Material modeling for parametric,anisotropic finite strain hyperelasticity based on machine learning with application in optimization of metamaterials

Mechanical metamaterials such as open- and closed-cell lattice structures, foams, composites, and so forth can often be parametrized in terms of their microstructural properties, for example, relative densities, aspect ratios, material, shape, or topological parameters. To model the effective constitutive behavior and facilitate efficient multiscale simulation, design, and optimization of such parametric metamaterials in the finite deformation regime, a machine learning-based constitutive model is presented in this work. The approach is demonstrated in application to elastic beam lattices with cubic anisotropy, which exhibit highly nonlinear effective behaviors due to microstructural instabilities and topology variations. Based on microstructure simulations, the relevant material and topology parameters of selected cubic lattice cells are determined and training data with homogenized stress-deformation responses is generated for varying parameters. Then, a parametric, hyperelastic, anisotropic constitutive model is formulated as an artificial neural network, extending a recent work of the author extending a recent work of the author, Comput Mech., 2021;67(2):653-677. The machine learning model is calibrated with the simulation data of the parametric unit cell. The authors offer public access to the simulation data through the GitHub repository https://github.com/CPShub/sim-data . For the calibration of the model, a dedicated sample weighting strategy is developed to equally consider compliant and stiff cells and deformation scenarios in the objective function. It is demonstrated that this machine learning model is able to represent and predict the effective constitutive behavior of parametric lattices well across several orders of magnitude. Furthermore, the usability of the approach is showcased by two examples for material and topology optimization of the parametric lattice cell.     

Lattice Metamaterials with Mesoscale Motifs: Exploration of Property Charts by Bayesian Optimization

Through the current work, the usefulness of the concept of architectured rod lattices based on unit cell motifs designed at mesoscale is demonstrated. Specifically, 2D triangular lattices with unit cells containing different numbers of rods are considered. Combinations of rods of two different types provide the lattices explored with a greater complexity and versatility. For mesocells with a large number of variable parameters, it is virtually impossible to calculate the entire set of the points mapping the material onto its property space, as the volume of calculations would be gigantic. The number of possible motifs increases exponentially with the number of rods. Herein, the lattice metamaterials with mesoscale motifs are investigated with the focus on their elastic properties by combining machine learning techniques (specifically, Bayesian optimization) with finite element computations. The proposed approach made it possible to construct property charts illustrating the evolution of the boundary of the elastic compliance tensor of lattice metamaterials with an increase in the number of rods of the mesocell when a full-factor experiment would not be possible.     

3D-Printed Micro/Nano-Scaled Mechanical Metamaterials: Fundamentals,Technologies, Progress,Applications, and Challenges

Micro/nano-scaled mechanical metamaterials have attracted extensive attention in various fields attributed to their superior properties benefiting from their rationally designed micro/nano-structures. As one of the most advanced technologies in the 21st century, additive manufacturing (3D printing) opens an easier and faster path for fabricating micro/nano-scaled mechanical metamaterials with complex structures. Here, the size effect of metamaterials at micro/nano scales is introduced first. Then, the additive manufacturing technologies to fabricate mechanical metamaterials at micro/nano scales are introduced. The latest research progress on micro/nano-scaled mechanical metamaterials is also reviewed according to the type of materials. In addition, the structural and functional applications of micro/nano-scaled mechanical metamaterials are further summarized. Finally, the challenges, including advanced 3D printing technologies, novel material development, and innovative structural design, for micro/nano-scaled mechanical metamaterials are discussed, and future perspectives are provided. The review aims to provide insight into the research and development of 3D-printed micro/nano-scaled mechanical metamaterials.     

Magnetoelastic metamaterials

The study of advanced artificial electromagnetic materials, known as metamaterials, provides a link from material science to theoretical and applied electrodynamics, as well as to electrical engineering. Being initially intended mainly to achieve negative refraction, the concept of metamaterials quickly covered a much broader range of applications, from microwaves to optics and even acoustics. In particular, nonlinear metamaterials established a new research direction giving rise to fruitful ideas for tunable and active artificial materials. Here we introduce the concept of magnetoelastic metamaterials, where a new type of nonlinear response emerges from mutual interaction. This is achieved by providing a mechanical degree of freedom so that the electromagnetic interaction in the metamaterial lattice is coupled to elastic interaction. This enables the electromagnetically induced forces to change the metamaterial structure, dynamically tuning its effective properties. This concept leads to a new generation of metamaterials, and can be compared to such fundamental concepts of modern physics as optomechanics of photonic structures or magnetoelasticity in magnetic materials.     

