Journal articles: 'Gyroid'

1

Keattitorn, Saranchana, Maria Carrillo-Munoz, and Bhisham Sharma. "Anomalous polarization in asymmetric gyroid structures." Journal of the Acoustical Society of America 151, no. 4 (April 2022): A97. http://dx.doi.org/10.1121/10.0010773.

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Recent studies show that structures with triply periodic minimal surfaces (TPMS) provide enhanced mechanical, acoustical, and energy abortion performance. Previously, we have shown that breaking the symmetry of the gyroid lattice—one of the most used TPMS geometry—results in the creation of directional and polarized bandgaps. Here, we focus on the effect of breaking symmetry on the effective wave speeds of the gyroid structure. We analyze the wave speeds of different asymmetric gyroid lattices using the finite element analysis approach. Our analysis shows that certain gyroid asymmetries result in the transverse waves propagating faster than the longitudinal waves in particular direction. Our research shows that breaking the symmetry leads to previously unobserved anomalous polarization of elastic waves in asymmetric gyroids.

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Winter, Benjamin, Benjamin Butz, Christel Dieker, Gerd E. Schröder-Turk, Klaus Mecke, and Erdmann Spiecker. "Coexistence of both gyroid chiralities in individual butterfly wing scales of Callophrys rubi." Proceedings of the National Academy of Sciences 112, no. 42 (October 5, 2015): 12911–16. http://dx.doi.org/10.1073/pnas.1511354112.

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The wing scales of the Green Hairstreak butterfly Callophrys rubi consist of crystalline domains with sizes of a few micrometers, which exhibit a congenitally handed porous chitin microstructure identified as the chiral triply periodic single-gyroid structure. Here, the chirality and crystallographic texture of these domains are investigated by means of electron tomography. The tomograms unambiguously reveal the coexistence of the two enantiomeric forms of opposite handedness: the left- and right-handed gyroids. These two enantiomers appear with nonequal probabilities, implying that molecularly chiral constituents of the biological formation process presumably invoke a chiral symmetry break, resulting in a preferred enantiomeric form of the gyroid structure. Assuming validity of the formation model proposed by Ghiradella H (1989) J Morphol 202(1):69–88 and Saranathan V, et al. (2010) Proc Natl Acad Sci USA 107(26):11676–11681, where the two enantiomeric labyrinthine domains of the gyroid are connected to the extracellular and intra-SER spaces, our findings imply that the structural chirality of the single gyroid is, however, not caused by the molecular chirality of chitin. Furthermore, the wing scales are found to be highly textured, with a substantial fraction of domains exhibiting the <001> directions of the gyroid crystal aligned parallel to the scale surface normal. Both findings are needed to completely understand the photonic purpose of the single gyroid in gyroid-forming butterflies. More importantly, they show the level of control that morphogenesis exerts over secondary features of biological nanostructures, such as chirality or crystallographic texture, providing inspiration for biomimetic replication strategies for synthetic self-assembly mechanisms.

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Dai, Rui, Dawei Li, Wenhe Liao, Haofan Sun, Yunlong Tang, and Qiong Nian. "Molecular dynamics simulations to understand the mechanical behavior of functional gradient nano-gyroid structures." Journal of Applied Physics 132, no. 13 (October 7, 2022): 135109. http://dx.doi.org/10.1063/5.0102297.

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Gyroid structure, a nature inspired cellular architecture, is under extensive exploration recently due to its structure continuity, uniform stress distribution under compression, and stable collapse mechanism during deformation. However, when combining with a functional gradient, the Gyroid structure can perform much different mechanical behavior from its homogeneous counterpart. Herein, bottom-up computational modeling is performed to investigate the mechanics of functional gradient nano-gyroid structure made of copper (Cu). Our work reveals that its mechanical properties degrade with a density that is much slower than those of homogeneous gyroid structure. The scaling of yield strength [Formula: see text] to the relative density [Formula: see text] for the functional gradient gyroid structure is in the factor of 1.5. Moreover, the layer-by-layer collapsing mechanism yields significantly better mechanical energy absorption ability. This study not only leads to insightful understanding of the deformation mechanisms in nonuniform gyroid structures but also promotes the development of the functional gradient cellular materials.

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Li, Dawei, Wenhe Liao, Ning Dai, and Yi Min Xie. "Comparison of Mechanical Properties and Energy Absorption of Sheet-Based and Strut-Based Gyroid Cellular Structures with Graded Densities." Materials 12, no. 13 (July 7, 2019): 2183. http://dx.doi.org/10.3390/ma12132183.

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Bio-inspired functionally graded cellular materials (FGCM) have improved performance in energy absorption compared with a uniform cellular material (UCM). In this work, sheet-based and strut-based gyroid cellular structures with graded densities are designed and manufactured by stereo-lithography (SLA). For comparison, uniform structures are also designed and manufactured, and the graded structures are generated with different gradients. The mechanical behaviors of these structures under compressive loads are investigated. Furthermore, the anisotropy and effective elastic modulus of sheet-based and strut-based unit gyroid cellular structures are estimated by a numerical homogenization method. On the one hand, it is found from the numerical results that the sheet-based gyroid tends to be isotropic, and the elastic modulus of sheet-based gyroid is larger than the strut-based gyroid at the same volume fraction. On the other hand, the graded cellular structure has novel deformation and mechanical behavior. The uniform structure exhibits overall deformation and collapse behavior, whereas the graded cellular structure shows layer-by-layer deformation and collapse behavior. Furthermore, the uniform sheet-based gyroid is not only stiffer but also better in energy absorption capacity than the uniform strut-based gyroid structure. Moreover, the graded cellular structures have better energy absorption capacity than the uniform structures. These significant findings indicate that sheet-based gyroid cellular structure with graded densities have potential applications in various industrial applications, such as in crashworthiness.

