Auxetic mechanical metamaterials: from soft to stiff

Auxetic mechanical metamaterials are artificially architected materials that possess negative Poisson’s ratio,demonstrating transversal contracting deformation under external vertical compression loading.Their physical properties are mainly determined by spatial topological configurations.Traditionally,classical auxetic mechanical metamaterials exhibit relatively lower mechanical stiffness,compared to classic stretching dominated architectures.Nevertheless,in recent years,several novel auxetic mechanical metamaterials with high stiffness have been designed and proposed for energy absorption,load-bearing,and thermal-mechanical coupling applications.In this paper,mechanical design methods for designing auxetic structures with soft and stiff mechanical behavior are summarized and classified.For soft auxetic mechanical metamaterials,classic methods,such as using soft basic material,hierarchical design,tensile braided design,and curved ribs,are proposed.In comparison,for stiff auxetic mechanical metamaterials,design schemes,such as hard base material,hierarchical design,composite design,and adding additional load-bearing ribs,are proposed.Multi-functional applications of soft and stiff auxetic mechanical metamaterials are then reviewed.We hope this study could provide some guidelines for designing programmed auxetics with specified mechanical stiffness and deformation abilities according to demand.

The design, manufacture and application of multistable mechanical metamaterials-a state-of-the-art review

Multistable mechanical metamaterials are a type of mechanical metamaterials with special features,such as reusability,energy storage and absorption capabilities,rapid deformation,and amplified output forces.These metamaterials are usually realized by series and/or parallel of bistable units.They can exhibit multiple stable configurations under external loads and can be switched reversely among each other,thereby realizing the reusability of mechanical metamaterials and offering broad engineering applications.This paper reviews the latest research progress in the design strategy,manufacture and application of multistable mechanical metamaterials.We divide bistable structures into three categories based on their basic element types and provide the criterion of their bistability.Various manufacturing techniques to fabricate these multistable mechanical metamaterials are introduced,including mold casting,cutting,folding and three-dimensional/4D printing.Furthermore,the prospects of multistable mechanical metamaterials for applications in soft driving,mechanical computing,energy absorption and wave controlling are discussed.Finally,this paper highlights possible challenges and opportunities for future investigations.The review aims to provide insights into the research and development of multistable mechanical metamaterials.

Multistable Mechanical Metamaterials:A Brief Review

Over the past decade,multistable mechanical metamaterials have been widely investigated because of their novel shape reconfigurability and programmable energy landscape.The ability to reversibly reshape among diverse stable states with different energy levels represents the most important feature of the multistable mechanical metamaterials.We summarize main design strategies of multistable mechanical metamaterials,including those based on self-assembly scheme,snap-through instability,structured mechanism and geometrical frustration,with a focus on the number and controllability of accessible stable states.Then we concentrate on unusual mechanical properties of these multistable mechanical metamaterials,and present their applications in a wide range of areas,including tunable electromagnetic devices,actuators,robotics,and mechanical logic gates.Finally,we discuss remaining challenges and open opportunities of designs and applications of multistable mechanical metamaterials.

Architectural Design and Additive Manufacturing of Mechanical Metamaterials:A Review

Mechanical metamaterials can be defined as a class of architected materials that exhibit unprecedented mechanical properties derived from designed artificial architectures rather than their constituent materials.While macroscale and simple layouts can be realized by conventional top-down manufacturing approaches,many of the sophisticated designs at various length scales remain elusive,due to the lack of adequate manufacturing methods.Recent progress in additive manufacturing(AM)has led to the realization of a myriad of novel metamaterial concepts.AM methods capable of fabricating microscale architectures with high resolution,arbitrary complexity,and high feature fidelity have enabled the rapid development of architected meta materials and drastically reduced the design-computation and experimental-validation cycle.This paper first provides a detailed review of various topologies based on the desired mechanical properties,including stiff,strong,and auxetic(negative Poisson’s ratio)metamaterials,followed by a discussion of the AM technologies capable of fabricating these metamaterials.Finally,we discuss current challenges and recommend future directions for AM and mechanical metamaterials.

Design,fabrication,and characterization of hierarchical mechanical metamaterials

Natural mechanical materials,such as bamboo and bone,often exhibit superior specific mechanical properties due to their hierarchical porous architectures.Using the principle of hierarchy as inspiration can facilitate the development of hierarchical mechanical metamaterials(HMMs)across multiple length scales via 3D printing.In this work,we propose self-similar HMMs that combine octet-truss(OCT)architecture as the first and second orders,with cubic architecture as the third or more orders.These HMMs were fabricated using stereolithography 3D printing,with the length sizes ranging from approximately 200µm to the centimeter scale.The compressive stress–strain behaviors of HMMs exhibit a zigzag characteristic,and the toughness and energy absorption can be significantly enhanced by the hierarchical architecture.The compressive moduli are comparable to that of natural materials,and the strengths are superior to that of most polymer/metal foams,alumina hollow/carbon lattices,and other natural materials.Furthermore,the flexural stress–strain curves exhibit a nonlinear behavior,which can be attributed to the hierarchical architecture and local damage propagation.The relatively high mechanical properties can be attributed to the synergistic effect of the stretch-dominated OCT architecture and the bending-dominated cube architecture.Lastly,an ultralight HMM-integrated unmanned aerial vehicle(HMM-UAV)was successfully designed and printed.The HMM-UAV is~85%lighter than its bulk counterpart,remarkably extending the flight duration time(~53%).This work not only provides an effective design strategy for HMMs but also further expands the application benchmark of HMMs.

