Titania Lattice Research Articles

Effect of the lattice structures on mechanical characterisation of additively manufactured Ti-6Al-4V for biomedical application

ABSTRACT In the last decades, most investigations in titanium bone implantology have applied lattice structures instead of dense materials to reduce weight and obtain the mechanical properties similar to human bones. However, there is still a need for more research on the optimal design of lattice titanium implants with proper mechanical behaviour and heat treatment investigations, which directly affects the mechanical, microstructural, and morphological characteristics. The present study aims to examine the effect of densities and unit cell sizes for Selective Laser Melting (SLM)-printed lattice structures created by MSLattice. TPMS lattice structures including Diamond, Gyroid, and Primitive generated by MSLattice software were subsequently printed using Ti-6Al-4 V ELI. Tensile testing of DTi (dense) produced an ultimate tensile strength of 1241.58 ± 23.92 MPa and a Yield strength of 1151 ± 8.6 MPa, while its compression test resulted in an ultimate value of 1424.8 ± 20.13 MPa. The increase in density from 20% to 30% has resulted in a doubling of some mechanical properties. The lattice structure of the Gyroid at 30% density presented a UCS value of 143.96 ± 0.89 MPa as the highest, while that of the Diamond at 20% density presented the lowest with 46.89 ± 0.43 MPa. The values for energy absorption and plateau stress follow in a precise sequence.

Prior implantation of hydrogen as a mechanism to delay helium bubbles, blistering, and exfoliation in titanium

This study explores the delaying of the formation of helium bubbles and blisters in pure titanium by hydrogen pre-implantation. Titanium, implanted with helium (40 KeV, 5 × 1017 ions/cm²), exhibited large bubbles that cause exfoliation after heat treatment, whereas hydrogen pre-implantation inhibited bubble growth at room temperature and reduced the exfoliation after heat treatment.In the samples pre-implanted with hydrogen, we found evidence of helium diffusion delay by: (a) a fourfold reduction in bubble pressure (b) faceted cavities in the samples (c) a smaller increase in titanium lattice parameters (d) a 16-fold reduction in average bubble size and a sixfold reduction in bubble area fraction (e) a more than twofold decrease in exfoliation (f) a tendency toward the formation of larger bubbles as a result of heat treatment. We believe that it is reasonable to assume that the inhibition of helium diffusion between tetrahedral interstitial lattice sites takes place because of the occupation of the intermediate octahedral sites by hydrogen atoms.Evidence for the opposite effect, that is inhibition of the diffusion of hydrogen in the presence of helium, is found in the retention of hydrogen in the specimens at elevated temperatures. This retention allowed the existence of titanium hydride after heat treatment at 680 °C. The present study sheds light on the intricate interplay between hydrogen and helium in titanium, providing insights into mechanisms that can potentially mitigate helium-induced damage in materials.

Hybrid Single Lap Joints between 3D Printed Titanium Lattices and CFRP Composites: Experimental and Numerical Insights

In the contemporary emphasis on weight reduction, the utilization of advanced materials like Carbon Fiber Reinforced Polymers (CFRPs) and cutting-edge technologies such as 3D printing of metal is increasingly crucial. This study delves into the junction of CFRP and titanium, aiming to conduct Single Lap shear tests on specimens featuring a co-lamination of long fiber composite onto a metal lattice structure. Different specimens with different dimensions of the Simple Cubic (SC) unit cell were subjected to testing. A microscope investigation facilitated an exploration of junction failure and epoxy resin infiltration into the lattice substrate. Employing an efficient 2D Finite Element Model, the homogenization process yielded theoretical models underestimating the Young Modulus by approximately 10% compared to real specimens. Despite the challenges in bonding titanium and CFRP, the novel junction exhibited a shear stress of 17.25 MPa, which is nearly equivalent to those of a co-lamination between sandblasted steel and CFRP, that is 17.15 MPa.