Hollow-walled lattice materials by additive manufacturing: Design,manufacture, properties,applications and challenges

The rapid growth of additive manufacturing (AM) technologies has enabled the emergence of geometrically sophisticated materials or structures with tailored and/or enhanced mechanical responses. In addition to dense-walled lattice structures, innovation within the past decade has identified that hollow-walled lattice topologies exhibit the multifaceted potential of competitive strength and rigidity, whilst displaying unique deformation behaviours, indicating that they may be an important subsequent step in lattice evolution. Hollow-walled sections facilitate density and geometrical parameters well below what is achievable by dense-walled sections, providing additional hierarchies of architecture at micrometre to even nanoscale proportion. Their wall thickness can range from 20 nm to 800 µm while the relative density can span three orders of magnitude between 0.01% and 30%. Despite nearly a decade of research into hollow-walled lattice topologies, no meta-analysis exists to provide an informative overview of these structures. This research addresses this deficiency and provides a data-driven review of hollow-walled lattice materials. It elucidates how these hollow-walled lattices deviate from the current limitations of dense-walled lattices and the underlying mechanisms that dictate their performance, with data accumulated from an exhaustive collection of literature sources. A range of new insights into their design and manufacture is discussed for their future research and applications in different engineering fields.     

Metasurfaces Atop Metamaterials: Surface Morphology Induces Linear Dichroism in Gyroid Optical Metamaterials

Optical metamaterials offer the tantalizing possibility of creating extraordinary optical properties through the careful design and arrangement of subwavelength structural units. Gyroid‐structured optical metamaterials possess a chiral, cubic, and triply periodic bulk morphology that exhibits a redshifted effective plasma frequency. They also exhibit a strong linear dichroism, the origin of which is not yet understood. Here, the interaction of light with gold gyroid optical metamaterials is studied and a strong correlation between the surface morphology and its linear dichroism is found. The termination of the gyroid surface breaks the cubic symmetry of the bulk lattice and gives rise to the observed wavelength‐ and polarization‐dependent reflection. The results show that light couples into both localized and propagating plasmon modes associated with anisotropic surface protrusions and the gaps between such protrusions. The localized surface modes give rise to the anisotropic optical response, creating the linear dichroism. Simulated reflection spectra are highly sensitive to minute details of these surface terminations, down to the nanometer level, and can be understood with analogy to the optical properties of a 2D anisotropic metasurface atop a 3D isotropic metamaterial. This pronounced sensitivity to the subwavelength surface morphology has significant consequences for both the design and application of optical metamaterials.     

2D Mechanical Metamaterials with Widely Tunable Unusual Modes of Thermal Expansion

Most natural materials expand uniformly in all directions upon heating. Artificial, engineered systems offer opportunities to tune thermal expansion properties in interesting ways. Previous reports exploit diverse design principles and fabrication techniques to achieve a negative or ultralow coefficient of thermal expansion, but very few demonstrate tunability over different behaviors. This work presents a collection of 2D material structures that exploit bimaterial serpentine lattices with micrometer feature sizes as the basis of a mechanical metamaterials system capable of supporting positive/negative, isotropic/anisotropic, and homogeneous/heterogeneous thermal expansion properties, with additional features in unusual shearing, bending, and gradient modes of thermal expansion. Control over the thermal expansion tensor achieved in this way provides a continuum‐mechanics platform for advanced strain‐field engineering, including examples of 2D metamaterials that transform into 3D surfaces upon heating. Integrated electrical and optical sources of thermal actuation provide capabilities for reversible shape reconfiguration with response times of less than 1 s, as the basis of dynamically responsive metamaterials.     