Design and mechanical properties analysis of a cellular Waterbomb origami structure

Cellular structures are commonly used to design energy-absorbing structures,and origami structures are becominga prevalent method of cellular structure design.This paper proposes a foldable cellular structure based on theWaterbomb origami pattern.The geometrical configuration of this structure is described.Quasi-static compressiontests of the origami tube cell of this cellular structure are conducted,and load-displacement relationship curvesare obtained.Numerical simulations are carried out to analyze the effects of aspect ratio,folding angle,thicknessand number of layers of origami tubes on initial peak force and specific energy absorption(SEA).Calculationformulas for initial peak force and SEA are obtained by the multiple linear regression method.The degree ofinfluence of each parameter on the mechanical properties of the single-layer tube cell is compared.The resultsshow that the cellular structure exhibits negative stiffness and periodic load-bearing capacity,as well as foldingangle has the most significant effect on the load-bearing and energy-absorbing capacity.By adjusting the designparameters,the stiffness,load-bearing capacity and energy absorption capacity of this cellular structure can beadjusted,which shows the programmable mechanical properties of this cellular structure.The foldability andthe smooth periodic load-bearing capacity give the structure potential for application as an energy-absorbing structure.

Mechanical Janus lattice with plug-switch orientation

In recent years,materials with asymmetric mechanical response properties(mechanical Janus materials)have been found possess numerous potential applications,i.e.shock absorption and vibration isolation.In this study,we propose a novel mechanical Janus lattice whose asymmetric mechanical response can be switched in orientation by a plug.Through finite element analysis and experimental verification,this lattice exhibits asymmetric displacement responses to symmetric forces.Furthermore,with such a plug structure inside,individual lattices can switch the orientation of asymmetry and thus achieve reprogrammable design of a mechanical structure with chained lattices.The reprogrammable asymmetry of this material will offer multiple functions in design of mechanical metamaterials.

Mechanical design and analysis of bio-inspired reentrant negative Poisson’s ratio metamaterials with rigid-flexible distinction

Aiming at achieving tunable reentrant structures with rigidity and uniformity,respectively,the C-shaped and S-shaped reentrant metamaterials were proposed by the bionic design of animal structures.Utilizing beam theory and energy methodology,the analytical expressions of the equivalent elastic modulus of the metamaterials were derived.Differences in deformation modes,mechanical properties,and energy absorption capacities were characterized by using experiments and the finite element analysis method.The effects of ligament angle and thickness on the mechanical characteristics of two novel metamaterials were investigated by using a parametric analysis.The results show that the stiffness,deformation mode,stress-strain curve,and energy absorption effects of three metamaterials are significantly different.This design philosophy can be extended from 2D to 3D and is applicable at multiple dimensions.

Plate-based cylinder metamaterial with negative Poisson's ratio and outstanding mechanical performance

Plate-based cellular materials exhibit greater stiffness and strength than conventional cellular materials formed by struts.In this study,we designed and fabricated a plate-based auxetic cylinder metamaterial using high-resolution projection micro-stereolithography three-dimensional printing technique.Experiment and modeling results validated the auxetic behavior of the plate-based cylinder.The normalized Young’s modulus and yield strength of a four-layer auxetic cylinder are increased by 141%and 32%,respectively,compared with the conventional auxetic honeycomb.This study presents a universal strategy for fabricating plate-based auxetic metamaterials with appropriate mechanical performance for various structural applications.

New type of overrunning clutch based on curved-plate compression-torsion metamaterial

Overrunning clutches are unidirectional drive mechanisms that are widely used in transmission systems.However,existing overrunning clutches have complex structures,require high preparation accuracy,and fail after a certain degree of wear.To address these issues,we propose a new type of overrunning clutch consisting of a conical structure and novel compression-torsion conversion(CTC)metamaterial with curved plates.Theoretical calculations are employed to guide the material distribution and ensure the deformation coordination of the curved-plate CTC metamaterial for greater ultimate torque.The transmission mechanism of the proposed overrunning clutch is derived to guide the parameter selection of the CTC metamaterial and the conical structure.Experiments and finite element simulations reveal that the curved-plate CTC metamaterial features excellent CTC efficiency,flexibility,and transverse stiffness,which is conducive reducing the resistance of the overrunning state and ensures stability during operation.The unidirectional transmission system constructed with the new overrunning clutch shows reliable performances under working and overrunning states.The constructed overrunning clutch provides an effective one-way transmission method.The clutch with simple construction and self-compensated ability for wear exhibits great potential in miniaturized and lightweight equipment or robots.