The coupled effect of aspect ratio and strut micro-deformation mode on the mechanical properties of lattice structures

Lattice structures have been integrated into various industrial applications owing to their unique compressive properties. Mechanical characterisation is usually done by testing a small specimen which is assumed representative of the utilised lattice. A specimen's aspect ratio (height to diameter/width ratio) is known to affect compressive properties in various engineering materials, yet its influence in lattices has not been investigated thoroughly. In this study, titanium lattice specimens designed with different aspect ratios (ranging from 0.5 to 3.0) and four different topologies (displaying bend and stretch-dominated micro-deformation modes) were fabricated using powder bed fusion and tested in quasi-static compression. Their compressive properties and failure modes were evaluated using acquired stress-strain curves and digital image correlation (DIC) analysis. Reducing the aspect ratio in the bend-dominated lattices increased the measured stiffness of the specimens by up to 40%. Conversely, increasing the aspect ratio of the stretch dominated lattices increased the measured stiffness of the specimens by up to 30%. For both topology types, decreasing the aspect ratio increased the measured strength of the specimens, but the effect was less than that observed for stiffness. Different responses were attributed to gradient strain accumulation and different failure patterns (densification versus shear banding) that were observed depending on the combination of aspect ratio and topology. These findings are particularly important for better predicting the mechanical behaviour of lattice-based components that have aspect ratios outside the range of conventional test specimens.

Build parameter influence on strut thickness and mechanical performance in additively manufactured titanium lattice structures

Additively manufactured lattices have been adopted in applications ranging from medical implants to aerospace components. For solid AM components, the effect of build parameters has been well studied but comparably little attention has been paid to the influence of build parameters on lattice performance. For this project, the main aim was to evaluate static compressive mechanical performance of regular and stochastic lattices as a function of build parameters. The second aim was to compare strut dimensions of the metal lattice structures as build parameters were changed. Both regular and stochastic lattices were fabricated with a designed strut diameter of either 200 μm or 300 μm on a laser powder bed fusion machine. A range of laser power (140–180 W), scan speed (1700–2100 mm/s), and laser offset (0–45 μm) were used in fabricating each lattice. Compression tests were performed following the ISO 13314 (2011) standard to measure modulus, yield strength, and ultimate compressive strength values. Laser power adjustments produced the most significant effect on lattice performance. A change of 50 W resulted in roughly a 2X increase in maximum load and modulus for both regular and stochastic lattice structures. Regular lattice structures had a higher mechanical response during the mechanical evaluation. Internal strut diameters varied between build parameters as well, with laser offset adjustments producing the most noticeable change in strut geometry between lattice samples. These findings suggest that build parameter optimization, in lieu of using OEM parameters developed for solid structures, is necessary to ensure the optimum mechanical performance of AM lattice structures.

Изменение состава твердых нестехиометрических соединений методом ионного переноса

The paper presents results of measuring electron and ion transfer numbers of titanium hydride, carbide and nitride. It is shown that these compounds had mixed electron-ionic (anionic) conductivity. The dependences of the ion transfer number on the non-metal content in titanium carbide and nitride were obtained, and the change of the non-metal content under the influence of an electric field was studied. The non-metal atoms in non-stoichiometric titanium carbide and nitride were located in the octahedral voids of the titanium cubic lattice, forming a non-metal sublattice. Non-stoichiometric titanium hydride had a fluorite-type cubic crystal lattice, and the hydrogen atoms were located in the tetrahedral voids of the cubic titanium lattice. In titanium boride, ionic conductivity appeared near compounds of stoichiometric composition. It is shown that the formation of interstitial phases corresponded to the Hegg criterion. Due to the existence of vacancies in the non-metal sublattice, ion transfer was possible under the influence of an electric field, resulting in a chemical composition change of non-stoichiometric compounds. Analysis of the physicochemical properties of non-stoichiometric transition metal compounds was carried out as an opportunity to detect the ionic conductivity of carbides, nitrides and oxides.

Effect of chemical–electrochemical surface treatment on the roughness and fatigue performance of porous titanium lattice structures

Additive manufacturing (AM) has enabled the fabrication of extremely complex components such as porous metallic lattices, which have applications in aerospace, automotive, and in particular biomedical devices. The fatigue resistance of these materials is currently an important limitation however, due to manufacturing defects such as semi-fused particles and weld lines. In this work a chemical–electrochemical surface treatment (Hirtisation®) is used for post-processing of Ti-6Al-4V lattices, reducing the strut surface roughness (Sa) from 12 to 6 μm, removing all visible semi-fused particles. The evenness of this treatment in lattices with relative density up to 18.3% and treatment depth of 6.5 mm was assessed, finding no evidence of reduced effectiveness on internal surfaces. After normalising to quasi-static mechanical properties to account for material losses during hirtisation (34%–37% reduction in strut diameter), the fatigue properties show a marked improvement due to the reduction in surface roughness. Normalised high cycle fatigue strength increased from around 0.1 to 0.16-0.21 after hirtisation, an average increase of 80%. For orthopaedic implant devices where matching the stiffness of surrounding bone is crucial, the fatigue strength to modulus ratio is a key metric. After hirtisation the fatigue strength to modulus ratio increased by 90%, enabling design of stiffness matched implant materials with greater fatigue strength. This work demonstrates that hirtisation is an effective method for improving the surface roughness of porous lattice materials, thereby enhancing their fatigue performance.