声学超构材料技术实用化的进展

声学超构材料是当前声学和材料学一个热门的研究领域。声学超构材料可定义为:通过对材料在特征物理尺度上进行人工设计制备,使其具有超越常规材料的声学性能的一种人工序构的复合材料。其亚波长特性、超常声学性能以及颠覆性应用的可能吸引了学界和工程界的关注。21世纪以来,随着增材制造技术的发展,声学超构材料的实验室加工与制备问题得以解决,然而,声学超构材料的工程应用仍然面临着批量制造困难、使用场景不明、生产成本高昂等方面的严峻挑战。介绍了各类常见的声学超构材料及其研究现状,讨论各类声学超构材料实用化面临的困难和挑战,简述声学超构材料研究和实验的最新方法,最后展望了未来声学超构材料实用化研究的方向。     

Multifield modelling and failure prediction of cellular cores produced by selective laser melting

A multifield simulation approach of cellular cores produced by additive manufacturing is presented. The analysis is aiming to derive the relation between the manufacturing process parameters and the resulting material failure behaviour. To this purpose, the selective laser melting manufacturing process is initially thermo‐mechanically simulated, followed by the mechanical analysis of the nonlinear core behaviour. The methodology is demonstrated in the case of open‐lattice body‐centred‐cubic (BCC) cellular cores.     

Effective optical properties of highly ordered mesoporous thin films

This paper expands our previous numerical studies predicting the optical properties of highly ordered mesoporous thin films from two-dimensional (2D) nanostructures with cylindrical pores to three-dimensional (3D) structures with spherical pores. Simple, face centered, and body centered cubic lattices of spherical pores and hexagonal lattice of cylindrical pores were considered along with various pore diameters and porosities. The transmittance and reflectance were numerically computed by solving 3D Maxwell's equations for transverse electric and transverse magnetic polarized waves normally incident on the mesoporous thin films. The effective optical properties of the films were determined by an inverse method. Reflectance of 3D cubic mesoporous thin films was found to be independent of polarization, pore diameter, and film morphology and depended only on film thickness and porosity. By contrast, reflectance of 2D hexagonal mesoporous films with cylindrical pores depended on pore shape and polarization. The unpolarized reflectance of 2D hexagonal mesoporous films with cylindrical pores was identical to that of 3D cubic mesoporous films with the same porosity and thickness. The effective refractive and absorption indices of 3D films show good agreement with predictions by the 3D Maxwell-Garnett and nonsymmetric Bruggeman effective medium approximations, respectively.     

Selective electron beam manufactured Ti-6Al-4V lattice structures for orthopedic implant applications: Current status and outstanding challenges

Additively manufactured Ti-6Al-4V lattices display unique mechanical and biological properties by virtue of their engineered structure. These attributes enable the innovative design of patient-specific medical implants that (i) are conformal to the intended surgical geometry, (ii) mimic the mechanical properties of natural bone, and (iii) provide superior biological interaction to traditional implants. Selective electron beam melting (SEBM) is an established metal additive manufacturing (AM) process that has enabled the design and fabrication of a variety of novel intricate lattices for implant applications over the last 15?years. This article reviews the technical and clinical characteristics of SEBM Ti-6Al-4V lattices, including (i) the SEBM process and its capabilities, (ii) the structures of human bones with an exhaustive list of corresponding mechanical properties from literature, (iii) the mechanical properties of SEBM Ti-6Al-4V lattices of various designs and their shortcomings when compared to human bones, (iv) microstructural control of SEBM Ti-6Al-4V lattices for improved performance, (v) the lattice manufacturability and associated geometric errors, and (vi) clinical cases. Existing literature on the mechanical response of SEBM Ti-6Al-4V lattice structures is exhaustively evaluated for documentation quality using established theoretical models. This extensive data-set allows novel insights into the effect of lattice design on mechanical response that is not possible with the individual data; and provides a comprehensive database for those who are actively involved in patient-specific SEBM implant design. On this basis, outstanding challenges and research opportunities for SEBM Ti-6Al-4V lattices in the biomedical domain are identified and discussed.     

Wire Metamaterials: Physics and Applications

The physics and applications of a broad class of artificial electromagnetic materials composed of lattices of aligned metal rods embedded in a dielectric matrix are reviewed. Such structures are here termed wire metamaterials. They appear in various settings and can operate from microwaves to THz and optical frequencies. An important group of these metamaterials is a wire medium possessing extreme optical anisotropy. The study of wire metamaterials has a long history, however, most of their important and useful properties have been revealed and understood only recently, especially in the THz and optical frequency ranges where the wire media correspond to the lattices of microwires and nanowires, respectively. Another group of wire metamaterials are arrays and lattices of nanorods of noble metals whose unusual properties are driven by plasmonic resonances.     