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Rammohan, Abhishek Vishwanath, Taeyong Lee, and V. B. C. Tan. "A Novel Morphological Model of Trabecular Bone Based on the Gyroid." International Journal of Applied Mechanics 07, no. 03 (June 2015): 1550048. http://dx.doi.org/10.1142/s1758825115500489.

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Human trabecular bone is known to be structurally very complex. The geometrical distribution of trabecular bone has major effects on its ability to perform its physiological function of load-bearing efficiently. Idealized unit cell models are very helpful in understanding the significance of micro-level properties on macro-level behavior. There is a need for a simple method to model trabecular bone, such that micro-level phenomena (like buckling) can be studied. We investigate a new model for trabecular bone, based on a minimal surface solid called a gyroid. The gyroid-based model is computationally easy to implement, and generates structures that possess strong morphometric and mechanical resemblance to real trabecular bone. We generated gyroid models for a range of volume fractions, representing trabecular bone samples obtained from various anatomic sites and ages. Finite element analysis was performed to obtain the mechanical properties of the gyroid structures. We calculated the small-strain elastic moduli values for each of the gyroid models and plotted these against corresponding apparent density. A power-law relationship was obtained for the gyroid models, in accordance with published studies on real trabecular bone mechanical behavior. The results showed that the gyroid could provide a suitable model for studying the effects of variations in trabecular structure on macro-level bone behavior.

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6

Grosse-Brauckmann, Karsten. "On Gyroid Interfaces." Journal of Colloid and Interface Science 187, no. 2 (March 1997): 418–28. http://dx.doi.org/10.1006/jcis.1996.4720.

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7

Naghavi, Seyed Ataollah, Haoyu Wang, Swastina Nath Varma, Maryam Tamaddon, Arsalan Marghoub, Rex Galbraith, Jane Galbraith, et al. "On the Morphological Deviation in Additive Manufacturing of Porous Ti6Al4V Scaffold: A Design Consideration." Materials 15, no. 14 (July 6, 2022): 4729. http://dx.doi.org/10.3390/ma15144729.

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Additively manufactured Ti scaffolds have been used for bone replacement and orthopaedic applications. In these applications, both morphological and mechanical properties are important for their in vivo performance. Additively manufactured Ti6Al4V triply periodic minimal surface (TPMS) scaffolds with diamond and gyroid structures are known to have high stiffness and high osseointegration properties, respectively. However, morphological deviations between the as-designed and as-built types of these scaffolds have not been studied before. In this study, the morphological and mechanical properties of diamond and gyroid scaffolds at macro and microscales were examined. The results demonstrated that the mean printed strut thickness was greater than the designed target value. For diamond scaffolds, the deviation increased from 7.5 μm (2.5% excess) for vertical struts to 105.4 μm (35.1% excess) for horizontal struts. For the gyroid design, the corresponding deviations were larger, ranging from 12.6 μm (4.2% excess) to 198.6 μm (66.2% excess). The mean printed pore size was less than the designed target value. For diamonds, the deviation of the mean pore size from the designed value increased from 33.1 μm (−3.0% excess) for vertical struts to 92.8 μm (−8.4% excess) for horizontal struts. The corresponding deviation for gyroids was larger, ranging from 23.8 μm (−3.0% excess) to 168.7 μm (−21.1% excess). Compressive Young’s modulus of the bulk sample, gyroid and diamond scaffolds was calculated to be 35.8 GPa, 6.81 GPa and 7.59 GPa, respectively, via the global compression method. The corresponding yield strength of the samples was measured to be 1012, 108 and 134 MPa. Average microhardness and Young’s modulus from α and β phases of Ti6Al4V from scaffold struts were calculated to be 4.1 GPa and 131 GPa, respectively. The extracted morphology and mechanical properties in this study could help understand the deviation between the as-design and as-built matrices, which could help develop a design compensation strategy before the fabrication of the scaffolds.

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Ashraf, Juveiriah M., Jing Fu, Kin Liao, Vincent Chan, and Rashid K. Abu Al-Rub. "Scalable synthesis, characterization and testing of 3D architected gyroid graphene lattices from additively manufactured templates." Journal of Micromechanics and Molecular Physics 06, no. 03 (September 2021): 13–24. http://dx.doi.org/10.1142/s2424913021430025.

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We have developed a novel, facile and architecturally versatile fabrication method for specially designed cellular graphene lattices using additively manufactured polymer-based gyroidal triply periodic minimal surface (TPMS) as the initial sacrificial scaffold. Three-dimensional (3D)-printed templates of the polymeric gyroid lattices were coated with a mixture of graphene oxide (GO) and hydrazine solution via the hydrothermal process, followed by drying and thermal etching of the polymer scaffold, which resulted in a neat reduced GO (rGO) lattice of the gyroidal TPMS structure. Scanning electron microscopy and micro-computed tomography were used to evaluate the morphology and size of the 3D rGO architectures, while a Raman response at 1360[Formula: see text]cm[Formula: see text] (D peak), 1589[Formula: see text]cm[Formula: see text] (G peak) and 2696[Formula: see text]cm[Formula: see text] (2D peak) verified the presence of rGO. Thermo–electro–mechanical properties of rGO gyroid lattices of different densities were characterized where the highest Young’s modulus recorded was 351[Formula: see text]kPa for a sample with a density of 45.9[Formula: see text]mg[Formula: see text][Formula: see text][Formula: see text]cm[Formula: see text]. The rGO gyroid lattice exhibits an electrical conductivity of 1.07[Formula: see text]S[Formula: see text][Formula: see text][Formula: see text]m[Formula: see text] and high thermal insulation property with a thermal conductivity of 0.102[Formula: see text]W[Formula: see text][Formula: see text][Formula: see text]m[Formula: see text][Formula: see text]K[Formula: see text]. It is demonstrated that the hydrothermal-assisted fabrication process is adaptable for different lattice architectures based on 3D-printed scaffolds and thus has wide functional applications.