Frequency dependent fatigue behaviour of additively manufactured titanium lattices

Additively manufactured (AM) porous titanium lattices, with their ability to match the mechanical properties of bone and avoid stress shielding, are a popular candidate material for orthopaedic implants. Such implants are now emerging as treatments for conditions like osteoarthritis and fixation of bone fractures. Fatigue tests are critical due to the cyclic loading environment and must be carried out at an accelerated loading rate to simulate many years of use. Tests are typically performed with servohydraulic instruments, which limits the cyclic compression to relatively low frequencies (15 Hz). Fatigue testing at a higher frequency would accelerate research, however, may introduce phenomena such as heat accumulation and strain rate effects. In this study the fatigue behaviour of a pure titanium stochastic lattice was determined at two test frequencies, 15 Hz and 110 Hz. Testing was conducted using an electromechanical dynamic system. The fatigue strengths at 106 cycles were 5.607 ± 0.106 MPa and 5.764 ± 0.214 MPa at 15 Hz and 110 Hz respectively. A hypothesis t-test at a 95% confidence level stated that there was significant evidence that the population means were not the same, demonstrating evidence of a difference in fatigue strength with testing frequency. However, we can conclude that the 2.8% increase in fatigue strength due to test frequency effects is inconsequential relative to the time saved (16 h per test) and typical batch-to-batch variability in fatigue strength of approximately 12%. The results of this study should help accelerate research into the fatigue properties of AM porous lattices.

Comparative Analysis of Bone Ingrowth in 3D-Printed Titanium Lattice Structures with Different Patterns.

In this study, metal 3D printing technology was used to create lattice-shaped test specimens of orthopedic implants to determine the effect of different lattice shapes on bone ingrowth. Six different lattice shapes were used: gyroid, cube, cylinder, tetrahedron, double pyramid, and Voronoi. The lattice-structured implants were produced from Ti6Al4V alloy using direct metal laser sintering 3D printing technology with an EOS M290 printer. The implants were implanted into the femoral condyles of sheep, and the animals were euthanized 8 and 12 weeks after surgery. To determine the degree of bone ingrowth for different lattice-shaped implants, mechanical, histological, and image processing tests on ground samples and optical microscopic images were performed. In the mechanical test, the force required to compress the different lattice-shaped implants and the force required for a solid implant were compared, and significant differences were found in several instances. Statistically evaluating the results of our image processing algorithm, it was found that the digitally segmented areas clearly consisted of ingrown bone tissue; this finding is also supported by the results of classical histological processing. Our main goal was realized, so the bone ingrowth efficiencies of the six lattice shapes were ranked. It was found that the gyroid, double pyramid, and cube-shaped lattice implants had the highest degree of bone tissue growth per unit time. This ranking of the three lattice shapes remained the same at both 8 and 12 weeks after euthanasia. In accordance with the study, as a side project, a new image processing algorithm was developed that proved suitable for determining the degree of bone ingrowth in lattice implants from optical microscopic images. Along with the cube lattice shape, whose high bone ingrowth values have been previously reported in many studies, it was found that the gyroid and double pyramid lattice shapes produced similarly good results.

