Lattice Metamaterials Research Articles

3D-printed highly stretchable curvy sandwich metamaterials with superior fracture resistance and energy absorption

This paper focuses on the potential of curvy mechanical metamaterials to show how topological design can significantly enhance fracture toughness along the in-plane and out-of-plane (through-depth) directions. The conventional re-entrant unit cell is first reformulated by introducing local curvy ligaments and then additively manufactured by three-dimensional (3D) printing to form a center/edge-notch lattice metamaterial. The new conceptual design provides multi-stiffness unit cells, helping to control stress distribution within a structure under tensile load, specifically in the vicinity of the notches where stress concentrations occur. In other words, curvy unit cells are capable of arresting and blunting the notch under tensile loads and toughening the metamaterials. The crack tip opening displacement (CTOD) method calculates the fracture toughness. Not only can the fracture of lattice metamaterials be controlled along the in-plane direction by replacing unit cells in the sensitive parts of the metamaterials, but a new assembly method is also proposed. This offers that different thin plates of metamaterials with different layouts can be sandwiched to control out-of-plane fracture propagation (through-depth propagation of opening mode fracture) for the first time in fracture mechanics. This novel sandwiching method offers a multi-step fracture and significantly improves the fracture behavior of the lattice metamaterials from brittle to ductile by taking advantage of multiple through-thickness thin plates instead of considering one thick specimen. A detailed analysis of the effects of the ligament curvature value on the fracture behavior is presented. The results reveal that the more curvature, the more extension (ductility) will be realized, but too large curvature design can provide lower energy absorption capacity.

Super-assembly strategy based on discretization design for composite lattice metamaterials

The manufacture, multi-component assembly, and connection of composite lattice metamaterials have seriously restricted its large-scale industrial application. For a feasible solution, a super-assembly strategy based on the discretization method has been designed to establish composite lattice metamaterials. They can assemble a wide variety of single- and multi-order super-hybrid structures using a few types of voxel elements. Two kinds of CFRP lattices are successfully fabricated by this strategy. Uniaxial compression responses of the manufactured structures are experimented, and the results have shown good agreement with theoretical predictions and FEA simulations. The deformation and failure modes are analyzed systematically to verify the rationality of this strategy. The assessment of mechanical properties has demonstrated that the proposed design strategy is quite superior to existing other lattices prepared using analogical discrete-assembly techniques. This work has shown promising potential for industrial production with the advantages of low cost, high flexibility, high efficiency, standardization, and large-scale.

Systematic design of 2D and 3D vibroacoustic fluidic cavity sensors using topology optimization

In this research we investigate a novel sensor concept, which utilizes a standing acoustic wave inside a liquid-filled cavity to probe volumetric properties of a fluid analyte. However, realizing a high-Q cavity resonator is a challenge because of low acoustic impedance contrast between liquids and solids. In our previous studies, we surround the cavity resonator with phononic crystal layers that provide a strong cavity resonance within the phononic band gap. The quality factor drastically depends on the geometry of the metamaterial lattice. Therefore, the main aim of this study is to find an optimal material layout of the solid domain around the cavity by employing topology optimization. We formulate the optimization problem as maximization of the Q-factor of the cavity resonance. We consider the sensor as a fully coupled vibroacoustic system, taking into account material losses and frequency-dependent material properties. Since resonance problems are very sensitive to minor variations in geometry, we apply a gray scale suppression constraint to minimize the influence of geometrical uncertainties and make the optimized designs suitable for additive manufacturing

Experiment Investigation of the Compression Behaviors of Nickel-Coated Hybrid Lattice Structure with Enhanced Mechanical Properties.

The lattice metamaterial has attracted extensive attention due to its excellent specific strength, energy absorption capacity, and strong designability of the cell structure. This paper aims to explore the functional nickel plating on the basis of biomimetic-designed lattice structures, in order to achieve higher stiffness, strength, and energy absorption characteristics. Two typical structures, the body-centered cubic (BCC) lattice and the bioinspired hierarchical circular lattice (HCirC), were considered. The BCC and HCirC lattice templates were prepared based on DLP (digital light processing) 3D printing. Based on this, chemical plating, as well as the composite plating of chemical plating followed by electroplating, was carried out to prepare the corresponding nickel-plated lattice structures. The mechanical properties and deformation failure mechanisms of the resin-based lattice, chemically plated lattice, and composite electroplated lattice structures were studied by using compression experiments. The results show that the metal coating can significantly improve the mechanical properties and energy absorption capacity of microlattices. For example, for the HCirC structure with the loading direction along the x-axis, the specific strength, specific stiffness, and specific energy absorption after composite electroplating increased by 546.9%, 120.7%, and 2113.8%, respectively. The shell-core structure formed through composite electroplating is the main factor for improving the mechanical properties of the lattice metamaterial. In addition, the functional nickel plating based on biomimetic structure design can further enhance the improvement space of mechanical performance. The research in this paper provides insights for exploring lighter and stronger lattice metamaterials and their multifunctional applications.