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Salvatore, Stefano, Silvia Vignolini, Julian Philpott, Morgan Stefik, Ulrich Wiesner, Jeremy J. Baumberg, and Ullrich Steiner. "A high transmission wave-guide wire network made by self-assembly." Nanoscale 7, no. 3 (2015): 1032–36. http://dx.doi.org/10.1039/c4nr04485a.

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Polymer self-assembly of a 3D continuous gyroid morphology was replicated into a network consisting of hollow gold struts causing a strong reduction of optical absorption compared to solid struts with equal amount of Au per gyroid unit cell.

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10

Schick, M. "Avatars of the gyroid." Physica A: Statistical Mechanics and its Applications 251, no. 1-2 (March 1998): 1–11. http://dx.doi.org/10.1016/s0378-4371(97)00590-6.

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Vakrčka, Petr, Aleš Jíra, and Petra Hájková. "MECHANICAL TESTING AND NUMERICAL MODELLING OF POROUS STRUCTURES IMPROVING OSEINTEGRATION OF IMPLANTS." Acta Polytechnica CTU Proceedings 26 (March 17, 2020): 126–32. http://dx.doi.org/10.14311/app.2020.26.0126.

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Implants, such as dental, are ordinary devices in medical care nowadays, even though they are quite expensive. In the present study, the use of trabecular and gyroid structures as external layer of implants is examined. The advantage of porous structures compared to surface modification of compact implants is the possibility to be fabricated by additive manufacturing together with the whole implant. The additive manufacturing also allows us to produce various shapes with controlled porosity for bone ingrowth. The design of 6 types of trabecular and 4 types of gyroid structures is part of the study. The trabecular structures are strut-based, whereas the gyroid structures are based on a wall system. The study is focused on mechanical testing of samples which were 3D printed from the titanium alloy Ti6Al4V. The gyroid structures, which we evaluated as more reliable, were chosen for numerical modelling. Other observed advantages and disadvantages of the structures are also discussed.

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12

Schönhöfer, Philipp W. A., Laurence J. Ellison, Matthieu Marechal, Douglas J. Cleaver, and Gerd E. Schröder-Turk. "Purely entropic self-assembly of the bicontinuous Ia 3 d gyroid phase in equilibrium hard-pear systems." Interface Focus 7, no. 4 (June 16, 2017): 20160161. http://dx.doi.org/10.1098/rsfs.2016.0161.

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We investigate a model of hard pear-shaped particles which forms the bicontinuous Ia d structure by entropic self-assembly, extending the previous observations of Barmes et al. (2003 Phys. Rev. E 68 , 021708. ( doi:10.1103/PhysRevE.68.021708 )) and Ellison et al. (2006 Phys. Rev. Lett. 97 , 237801. ( doi:10.1103/PhysRevLett.97.237801 )). We specifically provide the complete phase diagram of this system, with global density and particle shape as the two variable parameters, incorporating the gyroid phase as well as disordered isotropic, smectic and nematic phases. The phase diagram is obtained by two methods, one being a compression–decompression study and the other being a continuous change of the particle shape parameter at constant density. Additionally, we probe the mechanism by which interdigitating sheets of pears in these systems create surfaces with negative Gauss curvature, which is needed to form the gyroid minimal surface. This is achieved by the use of Voronoi tessellation, whereby both the shape and volume of Voronoi cells can be assessed in regard to the local Gauss curvature of the gyroid minimal surface. Through this, we show that the mechanisms prevalent in this entropy-driven system differ from those found in systems which form gyroid structures in nature (lipid bilayers) and from synthesized materials (di-block copolymers) and where the formation of the gyroid is enthalpically driven. We further argue that the gyroid phase formed in these systems is a realization of a modulated splay-bend phase in which the conventional nematic has been predicted to be destabilized at the mesoscale due to molecular-scale coupling of polar and orientational degrees of freedom.

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Rosi, Giuseppe, Nicolas Auffray, and Christelle Combescure. "On the Failure of Classic Elasticity in Predicting Elastic Wave Propagation in Gyroid Lattices for Very Long Wavelengths." Symmetry 12, no. 8 (July 28, 2020): 1243. http://dx.doi.org/10.3390/sym12081243.

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In this work we investigate the properties of elastic waves propagating in gyroid lattices. First, we rigorously characterize the lattice from the point of view of crystallography. Second, we use Bloch–Floquet analysis to compute the dispersion relations for elastic waves. The results for very long wavelengths are then compared to those given by classic elasticity for a cubic material. A discrepancy is found in terms of the polarization of waves and it is related to the noncentrosymmetry of the gyroid. The gyroid lattice results to be acoustically active, meaning that transverse waves exhibit a circular polarization when they propagate along an axis of rotational symmetry. This phenomenon is present even for very long wavelengths and is not captured by classic elasticity.