Multiscale Optimization of 3D-Printed Beam-Based Lattice Structures through Elastically Tailored Unit Cells

Herein, a numerical multiscale tool is developed to design 3D periodic lattice structures. The work is motivated by the high design freedom of additive manufacturing technologies, which enable complex multiscale lattice structures to be printed. A finite-element-based free-material optimization method is used to determine the ideal orthotropic material properties of a 3D macrostructure space. Subsequently, a population-based algorithm is established to design optimized microscopic lattice unit cells with the desired structural properties. The design variables are the coordinates of lattice skeleton nodes defined within the 3D lattice unit cell space, and the connectivities between them resulting in a truss skeleton. For the calculation of the mechanical properties of the individual lattice cells, an effective Timoshenko beam-based finite element calculation method is developed. The macroscale structure can be constructed by periodically filling the domain with the customized unit cell representing a metamaterial. The method is demonstrated by 3D beam problems with compliance constraints. These macroscopic demonstrators of the developed lattice structures were also 3D-printed. The benefit regarding the weight-specific structural performance is validated through benchmarking with periodic lattice design solutions using well-known standard lattice cells.     

An Experimental and Computational Modeling Study on Additively Manufactured Micro-Architectured Ti–24Nb–4Zr–8Sn Hollow-Strut Lattice Structures

Herein, the design, manufacturing, and mechanical testing of hollow-strut lattice structures of the metastable β-titanium alloy Ti–24Nb–4Zr–8Sn (Ti2448) are performed. Due to the absence of studies in the literature, this study focusses on two important aspects: 1) the designing of micro-architectured lattice structures and 2) metastable β-titanium alloy. Face-centered cubic (FCC) and body-centered cubic (BCC) hollow-strut lattices are designed by computer-aided design and manufactured by laser powder bed fusion. The microstructure of the hollow lattices shows plates of α″-martensite phase within the β phase. The FCC hollow lattice structure shows higher tensile strength compared to the BCC hollow lattice structure, while the load-bearing capability of the FCC hollow lattice structure is lower than that of the BCC hollow lattice structure. At lower strains, the tensile force-displacement curve of the hollow lattice structure matches the simulated tensile force-displacement curve. At higher strains, a large deviation in the force-displacement curve is observed in the hollow lattices.     

关于声学超构材料名词术语的探讨

近30年来,声学超构材料领域的理论与技术不断成熟与完善。以增材制造技术、飞秒激光加工等为代表的各种先进制造技术的发展,为复杂的声学超构材料的数字化设计制造奠定了基础,极大地推动了这类材料的实用化进程。这些发展吸引了学术界和产业界对声学超构材料的极大关注,因此,研讨声学超构材料领域的一些基本术语和概念,以方便学术界、研究机构和企业界之间的交流、沟通和讨论是十分必要的。从基础研究的科学概念出发,探讨了声学超构材料的定义、分类及其标准、研究手段与应用方向等有关声学超构材料的名词与术语,希望能够为建立声学超构材料有关技术标准提供一些有益的建议,供有兴趣的专家参考。     

Light‐Patterned Crystallographic Direction of a Self‐Organized 3D Soft Photonic Crystal

Uniform and patterned orientation of a crystallographic direction of ordered materials is of fundamental significance and of great interest for electronic and photonic applications. However, such orientation control is generally complicated and challenging with regard to inorganic and organic crystalline materials due to the occurrence of uncontrollable dislocations or defects. Achieving uniform lattice orientation in frustrated liquid‐crystalline phases, like cubic blue phases, is a formidable task. Taming and tailoring the ordering of such soft, cubic lattices along predetermined or desired directions, and even imparting a prescribed pattern on lattice orientation, are more challenging, due to the entropy‐domination attribute of soft matter. Herein, we disclose a facile way to realize designed micropatterning of a crystallographic direction of a soft, cubic liquid‐crystal superstructure, exhibiting an alternate uniform and random orientation of the lattice crystallographic direction enabled by a photoalignment technique. Because of the rewritable trait of the photoalignment film, the pattern can be erased and rewritten on‐demand by light. Such an oriented soft lattice sensitively responds to various external stimuli such as temperature, electric field, and light irradiation. Furthermore, advanced reflective photonic applications are achieved based on the patterned crystallographic orientation of the cubic blue phase, soft lattice.     