Multiscale modeling of functionally graded shell lattice metamaterials for additive manufacturing

In this work, an experimentally validated multiscale modeling framework for additively manufactured shell lattice structures with graded parameters is introduced. It is exemplified in application to the Schwarz primitive triply periodic minimal surface microstructure and 3D printing using masked stereolithography of a photopolymer material. The systematic procedure starts with the characterization of a hyperelastic material model for the 3D printed material. This constitutive model is then employed in the finite element simulation of shell lattices at finite deformations. The computational model is validated with experimental compression tests of printed lattice structures. In this way, the numerical convergence behavior and size dependence of the model are assessed, and the range in which it is reasonable to assume linear elastic behavior is determined. Then, representative volume elements subject to periodic boundary conditions are simulated to homogenize the mechanical behavior of Schwarz primitives with varying aspect ratios and shell thicknesses. Subsequently, the parameterized effective linear elasticity tensor of the metamaterial is represented by a physics-augmented neural network model. With this constitutive model, functionally graded shell lattice structures with varying microstructural parameters are simulated as macroscale continua using finite element and differential quadrature methods. The accuracy, reliability and effectiveness of this multiscale simulation approach are investigated and discussed. Overall, it is shown that this experimentally validated multiscale simulation framework, which is likewise applicable to other shell-like metamaterials, facilitates the design of functionally graded structures through additive manufacturing.Graphical

Controlling biofilm transport with porous metamaterials designed with Bayesian learning

Biofilm growth and transport in confined systems frequently occur in natural and engineered systems. Designing customizable engineered porous materials for controllable biofilm transportation properties could significantly improve the rapid utilization of biofilms as engineered living materials for applications in pollution alleviation, material self-healing, energy production, and many more. We combine Bayesian optimization (BO) and individual-based modeling to conduct design optimizations for maximizing different porous materials’ (PM) biofilm transportation capability. We first characterize the acquisition function in BO for designing 2-dimensional porous membranes. We use the expected improvement acquisition function for designing lattice metamaterials (LM) and 3-dimensional porous media (3DPM). We find that BO is 92.89% more efficient than the uniform grid search method for LM and 223.04% more efficient for 3DPM. For all three types of structures, the selected characterization simulation tests are in good agreement with the design spaces approximated with Gaussian process regression. All the extracted optimal designs exhibit better biofilm growth and transportability than unconfined space without substrates. Our comparison study shows that PM stimulates biofilm growth by taking up volumetric space and pushing biofilms’ upward growth, as evidenced by a 20% increase in bacteria cell numbers in unconfined space compared to porous materials, and 128% more bacteria cells in the target growth region for PM-induced biofilm growth compared with unconfined growth. Our work provides deeper insights into the design of substrates to tune biofilm growth, analyzing the optimization process and characterizing the design space, and understanding biophysical mechanisms governing the growth of biofilms.

Near-perfect turning of robot-based 3D printing continuous carbon fiber reinforced nylon composites based on fiber-scale internal stress characterization

Mechanical metamaterials based on continuous fiber reinforced composites exhibit excellent mechanical properties. Continuous fiber 3D printing is counted as an ideal manufacturing approach for mechanical metamaterials. Currently, most metamaterial lattice structures are printed at centimeter-scale. The significant change in the width of the printed filament caused by fiber twist and shift during steering is an obvious defect when turning with minor radius. Near-perfect turning is proposed herein as a turning under the smallest possible printing radius, and the printed filaments present superior width retention rate. The key to printing high-precision composite lattice structures below centimeter-scale is to assess the near-perfect turning radius. Therefore, a fiber near-perfect turning placement model was established and the near-perfect turning radius ra was assessed by measuring the fiber-scale internal stress required in the model. The precision evaluations show that the near-perfect turning radius calculated by the model is in good agreement with the experimental value, proving the model’s validity. In the case of the Robot-based printing platform and Nylon-carbon fiber composites, the near-perfect turning radius is 2.0 mm. This study establishes a solid process foundation for metamaterial manufacturing below the centimeter scale.