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Jin, Sangwoo, Jinhwan Yoon, Kyuyoung Heo, Hae-Woong Park, Jehan Kim, Kwang-Woo Kim, Tae Joo Shin, Taihyun Chang, and Moonhor Ree. "Detailed analysis of gyroid structures in diblock copolymer thin films with synchrotron grazing-incidence X-ray scattering." Journal of Applied Crystallography 40, no. 5 (September 5, 2007): 950–58. http://dx.doi.org/10.1107/s0021889807037880.

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In this study, a grazing-incidence X-ray scattering (GIXS) formula was derived for gyroid structures formed in thin films supported on substrates. Two-dimensional GIXS patterns were measured for gyroid structures formed in polystyrene-b-polyisoprene (PS-b-PI) diblock copolymer nanometre-scale thin films supported on silicon substrates, and a quantitative analysis of the obtained two-dimensional GIXS data was conducted with the scattering formula. This analysis provided details (lattice parameter, width of the PS phase, positional distortion factor, orientation and orientation distribution) of the gyroid structures developed in the diblock copolymer thin films that are not easily obtained using conventional techniques. Moreover, it was possible to simulate complete and detailed two-dimensional GIXS patterns with the determined structure parameters.

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Sharp, Rachael, Matthew H. Pelletier, William R. Walsh, Cambre N. Kelly, and Ken Gall. "Corrosion Resistance of 3D Printed Ti6Al4V Gyroid Lattices with Varying Porosity." Materials 15, no. 14 (July 9, 2022): 4805. http://dx.doi.org/10.3390/ma15144805.

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Corrosion of medical implants is a possible failure mode via induced local inflammatory effects, systemic deposition and corrosion related mechanical failure. Cyclic potentiodynamic polarisation (CPP) testing was utilized to evaluate the effect of increased porosity (60% and 80%) and decreased wall thickness in gyroid lattice structures on the electrochemical behaviour of LPBF Ti6Al4V structures. The use of CPP allowed for the landmarks of breakdown potential, resting potential and vertex potential to be analysed, as well as facilitating the construction of Tafel plots and qualitative Goldberg analysis. The results indicated that 60% gyroid samples were most susceptible to the onset of pitting corrosion when compared to 80% gyroid and solid samples. This was shown through decreased breakdown and vertex potentials and were found to correlate to increased lattice surface area to void volume ratio. Tafel plots indicated that despite the earlier onset of pitting corrosion, both gyroid test groups displayed lower rates of corrosion per year, indicating a lower severity of corrosion. This study highlighted inherent tradeoffs between lattice optimisation and corrosion behaviour with a potential parabolic link between void volume, surface area and corrosion being identified. This potential link is supported by 60% gyroid samples having the lowest breakdown potentials, but investigation into other porosity ranges is suggested to support the hypothesis. All 3D printed materials studied here showed breakdown potentials higher than ASTM F2129′s suggestion of 800 mV for evaluation within the physiological environment, indicating that under static conditions pitting and crevice corrosion should not initiate within the body.

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Arañez, Shaun Angelo C., Blessie A. Basilia, Cyron L. Custodio, and Marianito T. Margarito. "Mechanical Behavior of Functionally Graded ABS Gyroid Lattice Structures Using Fused Deposition Modeling." Solid State Phenomena 337 (October 14, 2022): 19–24. http://dx.doi.org/10.4028/p-818691.

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Functionally graded additive manufacturing (FGAM) is a fused deposition modeling (FDM) technique that steadily varies the ratio of the material distribution in a single specimen depending on a specific function. The gyroid design is used in a variety of applications because of its high porosity, surface area, and its good mechanical properties. This work investigated the relationship between the geometric design and the mechanical performance of the acrylonitrile butadiene styrene (ABS) gyroid structure using FDM. Tensile, compression, and flexural tests were performed to determine the mechanical behavior of the functionally graded lattice structures with controlled infill densities per layer. Results showed that the performance of the ABS gyroids is dominated by their geometrical design. The tensile strength of the single-layered structure increased linearly with respect to the increase in infill density from 15% to 35% however, compression and flexural results from 25% to 35% showed an exponential increase of 175.52% and 112.14%, respectively. Increasing the outer layer density from 15% to 35% for the three-layered structures resulted in an increase in tensile strength up to 62%. It was observed that the three-layered structures having the same amount of infill densities provided similar mechanical behavior in all the tests conducted. Fracture failures occurred in the adjoining layers wherein the density of the interconnected structures is a function of its material distribution.

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Beloshenko, Victor, Yan Beygelzimer, Vyacheslav Chishko, Bogdan Savchenko, Nadiya Sova, Dmytro Verbylo, Andrei Voznyak, and Iurii Vozniak. "Mechanical Properties of Flexible TPU-Based 3D Printed Lattice Structures: Role of Lattice Cut Direction and Architecture." Polymers 13, no. 17 (September 3, 2021): 2986. http://dx.doi.org/10.3390/polym13172986.