Electropolishing influence on biocompatibility of additively manufactured Ti-Nb-Ta-Zr: in vivo and in vitro

Balling defect of the additively manufactured titanium lattice implants easily leads to muscle tissue rejection, which might cause failure of implantation. Electropolishing is widely used in surface polishing of complex components and has potential to deal with the balling defect. However, a clad layer could be formed on the surface of titanium alloy after electropolishing, which may affect the biocompatibility of the metal implants. To manufacture lattice structured β-type Ti-Ni-Ta-Zr (TNTZ) for bio-medical applications, it is necessary to investigate the impact of electropolishing on material biocompatibility. In this study, animal experiments were conducted to investigate the in vivo biocompatibility of the as-printed TNTZ alloy with or without electropolishing; and proteomics technology was used to elaborate the results. The following conclusions were drawn: (a) a 30% oxalic acid electropolishing treatment was effective in solving balling defects, and ~21 nm amorphous clad layer would be formed on the surface of the material after polishing; (b) the electropolished TNTZ suggested decreased cell cytotoxicity and improved blood biocompatibility as compared to as-printed TNTZ; (c) the amorphous clad layer could make a barrier to prevent Ta and Zr ions from penetrating into the muscle tissue, and could form a good tissue regeneration at the implantation site during 4 weeks, indicating that the electropolished TNTZ has the potential as implants; and (d) the cells attached to the electropolished TNTZ showed higher antioxidant capacity but less proliferation than attached to as-printed TNTZ.Graphical

Direct Evidence for Sulfur-Induced Deep Electron and Hole Traps in Titania and Implications for Photochemistry

Numerous studies show that sulfating titania narrows its band gap, facilitating longer-wavelength photochemistry, but there are contradictory reports on whether this improves or degrades UV photocatalysis and whether reactions proceed via electron- or hole-mediated pathways. The widely proposed role of sulfur is that it induces deep electron traps, which increase hole lifetimes. There is, however, no direct evidence for unoccupied states deep in the band gap. By contrast, transient absorption spectroscopy indicates that sulfur induces hole traps. We present experiments on sulfur-free and sulfated titania in which dissociation of hydrogen generates electrons that fill the lowest unoccupied states. The energy of these electrons relative to the conduction band minimum (CBM) was measured with diffuse reflectance spectroscopy in the infrared and UV–vis ranges. For all commercial sulfur-containing anatase materials, conversion of tridentate sulfate species into sulfur substituted on lattice sites occurred under highly oxidizing conditions above 400 °C and led to partially unoccupied states ∼2.8 eV below the CBM. We assign this deep trap state to sulfur atoms substituted on a titanium lattice site with a formal charge of S5+ in non-stoichiometric TiO2+x, based on agreement between the experiment and the predicted UV–vis spectrum of Harb, Sautet, and Raybaud, using HSE06 density functional perturbation theory. Our band structure calculations demonstrate that titanium vacancies (or excess oxygen) are necessary to create partially unoccupied states, and X-ray diffraction Rietveld analysis confirms the existence of these vacancies. The partial occupancy of these states, along with sulfur’s ability to switch oxidation states, explains their role as both electron (S5+ + e– → S4+) and hole (S5+ + h+ → S6+) traps, reconciling previous work. We discuss how relative rates of electron vs hole trapping can enhance or degrade activity depending on the pathway and the TiO2+x non-stoichiometry. We consider how increasing the dopant concentration can induce band bending or pin the Fermi level and shift the redox reactions that are thermodynamically accessible.

Titanium Lattice Structures Produced via Additive Manufacturing for a Bone Scaffold: A Review.

The progress in additive manufacturing has remarkably increased the application of lattice materials in the biomedical field for the fabrication of scaffolds used as bone substitutes. Ti6Al4V alloy is widely adopted for bone implant application as it combines both biological and mechanical properties. Recent breakthroughs in biomaterials and tissue engineering have allowed the regeneration of massive bone defects, which require external intervention to be bridged. However, the repair of such critical bone defects remains a challenge. The present review collected the most significant findings in the literature of the last ten years on Ti6Al4V porous scaffolds to provide a comprehensive summary of the mechanical and morphological requirements for the osteointegration process. Particular attention was given on the effects of pore size, surface roughness and the elastic modulus on bone scaffold performances. The application of the Gibson-Ashby model allowed for a comparison of the mechanical performance of the lattice materials with that of human bone. This allows for an evaluation of the suitability of different lattice materials for biomedical applications.