Influence of structural arrangements on static and dynamic properties of additively manufactured polyester elastomer lattice metamaterials

In the current study, we present novel carbon organic framework-inspired lattice metamaterials (CFLM) with thermoplastic polyester elastomer (TPEE) to analyze the structural effects. The CFLMs (S1, S2, S3, and SS) from TPEE were successfully produced by material extrusion (MEX) via fused-filament fabrication and had never been reported previously. In the beginning stage, static compression tests were utilized to evaluate mechanical properties, densification strain, and energy absorption, which were validated using the finite element method (FEM). According to static compression results, S2 had the largest energy absorption, followed by the SS structure. In the second stage based on the static test, dynamic sinusoidal compression was performed to calculate the dynamic elastic recovery (DER), hysteresis work absorption, and Tan δ. The results showed that the proposed lattice metamaterials showed different the hysteresis energy absorption, DER, and viscoelasticity nature from Tan δ. To apply static and dynamic compression results to shoe midsoles, they were subjected to a dynamic drop weight impact test. Based on static and dynamic compression testing, including the results of dynamic drop weight impact tests, S1 was the most suitable for the toe part of the shoe midsole, whereas SS was the best for the heel part of the shoe midsole. From the overall results of all characterizations, it was concluded that the structural effect of CFLMs successfully provided different mechanical properties in the static and dynamic tests from the signal TPEE material.

Prestress-mediated damage strength of lattice metamaterials and its optimization

Prestress-mediated damage strength of lattice metamaterials and its optimization

Creep Characterization of Inconel 718 Lattice Metamaterials Manufactured by Laser Powder Bed Fusion

Lattice metamaterials manufactured by laser powder bed fusion (LPBF) are limited by their performance for critical applications. LPBF materials have microstructural or macroscale anomalies, such as suboptimal grain size, morphology, and lack of fusion. This results in LPBF metamaterials performance degradation for various mechanical properties, such as creep, which has seldom been researched. To understand the creep behavior of LPBF Inconel 718, body‐centered cubic metamaterials are fabricated for creep test at 650 °C. Kachanov's damage modeling is used to predict the creep performance of the metamaterials under different loading conditions. Microstructural characterization is performed with scanning electron microscopy to identify critical microstructure defects affecting the failure mechanisms and creep behaviors of the metamaterials. It is shown in the results that the loading conditions affect the fracture process of the metamaterials owing to different failure mechanisms. In the simulation and test results, the logarithmic decline in creep life is shown when loading increases; also, logarithmic increase in the creep life is shown when relative density increases.

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.

Breaking the Tradeoffs between Different Mechanical Properties in Bioinspired Hierarchical Lattice Metamaterials

AbstractIt is a long‐standing challenge to break the tradeoffs between different mechanical property indicators such as the strength versus toughness in the design of lightweight lattice materials. To tackle this challenge, a hierarchical lattice metamaterial with modified face‐centered cubic (FCC) cell configuration, inspired by the glass sponge skeletal system, is proposed. The proposed lattice metamaterial simultaneously possesses high strength, high energy absorption, considerable toughness, as well as controllable deformation patterns through integration of both bionic features of double diagonal reinforcement and hierarchical circular modification. The compressive strength and energy absorption can reach 69.13 MPa and 53.39 J cm3, respectively. Furthermore, the proposed lattice also exhibits exceptionally high damage tolerance compared with existing lattice metamaterials with comparable strength by attenuating stress and deformation concentration that may cause catastrophic collapse. This design approach combines the advantages of tensile‐dominated and bending‐dominated lattices. Quantitatively, in terms of specific strength, specific energy absorption, and crushing force efficiency, the modified hierarchical circular FCC (MHCFCC) lattice metamaterial outperforms the Octet lattice by 14.85%, 53.28%, and 110.52%, respectively. This multibionic feature integration approach provides advanced design strategies for high‐performance architected metamaterials with promising application potential.

A programmable modular lattice metamaterial with multiple deformations

This paper describes a class of lattice metamaterials with tunable mechanical properties controlled by the material modulus and structural parameters of the cellular units. The deformation shapes can also be changed by external control. We have developed 3D printed quadrilateral cellular TPU units with specially shaped edge walls. A simplified mechanical model of the different cell deformation processes is established and verified by numerical simulations and experiments. On this basis, by tessellating and matching these transformations together, we create assembly grids with adjustable stiffness and deformation shapes controlled by thermal and displacement constraints.