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This study addresses the mechanical behavior of lattice materials based on flexible thermoplastic polyurethane (TPU) with honeycomb and gyroid architecture fabricated by 3D printing. Tensile, compression, and three-point bending tests were chosen as mechanical testing methods. The honeycomb architecture was found to provide higher values of rigidity (by 30%), strength (by 25%), plasticity (by 18%), and energy absorption (by 42%) of the flexible TPU lattice compared to the gyroid architecture. The strain recovery is better in the case of gyroid architecture (residual strain of 46% vs. 31%). TPUs with honeycomb architecture are characterized by anisotropy of mechanical properties in tensile and three-point bending tests. The obtained results are explained by the peculiarities of the lattice structure at meso- and macroscopic level and by the role of the pore space.

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Feng, Xueyan, Mujin Zhuo, Hua Guo, and Edwin L. Thomas. "Visualizing the double-gyroid twin." Proceedings of the National Academy of Sciences 118, no. 12 (March 15, 2021): e2018977118. http://dx.doi.org/10.1073/pnas.2018977118.

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Periodic gyroid network materials have many interesting properties (band gaps, topologically protected modes, superior charge and mass transport, and outstanding mechanical properties) due to the space-group symmetries and their multichannel triply continuous morphology. The three-dimensional structure of a twin boundary in a self-assembled polystyrene-b-polydimethylsiloxane (PS-PDMS) double-gyroid (DG) forming diblock copolymer is directly visualized using dual-beam scanning microscopy. The reconstruction clearly shows that the intermaterial dividing surface (IMDS) is smooth and continuous across the boundary plane as the pairs of chiral PDMS networks suddenly change their handedness. The boundary plane therefore acts as a topological mirror. The morphology of the normally chiral nodes and strut loops within the networks is altered in the twin-boundary plane with the formation of three new types of achiral nodes and the appearance of two new classes of achiral loops. The boundary region shares a very similar surface/volume ratio and distribution of the mean and Gaussian curvatures of the IMDS as the adjacent ordered DG grain regions, suggesting the twin is a low-energy boundary.

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Fogden, A., M. Haeberlein, and S. Lidin. "Generalizations of the gyroid surface." Journal de Physique I 3, no. 12 (December 1993): 2371–85. http://dx.doi.org/10.1051/jp1:1993250.

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Nishimura, Taiki, Satoshi Katsuhara, Chaehun Lee, Brian J. Ree, Redouane Borsali, Takuya Yamamoto, Kenji Tajima, Toshifumi Satoh, and Takuya Isono. "Fabrication of Ultrafine, Highly Ordered Nanostructures Using Carbohydrate-Inorganic Hybrid Block Copolymers." Nanomaterials 12, no. 10 (May 12, 2022): 1653. http://dx.doi.org/10.3390/nano12101653.

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Block copolymers (BCPs) have garnered considerable interest due to their ability to form microphase-separated structures suitable for nanofabrication. For these applications, it is critical to achieve both sufficient etch selectivity and a small domain size. To meet both requirements concurrently, we propose the use of oligosaccharide and oligodimethylsiloxane as hydrophilic and etch-resistant hydrophobic inorganic blocks, respectively, to build up a novel BCP system, i.e., carbohydrate-inorganic hybrid BCP. The carbohydrate-inorganic hybrid BCPs were synthesized via a click reaction between oligodimethylsiloxane with an azido group at each chain end and propargyl-functionalized maltooligosaccharide (consisting of one, two, and three glucose units). In the bulk state, small-angle X-ray scattering revealed that these BCPs microphase separated into gyroid, asymmetric lamellar, and symmetric lamellar structures with domain-spacing ranging from 5.0 to 5.9 nm depending on the volume fraction. Additionally, we investigated microphase-separated structures in the thin film state and discovered that the BCP with the most asymmetric composition formed an ultrafine and highly oriented gyroid structure as well as in the bulk state. After reactive ion etching, the gyroid thin film was transformed into a nanoporous-structured gyroid SiO2 material, demonstrating the material’s promising potential as nanotemplates.

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Pouya, C., and P. Vukusic. "Electromagnetic characterization of millimetre-scale replicas of the gyroid photonic crystal found in the butterfly Parides sesostris." Interface Focus 2, no. 5 (February 2012): 645–50. http://dx.doi.org/10.1098/rsfs.2011.0091.

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We have used three-dimensional stereolithography to synthetically replicate the gyroid photonic crystal (PC) structure that occurs naturally in the butterfly Parides sesostris . We have experimentally characterized the transmission response of this structure in the microwave regime at two azimuthal angles ( ϕ ) over a comprehensive range of polar angles ( θ ). We have modelled its electromagnetic response using the finite-element method (FEM) and found excellent agreement with experimental data. Both theory and experiment show a single relatively broad transmission minimum at normal incidence ( θ = 0°) that comprises several narrow band resonances which separate into clearly identifiable stop-bands at higher polar angles. We have identified the specific effective geometric planes within the crystal, and their associated periodicities that give rise to each of these stop-bands. Through extensive theoretical FEM modelling of the gyroid PC structure, using varying filling fractions of material and air, we have shown that a gyroid PC with material volume fraction of 40 per cent is appropriate for optimizing the reflected bandwidth at normal incidence (for a refractive index contrast of 1.56). This is the same gyroid PC material volume fraction used by the butterfly P. sesostris itself to produce its green structurally coloured appearance. This infers further optimization of this biological PC beyond that of its lattice constant alone.

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Goi, Elena, Benjamin Cumming, and Min Gu. "Impact of Cubic Symmetry on Optical Activity of Dielectric 8-srs Networks." Applied Sciences 8, no. 11 (November 1, 2018): 2104. http://dx.doi.org/10.3390/app8112104.