Quasi-static compressive behaviors of large-size titanium lattice sandwich structure based on pulse hot-wire arc additive manufacturing

Large-size lattice sandwich structure (LSS) has broad application prospects in the industrial field because of its specific stiffness and high strength. Quasi-static compression behavior is one of the basic mechanical properties of LSS. In this paper, large size titanium pyramid lattice sandwich structures were fabricated by pulse hot-wire arc additive manufacturing (PHWAAM). The mechanical properties and failure modes of pyramid LSS were studied by quasi-static axial compression tests. Theoretical and experimental analyses showed that the compression strength of 4-cells LSS differs greatly from that of 5-cells LSS, and the specific strength and specific stiffness also differ significantly. 5-cells LSS has better compression behavior, strength is 608.23 MPa higher than the 4-cells LSS. The process of lattice damage during the experiment was observed, and the failure mode was analyzed by theoretical calculation together with metallography and fracture. The main failure mode is brittle fracture, but there is plastic deformation in some lattice cells. The compression properties of the two kinds of LSS are studied by finite element method (FEM) and compared with the theoretical and experimental results. The research findings presented in this study provide a concise and effective guidance for quasi-static compressive behaviors of large-size LSS. The proposed conclusion is of great significance to the explore of the mechanical properties of LSS manufactured by WAAM.

Design, Simulation, and Mechanical Testing of 3D-Printed Titanium Lattice Structures

Lattice structure topology is a rapidly growing area of research facilitated by developments in additive manufacturing. These low-density structures are particularly promising for their medical applications. However, predicting their performance becomes a challenging factor in their use. In this article, four lattice topologies are explored for their suitability as implants for the replacement of segmental bone defects. The study introduces a unit-cell concept for designing and manufacturing four lattice structures, BCC, FCC, AUX, and ORG, using direct melt laser sintering (DMLS). The elastic modulus was assessed using an axial compression strength test and validated using linear static FEA simulation. The outcomes of the simulation revealed the disparity between the unit cell and the entire lattice in the cases of BCC, FCC, and AUX, while the unit-cell concept of the full lattice structure was successful in ORG. Measurements of energy absorption obtained from the compression testing revealed that the ORG lattice had the highest absorbed energy (350 J) compared with the others. The observed failure modes indicated a sudden collapsing pattern during the compression test in the cases of BCC and FCC designs, while our inspired ORG and AUX lattices outperformed the others in terms of their structural integrity under identical loading conditions.

Comparative analysis of the subsidence of solid polyetheretherketone (PEEK) and 3D printed lattice titanium interbody fusion cages

Spinal interbody fusion cages are commonly used to treat various spinal conditions, but their traditional manufacturing methods have limitations in customization and fitting. With the advancement of 3D printing, it is now possible to design and manufacture interbody fusion cages with previously unachievable features and structures. Southern Medical™ is investigating the technical feasibility of 3D-printed cages based on their existing designs and exploring the new features and capabilities enabled by additive manufacturing (AM). The mechanical performance in the subsidence of the 3D-printed devices will be compared to their existing devices as one of the feasibility points for the additively manufactured implants. A gyroid structure is used as the inner lattice of the structures. To investigate the performance of the cages with the new gyroid lattices, subsidence testing according to the ASTM F2267 methods was conducted to compare existing cages to the 3D-printed cages. The 3D printed devices outperformed the PEEK counterparts with a higher test block stiffness of 0.81 kN/mm compared to 0.55 kN/mm.

Mechanical Properties of LPBF-Built Titanium Lattice Structures—A Comparative Study of As-Built and Hot Isostatic Pressed Structures for Medical Implants

We compare different lattice structures with various elementary cell sizes built by laser powder bed fusion with and without hot isostatic pressing as post treatment. Cylindrical lattice structures are mechanically tested upon static and dynamic load in order to achieve high elasticity, high fracture strength and a high number of cycles to failure with respect to applications as medical implants. Evaluating the Young’s modulus, a high stiffness for the body diagonal structure and a low fracture stress for the G-structure are measured. Hot isostatic pressing results in a higher Young’s modulus and is ambiguous in terms of fractural stress. While samples without hot isostatic pressing reveal a shear fracture, the hot isostatic pressed samples have a high ductile area where the lattice layers are wrapped and pressed into the underlying layers without a fracture. Under dynamic load, the samples without hot isostatic pressing mostly are unable withstand 106 cycles at typical loads of the human body. Hot isostatic pressing has no significant influence on the strength at high loads and low cycle numbers, but at low loads all samples survived 106 cycles. As a consequence, dode-thick and rhombic dodecahedrons with 2 mm and 1.5 mm lattice size after hot isostatic pressing are recommended for medical implants because of the high elasticity, high fracture stress and high resistance against dynamic loads, which fulfill implant requirements.