Deformation behaviors and energy absorption characteristics of a hollow re-entrant auxetic lattice metamaterial

Designing innovative architected metamaterials with enhanced energy absorption is a long-term pursuit to provide impact protection capacity for human beings and crucial structural components. Numerous natural materials prove that hollow structures present unique combinations of mechanical properties and functionalities with minimal weight cost. Therefore, a novel 3D hollow re-entrant auxetic (HRA) lattice metamaterial is proposed to improve the energy absorption capacity. To investigate the mechanical properties of the HRA lattices, an analytical model based on plastica theory is established to predict the crushing force. The energy absorption behaviors of the HRA lattices under quasi-static crushing load are studied based on finite element method, and the analytical predictions are in good agreement with the numerical simulation results. The analytical model can be used to optimize the appropriate design parameters of the HRA lattice and explain the simulation results in the parametric studies. Compared with the solid re-entrant auxetic (SRA) lattice with the same density, specific energy absorption of the HRA lattice can be improved by up to 27.43%. Finally, a parametric investigation is carried out to comprehend the influences of the length-to-height ratio, the re-entrant angle, the width-to-height ratio, and the wall thickness-to-height ratio on the energy absorption capacity of the HRA lattices. According to various energy absorption demands, the HRA lattices with different energy absorption properties can be designed by tuning these design parameters. This concept of building hollow auxetic lattice metamaterials can open up a new solution to design metamaterials with negative Poisson's ratio effects and enhanced energy absorption for potential engineering applications.

Modal analysis of a lattice type metamaterial by modeling cell structures using Euler–Bernoulli beams

Metamaterials have superior properties compared to materials found in nature and allow the tailoring of static and dynamic characteristics of the cell structures. In this study, the vibration characteristics of the sandwich plate systems composed of lattice beam structures are investigated and their behavior under various loading conditions is determined. In this context, a matrix-based solution method is developed to calculate the natural frequencies of the structure by assuming lattice elements as individual Euler–Bernoulli beams. The same structures are also analyzed with a commercial finite-element solver (ANSYS) to compare the results. In order to verify the results and determine the applicability of the proposed approach, an experimental study is conducted. Unit cell structures are additively manufactured with Stereolithography (SLA) and experimental modal analysis is performed using impact testing. Also, the amount of deflections on the structures under various loading conditions is determined experimentally by performing three-point bending tests on the plates. It has been concluded that approximate vibration characteristics of lattice-type metamaterial structures with various unit cell geometries can be determined in a short time by utilizing the matrix-based method without the need for any commercial software or performing complex experiments.

Defect sensitivity mitigation in the compressive mechanical response of two-phase lattice metamaterials

Engineered materials commonly referred to as metamaterials are materials that offer appealing features such as customisable stiffness and strength, auxetic behaviour and energy absorption. This work focuses on the classical 2D lattice metamaterial configuration with regular triangular unit cell. A combination of two dissimilar materials is employed in the design process: the primary material that constitutes the lattice structure is composed of thermoplastic polyurethane (TPU), while an incompressible silicone serves as the secondary material, completely filling selected lattice cells. In order to investigate the mechanical response of such lattices to intrinsic defects, geometric imperfections are intentionally introduced. Three distinct types of geometric anomalies, i.e. curvature of some elements, lateral shift of some lattice nodes, and reduced beam thickness, are randomly introduced. Additively manufactured perfect and defective lattices are subjected to compressive loading for both empty and silicone filled cases. Overall, the results reveal that the lattices show a significant improvement with the assumed reinforcing filling pattern, helping to prevent the buckling of the beams under compression and enhancing the load bearing capacity of the structure at higher deformations. Finite element (FE) analyses are performed to validate the experimental results, demonstrating how the filling pattern enhances the mechanical response of the lattices.

Additive Manufacturing of Body-Centered Cubic Metamaterials with Novel I-Shaped Beam Lattice Towards Enhanced Mechanical Properties

