of the next-generation multi-functional lattices and cellular metamaterials with highly tailored effective elastic properties.

Physics-based discrete models for magneto-mechanical metamaterials

Magneto-mechanical metamaterials are emerging smart materials whose mechanical responses can be tailored through structure architecture and magnetic interactions. The latter provides additional freedom in the material design space and leads to novel behaviors due to its nonlocal nature. The enriched functionalities open new possibilities in various applications, such as actuators, energy absorbers, and soft robots. However, the nonlinear and nonlocal coupling between elastic and magnetic forces poses a great challenge in the modeling and simulation of these systems, further hindering theory-based rational design strategies. Here, we focus on a class of magneto-mechanical metamaterials comprising elastic solids embedded with rigid permanent magnets. The clear separation between elastic and magnetic forces simplifies the design and fabrication process, yet their nonlocal interplay still allows for complex behaviors. We present a simulation framework for such magneto-mechanical metamaterials by combining a lattice spring model for the elastic solid with the dipole model for the magnetic interactions and implementing it in the LAMMPS molecular dynamics software. We demonstrate the capabilities of our framework by simulating a few representative structures, including shape-locking lattice metamaterials, a soft cellular solid with controllable buckling, and a metamaterial chain with phase-transforming behavior. For the shape-locking lattice metamaterials, we successfully capture the magnetic-actuation-driven reconfiguration and the nonlinear mechanical response of the curved lattices. For the soft cellular solid, we identify its buckling patterns under external non-uniform magnetic fields and simulate a buckling evolution process consistent with experiments. For the metamaterial chain, we include the strong long-range interactions among the embedded magnets and reproduce the controllable phase transitions in the experiments. Our work provides a simple yet versatile simulation methodology to investigate the nonlinear mechanical behaviors in the presence of strong external and internal magnetic forces, which will facilitate the design and analysis of magneto-mechanical materials. It can also be applied to other magnetically-driven smart structures, such as soft robots.

Ti–6Al–4V hybrid-strut lattice metamaterials: A design strategy for improved performance

Metal hollow-strut lattices manipulate the strut and node sections to achieve higher strength. Although these metamaterials have recently surpassed the structural efficiency of conventional solid-strut lattices of comparable density and topology, they often observe localised yielding and fragmentation through the nodes that limit their structural efficiency. To quantify the effect of this localised failure and to develop mitigating strategies, we have integrated solid and hollow strut and node sections in singular Ti–6Al–4V simple cubic hybrid-strut lattices for a deployable relative density range of 15–30%. Fabricated through laser powder bed fusion these hybrid-strut lattices are stronger (32%), stiffer (15%), and tougher (65%) than solid-strut lattices of equivalent density. Interestingly, the metamaterials with hollow beams can transition from a bending-dominated to a stretch-dominated deformation response with increasing density, while the lattices with solid beams only observed a uniformly stretch-dominated deformation response. The combination of solid and hollow strut and node sections in the hybrid-strut lattice establishes a simple yet effective strategy to enhance structural efficiency and control of failure response without increasing density or manipulating unit cell topology.