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Photonic crystals are engineered structures able to control the propagation and properties of light. Due to this ability, they can be fashioned into optical components for advanced light manipulation and sensing. For these applications, a particularly interesting case study is the gyroid srs-network, a three-dimensional periodic network with both cubic symmetry and chirality. In this work we present the fabrication and characterization of three-dimensional cubically symmetric 8-srs photonic crystals derived from combination of eight individual gyroid srs-networks. We numerically and experimentally investigate optical properties of these photonic crystals and study in particular, the impact of cubic symmetry on transmission and optical activity (OA). Gyroid photonic crystals fabricated in this work can lead to the development of smaller, cheaper, and more efficient optical components with functionalities that go beyond the concept of lenses.

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Li, Fenglei, and Bing Li. "Dynamic Load Mitigation of 3D-printed Triply Periodic Minimal Surface Structures." Journal of Physics: Conference Series 2417, no. 1 (December 1, 2022): 012019. http://dx.doi.org/10.1088/1742-6596/2417/1/012019.

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Three types of triply periodic minimal surface (TPMS) structures are chosen to investigate the quasi-static and dynamic compressive behaviors in this paper. All the TPMS lattices (Primitive, Gyroid, IWP) have the same relative density of 37.5%, and the samples are fabricated by the 3D printing of selective laser melting technique using AlSi10Mg powder. The energy absorption performance and dynamic load mitigation of the 3D printed TPMS structures under three different impact velocities are compared, and the corresponding engineering strain rates are 143 s −1, 286 s −1, and 571 s −1, respectively. The results of numerical simulation indicate that the IWP structure has the highest specific energy absorption (SEA) and plateau stress, followed by the Gyroid structure, and finally the Primitive structure. The SEA of Primitive and Gyroid structures increases with the impact velocity and decreases for IWP structure.

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Bean, Philip, Roberto A. Lopez-Anido, and Senthil Vel. "Numerical Modeling and Experimental Investigation of Effective Elastic Properties of the 3D Printed Gyroid Infill." Applied Sciences 12, no. 4 (February 19, 2022): 2180. http://dx.doi.org/10.3390/app12042180.

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A numerical homogenization approach is presented for the effective elastic moduli of 3D printed cellular infills. A representative volume element of the infill geometry is discretized using either shell or solid elements and analyzed using the finite element method. The elastic moduli of the bulk cellular material are obtained through longitudinal and shear deformations of a representative volume element under periodic boundary conditions. The method is used to analyze the elastic behavior of gyroid infills for varying infill densities. The approach is validated by comparing the Young’s modulus and Poisson’s ratio with those obtained from compression experiments. Results indicate that although the gyroid infill exhibits cubic symmetry, it is nearly isotropic with a low anisotropy index. The numerical predictions are used to develop semi-empirical equations of the effective elastic moduli of gyroid infills as a function of infill density in order to inform design and topology optimization workflows.

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Michielsen, K., and D. G. Stavenga. "Gyroid cuticular structures in butterfly wing scales: biological photonic crystals." Journal of The Royal Society Interface 5, no. 18 (June 13, 2007): 85–94. http://dx.doi.org/10.1098/rsif.2007.1065.

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We present a systematic study of the cuticular structure in the butterfly wing scales of some papilionids ( Parides sesostris and Teinopalpus imperialis ) and lycaenids ( Callophrys rubi , Cyanophrys remus , Mitoura gryneus and Callophrys dumetorum ). Using published scanning and transmission electron microscopy (TEM) images, analytical modelling and computer-generated TEM micrographs, we find that the three-dimensional cuticular structures can be modelled by gyroid structures with various filling fractions and lattice parameters. We give a brief discussion of the formation of cubic gyroid membranes from the smooth endoplasmic reticulum in the scale's cell, which dry and harden to leave the cuticular structure behind when the cell dies. The scales of C. rubi are a potentially attractive biotemplate for producing three-dimensional optical photonic crystals since for these scales the cuticle-filling fraction is nearly optimal for obtaining the largest photonic band gap in a gyroid structure.

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Finnemore, Alexander S., Maik R. J. Scherer, Richard Langford, Sumeet Mahajan, Sabine Ludwigs, Fiona C. Meldrum, and Ullrich Steiner. "Gyroid Single Crystals: Nanostructured Calcite Single Crystals with Gyroid Morphologies (Adv. Mater. 38â39/2009)." Advanced Materials 21, no. 38â39 (October 19, 2009): NA. http://dx.doi.org/10.1002/adma.200990146.

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Grafskaia, Kseniia N., Azaliia F. Akhkiamova, Dmitry V. Vashurkin, Denis S. Kotlyarskiy, Diego Pontoni, Denis V. Anokhin, Xiaomin Zhu, and Dimitri A. Ivanov. "Bicontinuous Gyroid Phase of a Water-Swollen Wedge-Shaped Amphiphile: Studies with In-Situ Grazing-Incidence X-ray Scattering and Atomic Force Microscopy." Materials 14, no. 11 (May 28, 2021): 2892. http://dx.doi.org/10.3390/ma14112892.

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We report on formation of a bicontinuous double gyroid phase by a wedge-shaped amphiphilic mesogen, pyridinium 4′-[3″,4″,5″-tris-(octyloxy)benzoyloxy]azobenzene-4-sulfonate. It is found that this compound can self-organize in zeolite-like structures adaptive to environmental conditions (e.g., temperature, humidity, solvent vapors). Depending on the type of the phase, the structure contains 1D, 2D, or 3D networks of nanometer-sized ion channels. Of particular interest are bicontinuous phases, such as the double gyroid phase, as they hold promise for applications in separation and energy. Specially designed environmental cells compatible with grazing-incidence X-ray scattering and atomic force microscopy enable simultaneous measurements of structural parameters/morphology during vapor-annealing treatment at different temperatures. Such in-situ approach allows finding the environmental conditions at which the double gyroid phase can be formed and provide insights on the supramolecular structure of thin films at different spatial levels.