Preparation of Iron-Doped Titania Nanoparticles and Their UV-Blue Light-Shielding Capabilities in Polyurethane.

It is well known that ultraviolet (UV) and blue light cause a series of health problems and damages to polymer materials. Therefore, there are increasing demands for UV-blue light-shielding. Herein, a new type of iron-doped titania (Fe-TiO2) nanoparticle was synthesized. Fe-TiO2 nanoparticles with small particle size (ca. 10 nm) are composed of anatase and brookite. The iron element is incorporated into the lattice of titania and forms a hematite phase (α-Fe2O3). The iron doping imparted full-band UV and blue light absorption to Fe-TiO2 nanoparticles, and greatly suppressed the photocatalytic activity. The prepared Fe-TiO2/polyurethane (PU) films exhibited prominent UV-blue light-shielding performance and high transparency, which showed great potential in light-shielding fields.

A Study on the Shape and Dimensional Accuracy of Additively Manufactured Titanium Lattice Structures for Orthopedic Purposes

The deviation between the designed lattice structures and the 3D-printed ones has been studied in this research. Three types of lattice structures were designed using the SpaceClaim application in the ANSYS software and then fabricated using Direct Metal Laser Sintering (DMLS) via EOS M 290 3D printer. Considering the orthopedic application, Ti6Al4V alloy of grade 23 was selected as a material for all samples of the structures. A thorough comparison was done on the volume, mass, and porosity to effectively map the possible deviations between the designed and the printed version. The shape accuracy of the 3D printing process was discussed during the study. As the complexity of the shape of the unit cell increases, the accuracy of the printing process becomes lower. Dimensional accuracy in the XY plane is higher than accuracy in the Z plane. Simple unit cell shape was proven to be more accurate in the 3D printing process.

Enhancing specific energy absorption of additively manufactured titanium lattice structures through simultaneous manipulation of architecture and constituent material

Titanium lattice structures have found a wide range of lightweight applications. However, lattice structures made from the commonly-used commercially pure titanium (CP−Ti) and Ti−6Al−4V exhibit either low strength or post-yielding softening/collapse under uniaxial compression, making them less attractive to energy absorbing applications. In the present work, a series of titanium gyroid lattice structures have been designed and additively manufactured by laser powder bed fusion ( L -PBF) to enhance the specific energy absorption (SEA) through manipulation of the architecture and the constituent material. Experimental results show that tailoring the sheet thickness gradient of gyroid lattice structures enables the transformation of the macroscopic deformation mode from hardening followed by softening, which is commonly seen in lattice structures, to continuous hardening. The addition of MgO nanoparticles to CP−Ti feedstock further improves the yield strength through oxygen solute strengthening, while maintaining the continuous hardening behaviour without any post-yielding softening or collapse. As a result, when both sheet thickness gradient and MgO are introduced, the SEA of the uniform gyroid lattice structure is enhanced by approximately 63% due to the combination of continuous hardening behaviour and high strength. Finite element analysis based on the modified volumetric hardening model has been performed to shed light on the underlying mechanism that governs the continuous hardening behaviour. This study demonstrates the tremendous potential of marrying architecture engineering with material design to create high performance lightweight lattice structures by L -PBF.

Viscoelastic Damping and Wave Cutoff of Titanium Alloy and Lattices

3D printed titanium alloy Ti5553 solid and octet truss lattice specimens were studied via resonant ultrasound spectroscopy, free decay of vibration and quasi-static methods to determine viscoelastic damping. Damping in solid alloy and a lattice was between 10−4 and 10−3. Much of the damping at high sonic frequency is attributed to stress induced heat flow between heterogeneities due to 3D printing. Pulsed wave ultrasound experiments disclosed reverberation in the cell structure of the lattice. Continuous wave ultrasound experiments showed that the transmissibility in the lattice rolls off beginning at about 50 kHz and becomes negligible above 110 kHz. By contrast, the polymer PMMA, though it is viscoelastic, readily transmits waves up to 1 MHz. The cut off frequency in the lattice is associated with the structure size, not intrinsic damping in the alloy. The octet truss lattice, in addition to providing good mechanical performance, is also an ultrasonic metamaterial. This article is protected by copyright. All rights reserved.