The recent advancement of additive manufacturing paves the way to achieve the highly complex design of metamaterials. Mechanical metamaterials are promising materials for high-yield industrial applications since they demonstrate superior mechanical behaviors that cannot be found in natural materials. Designing metamaterials is crucial to ensure enhanced mechanical performances. The objective of this research is to explore different metamaterial lattices utilizing a numerical approach in order to obtain higher mechanical strength. This research employs a Mechanics of Structure Genome (MSG) method to design a novel I-shaped beam with reinforcement lattice metamaterials to attain higher mechanical properties. Three cross-sectional shapes including circular, Ibeam, and Ibeam with reinforcement and their corresponding Body-Centered Cubic (BCC) metamaterials, have been designed applying the MSG modeling approach. The Stereolithography (SLA) based additive manufacturing process is leveraged to fabricate the designed metamaterials. A standard compressive test is performed to characterize the mechanical properties. The test results reveal a remarkable improvement in the mechanical behaviors of the proposed I-shaped beam with reinforcement (Reinf Ibeam). The Reinf Ibeam demonstrates higher energy absorption capacity, stiffness, and strength compared to the other two metamaterials. A 40.57% increased energy absorption/weight ratio, 140% higher stiffness/weight ratio, and 74% larger yield strength/weight ratio are obtained for the Reinf Ibeam in comparison with circular beam lattice metamaterial.

Multifunctional mechanical metamaterials with tunable double-negative isotropic properties

This research was focused on innovative design of lattice metamaterials that can exhibit tunable double-negative mechanical properties and elastic isotropy simultaneously. A discrete topology optimization method using a multi-material ground structure was developed to create microlattices exhibiting both negative thermal expansion coefficient and negative Poisson’s ratio in a single integrated design, while maintaining elastic isotropy. First, the numerical homogenization method with beam elements was used to estimate the effective thermal and elastic properties of a microlattice. Second, the topological design, subject to required geometric constraints, was formulated as a mixed integer programming problem to discover a series of multi-material microlattices that present customized isotropic values of negative thermal expansion coefficient and negative Poisson’s ratio. Finally, several three-dimensional multi-material microstructures were produced by altering either the cross-sections or constituent materials of struts to demonstrate their tunable mechanical properties.

On vibration isolation performance and crashworthiness of a three-dimensional lattice metamaterial

This work investigates the vibration isolation performance and crashworthiness of a novel three-dimensional (3D) lattice metamaterial, whose unit cell is constructed by combining a hollow rhombic dodecahedron and six cylindrical tubes. The transmission of elastic waves in the 3D metamaterial can be suppressed for the existence of band gaps in the metamaterial. Meanwhile, the 3D metamaterial can absorb the crushing energy through plastic deformation when a collision occurs. The influence of structural parameters on the band gap features and crashing behaviors of the novel 3D metamaterial are examined. It is shown that the structural parameters play a vital role in determining the band gap features and crashing behaviors. Thus, the required vibration isolation performance and crashworthiness can be obtained by adjusting the structural parameters reasonably. Finally,multi-objective optimization is performed from the comprehensive aspects of vibration isolation performance and crashworthiness to obtain the optimal design of the novel 3D metamaterial. This work provides a new possibility for the development of multifunctional metamaterials with vibration isolation performance and crashworthiness simultaneously.

Non-invariant elastic moduli of bi-level architected lattice materials through programmed domain discontinuity

Effective elastic moduli of lattice-based materials are one of the most crucial parameters for the adoption of such artificial microstructures in advanced mechanical and structural systems as per various application-specific demands. In conventional naturally occurring materials, these elastic moduli remain invariant under tensile and compressive normal modes or clock-wise and anti-clock-wise shear modes. Here we introduce programmed domain discontinuities in the cell walls of the unit-cells of lattice metamaterials involving a bi-level microstructural design to achieve non-invariant elastic moduli under tensile and compressive normal modes or clock-wise and anti-clock-wise shear modes. More interestingly, such non-invariance can be realized in the linear small deformation regime and the elastic moduli can be tailored to have higher or lower value in any mode compared to the other depending on the placement and intensity of the discontinuities in a programmable paradigm. We have derived an efficient analytical framework for the effective elastic moduli of lattice materials taking into account the influence of domain discontinuity. The axial and shear deformations at the beam level are considered along with bending deformation in the proposed analytical expressions. The numerical results ascertain that the domain discontinuities, in conjunction with unit cell level geometric parameters, can impact the effective elastic constants significantly under different modes of far-field stresses. It is further revealed that the degree of auxeticity of such lattices can be programmed to have target values (including non-invariance under different modes of deformation) as a function of the intensity and location of domain discontinuity when axial and shear deformations are included at the beam level. Realization of the unusual non-invariant elastic moduli of bi-level architected lattice materials would lead to a range of technologically demanding niche applications where one mode of deformation requires more or less force to deform compared to the opposite mode. Besides being able to perform as a load-bearing component, the proposed metamaterial can be used as an integrated sensor for measuring the level of stress or strain in structures.