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Michielsen, K., H. De Raedt, and D. G. Stavenga. "Reflectivity of the gyroid biophotonic crystals in the ventral wing scales of the Green Hairstreak butterfly, Callophrys rubi." Journal of The Royal Society Interface 7, no. 46 (October 14, 2009): 765–71. http://dx.doi.org/10.1098/rsif.2009.0352.

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We present a comparison of the computer simulation data of gyroid nanostructures with optical measurements (reflectivity spectra and scattering diagrams) of ventral wing scales of the Green Hairstreak butterfly, Callophrys rubi . We demonstrate that the omnidirectional green colour arises from the gyroid cuticular structure grown in the domains of different orientation. We also show that this three-dimensional structure, operating as a biophotonic crystal, gives rise to various polarization effects. We briefly discuss the possible biological utility of the green coloration and polarization effects.

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Torun, Ahmet Refah, Ali Sinan Dike, Ege Can Yıldız, İsmail Sağlam, and Naghdali Choupani. "Fracture characterization and modeling of Gyroid filled 3D printed PLA structures." Materials Testing 63, no. 5 (May 1, 2021): 397–401. http://dx.doi.org/10.1515/mt-2020-0068.

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Abstract Polylactic acid (PLA) is a commonly used biodegradable material in medical and increasingly in industrial applications. These materials are often exposed to various flaws and faults due to working and production conditions, and increasing the demand for PLA for various applications requires a full understanding of its fracture behavior. In addition to ABS, PLA is a widely used polymeric material in 3D printing. The gyroid type of filling is advantageous for overcoming the relatively higher brittleness of PLA in comparison with conventional thermoplastic polymers. In this study, the effects of various filling ratios on the fracture toughness of 3D printed PLA samples with gyroid pattern were investigated numerically and experimentally for pure mode I, combined mode I/II, and pure mode II. Two-dimensional finite element modeling was created, and the two-dimensional functions of stress intensity coefficients were extracted in loading mode I, mode I/II, and mode II at varied filling ratios of the gyroid PLA samples. Mixed-mode fracture tests for 3D printed PLA samples with a gyroid pattern at various filling ratios were performed by using a specially developed fracture testing fixture. The results showed that the amount of fracture toughness of the samples under study in tensile mode was much higher than those values in shear mode. Also, as the percentages of the filling ratios in the samples increased, both tensile and shear fracture toughness improved.

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Chin, Jonathan, and Peter V. Coveney. "Chirality and domain growth in the gyroid mesophase." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2076 (June 23, 2006): 3575–600. http://dx.doi.org/10.1098/rspa.2006.1741.

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We describe the first dynamical simulations of domain growth during the self-assembly of the gyroid mesophase from a ternary amphiphilic mixture, using the lattice Boltzmann method. The gyroid is a chiral structure; we demonstrate that, for a symmetric amphiphile with no innate preference for left- or right-handed morphologies, the self-assembly process may give rise to a racemic mixture of domains. We use measurements of the averaged mean curvature to analyse the behaviour of domain walls, and suggest that diffusive domain growth may be present in this system.

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Jung, Gang Seob, Jingjie Yeo, Zhiting Tian, Zhao Qin, and Markus J. Buehler. "Unusually low and density-insensitive thermal conductivity of three-dimensional gyroid graphene." Nanoscale 9, no. 36 (2017): 13477–84. http://dx.doi.org/10.1039/c7nr04455k.

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Yao, Xiaomei, Jie Xu null, and Lei Zhang. "Transition pathways in Cylinder-Gyroid interface." Communications in Computational Physics 32, no. 3 (June 2022): 810–28. http://dx.doi.org/10.4208/cicp.oa-2022-0038.

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Guo, Fengxiao, Lars Schulte, Weimin Zhang, Martin E. Vigild, Sokol Ndoni, and Jun Chen. "Gyroid nanoporous scaffold for conductive polymers." Polym. Chem. 2, no. 3 (2011): 553–55. http://dx.doi.org/10.1039/c0py00322k.

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Imai, M., K. Sakai, M. Kikuchi, K. Nakaya, A. Saeki, and T. Teramoto. "Kinetic pathway to double-gyroid structure." Journal of Chemical Physics 122, no. 21 (June 2005): 214906. http://dx.doi.org/10.1063/1.1905585.

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Dotera, Tomonari, Masakiyo Kimoto, and Junichi Matsuzawa. "Hard spheres on the gyroid surface." Interface Focus 2, no. 5 (January 18, 2012): 575–81. http://dx.doi.org/10.1098/rsfs.2011.0092.

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We find that 48/64 hard spheres per unit cell on the gyroid minimal surface are entropically self-organized. Striking evidence is obtained in terms of the acceptance ratio of Monte Carlo moves and order parameters. The regular tessellations of the spheres can be viewed as hyperbolic tilings on the Poincaré disc with a negative Gaussian curvature, one of which is, equivalently, the arrangement of angels and devils in Escher's Circle Limit IV .