Notch Flexure as Kirigami Cut for Tunable Mechanical Stretchability towards Metamaterial Application

Kirigami is an art of paper cutting,which can be used in mechanical metamaterials,actuators,and energy absorption based on its deployable and load-deflection characteristics.Traditional cuts with zero width produce undesirable plastic deformation or even tear fracture due to stress concentration in stretching.This study proposes to enlarge the cut width into a notch flexure,which is applied to an orthogonality-cutted kirigami sheet,which buckles out of plane into a 3D configuration patterns under uniaxial tension.The use of compliant beam as the notch makes the stress distribution around the cuts more uniform in both elastic and elastoplastic regime.The experimental and numerical results show that by tuning the geometric parameters of cuts and material properties of the sheets,the trigger condition of 3D patterns can be adjusted.Potential capability of tunable phononic wave propagation in this kirigami-inspired metamaterial is demonstrated.This design methodology offers a theoretical guide for kirigami-based structures.

Multifunctional application of nonlinear metamaterial with two-dimensional bandgap

Mechanical metamaterials with low-frequency and broadband bandgaps have great potential for elastic wave control.Inspired by the ancient window mullions,a novel plate-type metamaterial with a two-dimensional bandgap is designed.Based on the local resonance mechanism,the broadband low-frequency in-plane and out-of-plane bandgaps on the designed structure are realized.The bandgaps can be adjusted by the mass re-distribution of the main-slave resonators,the stiffness design of the support beam,and the adjustment of the excitation amplitude.A semi-analytical method is proposed to calculate the in-plane and out-of-plane bandgaps and the corresponding wave attenuation characteristics of the infinite periodic metamaterial.We explored how mass re-distribution,stiffness changes,and geometric nonlinearity influence the bandgap.Then,to verify the conclusions,we fabricated a finite periodic structure and obtained its wave transmission characteristics both numerically and experimentally.Finally,the designed metamaterial is applied to the waveguide control,elastic wave imaging,and vibration isolation.This study may provide new ideas for structural design and engineering applications of mechanical metamaterials.

Optimizing film thickness to delay strut fracture in high-entropy alloy composite microlattices

Incorporating high-entropy alloys(HEAs) in composite microlattice structures yields superior mechanical performance and desirable functional properties compared to conventional metallic lattices. However, the modulus mismatch and relatively poor adhesion between the soft polymer core and stiff metallic film coating often results in film delamination and brittle strut fracture at relatively low strain levels(typically below 10%). In this work, we demonstrate that optimizing the HEA film thickness of a CoCrNiFe-coated microlattice completely suppresses delamination,significantly delays the onset of strut fracture(~100% increase in compressive strain),and increases the specific strength by up to 50%. This work presents an efficient strategy to improve the properties of metal-composite mechanical metamaterials for structural applications.

Manufacturing size effect on the structural and mechanical properties of additively manufactured Ti-6Al-4V microbeams

The size effect of Ti-6Al-4V submillimeter structures manufactured by selective laser melting,which is critical for metallic mechanical metamaterials of unique mechanical properties,for example,nega-tive Poisson’s ratio and ultrahigh modulus,which show promise in biomedical,environmental,energy-related applications,has not been systematically investigated.Presented here are the quantification of the porosities by X-ray microtomography scans,texture analysis,and mechanical characterization of the addi-tively manufactured Ti-6Al-4V microbeams.We found linearly decreasing porosities,increasing mechan-ical properties,and increasing texture in the microbeam with increasing diameter from 250 to 500μm.The variation of microstructure in microbeams of different diameters and along the sample height,result-ing from the printing parameters and the thermal conditions,leads to the discrepancy between the be-havior observed in experiments and finite element simulation.Our results provide the structure-property-processing correlation to improve the manufacturing and prediction of the mechanical behavior of metal-lic mechanical metamaterials.

Planar bi-metallic lattice with tailorable coefficient of thermal expansion

A mechanical metamaterial that has a tailorable coefficient of thermal expansion(CTE)is promising for guaranteeing the reliability of electrical and optical instruments under thermal fluctuations.Despite growing research on the design and manufacturing of metamaterials with extraordinary CTEs,it remains challenging to achieve a nearly isotropic tailorable CTE while ensuring a sufficient load bearing capacity for applications,such as mechanical supporting frames.In this research,we propose a type of bi-metallic lattice whose CTE is artificially programmed from positive(75 ppm/K)to negative(−45 ppm/K),and whose equivalent modulus can be as high as 80 MPa.The bi-metallic lattice with a tailorable CTE in two orthogonal directions can be readily assembled without special modifications to construct large-scale planar structures with desired isotropic CTEs.A theoretical model that considers the actual configuration of the bi-metallic joint is developed;the model precisely captures the thermal deformations of lattice structures with varied geometries and material compositions.Guided by our theoretical design method,planar metallic structures that were manufactured using Al,Ti,and Invar alloy were experimentally characterized;the structures exhibited outstanding performance when compared with typical engineering materials.