Soft Pneumatic Actuators with Controllable Stiffness by Bio-Inspired Lattice Chambers and Fused Deposition Modeling 3D Printing

This article shows how changing 3D printing parameters and using bio-inspired lattice chambers can engineer soft pneumatic actuators (SPAs) with different behaviors in terms of controlling tip deflection and tip force using the same input air pressure. Fused deposition modeling (FDM) is employed to 3D print soft pneumatic actuators using varioShore thermoplastic polyurethane (TPU) materials with a foaming agent. The effects of material flow and nozzle temperature parameters on the material properties and stiffness are investigated. Auxetic, columns, face-centered cubic, honeycomb, isotruss, oct vertex centroid, and square honeycomb lattices are designed to study actuators’ behaviors under the same input pressure. Finite-element simulations based on the nonlinear hyper-elastic constitutive model are carried out to precisely predict the behavior, deformation, and tip force of the actuators. A closed-loop pneumatic system and sensors are developed to control the actuators. Results show that lattice designs can control the bending angle and generated force of actuators. Also, the lattices increase the ultimate strength by controlling the contact area inside the chambers. They demonstrate variable stiffness behaviors and deflections under the same pressure between 100 and 500 kPa. The proposed actuators could be instrumental in designing wearable hand rehabilitative devices that assist customized finger and wrist flexion-extension.     

The Gibson-Ashby model for additively manufactured metal lattice materials: Its theoretical basis,limitations and new insights from remedies

The Gibson-Ashby (G-A) model has been instrumental in the design of additively manufactured (AM-ed) metal lattice materials or mechanical metamaterials. The first part of this work reviews the proposition and formulation of the G-A model and emphasizes that the G-A model is only applicable to low-density lattice materials with strut length-to-diameter ratios greater than 5. The second part evaluates the applicability of the G-A model to AM-ed metal lattice materials and reveals the fundamental disconnections between them. The third part assesses the deformation mechanisms of AM-ed metal lattices in relation to their strut length-to-diameter ratios and identifies that AM-ed metal lattices deform by concurrent bending, stretching, and shear, rather than just stretching or bending considered by the G-A model. Consequently, mechanical property models coupling stretching, bending and shear deformation mechanisms are developed for various lattice materials, which show high congruence with experimental data. The last part discusses new insights obtained from these remedies into the design of strong and stiff metal lattices. In particular, we recommend that the use of inclined struts be avoided.     

Transverse localization in disordered lattices containing left-handed metamaterials

A numerical study is reported of the propagation of an initially localized wave in a one-dimensional disordered lattice composed of left-handed metamaterials. We first consider the structure made of right-handed and left-handed materials arranged periodically. By allowing disorder in the refractive index of the right-handed materials, the injected wave becomes localized as propagating through the disordered lattice. Then, we consider another photonic lattice comprising only left-handed metamaterials. It is found that the inclusion of disorder in the negative refractive index of the constituents of the system leads to transverse Anderson localization. We also investigate the dispersion effect of metamaterials on the localization behavior. It is demonstrated that inclusion of a dispersive metamaterial in the disordered photonic lattices causes the quality of transverse localization to enhance with increasing wavelength.     

Additive Manufacturing of Composite Foam Metamaterial Springs for Vibration Isolation

This research introduces a novel approach for reducing the vibrations experienced by passengers in vehicles using metamaterials embedded in polyurethane foam to improve the existing vibration isolation capacity of car seats. An exploration of quasizero and negative stiffness metamaterials is conducted to develop metamaterial springs that exhibit a region of high-static and low-dynamic stiffness to achieve vibration isolation. Metamaterials are developed using low-cost open-source additive manufacturing methods and thermoplastic polyurethane filament. This investigation follows a process of determining the geometric, material, and systemic design requirements, to identify the quasizero and negative-stiffness force–displacement regions. Small-scale models of a car seat are developed by embedding the designed metamaterials into different grades of polyurethane foam and completing static and dynamic testing. The results demonstrate practical applications for implementing metamaterial springs into polyurethane foam to enhance vibration isolation under dynamic loading. The developed material library and the key geometric variables in the metamaterial design allow for application-specific solutions where the selection of the appropriate metamaterial and foam combination can be tailored to suit the system requirements.