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Li, Li, Lars Schulte, Lydia D. Clausen, Kristian M. Hansen, Gunnar E. Jonsson, and Sokol Ndoni. "Gyroid Nanoporous Membranes with Tunable Permeability." ACS Nano 5, no. 10 (September 14, 2011): 7754–66. http://dx.doi.org/10.1021/nn200610r.

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Li, Li, Piotr Szewczykowski, Lydia D. Clausen, Kristian M. Hansen, Gunnar E. Jonsson, and Sokol Ndoni. "Ultrafiltration by gyroid nanoporous polymer membranes." Journal of Membrane Science 384, no. 1-2 (November 2011): 126–35. http://dx.doi.org/10.1016/j.memsci.2011.09.012.

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Urade, Vikrant N., Ta-Chen Wei, Michael P. Tate, Jonathan D. Kowalski, and Hugh W. Hillhouse. "Nanofabrication of Double-Gyroid Thin Films." Chemistry of Materials 19, no. 4 (February 2007): 768–77. http://dx.doi.org/10.1021/cm062136n.

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Urade, Vikrant N., Ta-Chen Wei, Michael P. Tate, Jonathan D. Kowalski, and Hugh W. Hillhouse. "Nanofabrication of Double-Gyroid Thin Films." Chemistry of Materials 19, no. 9 (May 2007): 2382. http://dx.doi.org/10.1021/cm0799964.

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Siddique, Suhail K., Hassan Sadek, Tsung-Lun Lee, Cheng-Yuan Tsai, Shou-Yi Chang, Hsin-Hsien Tsai, Te-Shun Lin, Gkreti-Maria Manesi, Apostolos Avgeropoulos, and Rong-Ming Ho. "Block Copolymer Modified Nanonetwork Epoxy Resin for Superior Energy Dissipation." Polymers 14, no. 9 (May 5, 2022): 1891. http://dx.doi.org/10.3390/polym14091891.

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Herein, this work aims to fabricate well-ordered nanonetwork epoxy resin modified with poly(butyl acrylate)-b-poly(methyl methacrylate) (PBA-b-PMMA) block copolymer (BCP) for enhanced energy dissipation using a self-assembled diblock copolymer of polystyrene-b-poly(dimethylsiloxane) (PS-b-PDMS) with gyroid and diamond structures as templates. A systematic study of mechanical properties using nanoindentation of epoxy resin with gyroid- and diamond-structures after modification revealed significant enhancement in energy dissipation, with the values of 0.36 ± 0.02 nJ (gyroid) and 0.43 ± 0.03 nJ (diamond), respectively, when compared to intrinsic epoxy resin (approximately 0.02 ± 0.002 nJ) with brittle characteristics. This enhanced property is attributed to the synergic effect of the deliberate structure with well-ordered nanonetwork texture and the toughening of BCP-based modifiers at the molecular level. In addition to the deliberate structural effect from the nanonetwork texture, the BCP modifier composed of epoxy-philic hard segment and epoxy-phobic soft segment led to dispersed soft-segment domains in the nanonetwork-structured epoxy matrix with superior interfacial strength for the enhancement of applied energy dissipation.

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Kobayashi, Tsubasa, Ya-xin Li, Ayaka Ono, Xiang-bing Zeng, and Takahiro Ichikawa. "Gyroid structured aqua-sheets with sub-nanometer thickness enabling 3D fast proton relay conduction." Chemical Science 10, no. 25 (2019): 6245–53. http://dx.doi.org/10.1039/c9sc00131j.

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Guo, Yuning, Matheus Rosa, and Massimo Ruzzene. "Symmetry-enforced gapless surface states in three-dimensional acoustic gyroid structures." Journal of the Acoustical Society of America 151, no. 4 (April 2022): A97. http://dx.doi.org/10.1121/10.0010772.

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The discovery of topological gapless phases challenges the perception that topological features necessarily require a bandgap, expanding the understanding of topological phases of matter in various realms including electric, photonic, and phononic systems. The progress on 3D topological gapless states in elastic and acoustic systems is still in its early stages of formulation and design. We here investigate 3D acoustic gyroid crystals supporting symmetry-enforced gapless surface states in minimal surface-based structures. The inherent chirality and morphology of gyroid surfaces enable the implementation of 3D acoustic crystals hosting symmetry-enforced Dirac points and topologically gapless surface states. The associated fourfold degeneracy is protected by the nonsymmorphic space group featuring a combination of screw symmetry and glide reflections. The presence of gapless surface arcs relies on band structure calculations conducted using finite element simulations, while preliminary experimental results on additively manufactured samples validate their occurrence in the proposed gyroid surfaces. With the continuous development in additive manufacturing techniques, the presented surface-based framework provides a platform to explore a variety of topological wave physics phenomena in 3D load-bearing, continuum materials of potential engineering relevance, among which superior acoustic absorption may be particularly promising.

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Chiu, Po-Ting, Yu-Cheng Chien, Prokopios Georgopanos, Ya-Sen Sun, Apostolos Avgeropoulos, and Rong-Ming Ho. "Examination of well ordered nanonetwork materials by real- and reciprocal-space imaging." IUCrJ 6, no. 2 (February 15, 2019): 259–66. http://dx.doi.org/10.1107/s2052252518018389.

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The development of well ordered nanonetwork materials (in particular gyroid-structured materials) has been investigated using a block-copolymer template for templated electroless plating as an example system for the examination of network formation using X-ray scattering. By taking advantage of the nucleation and growth mechanism of templated electroless plating, gyroid-structured Au was successfully fabricated through the development of Au nanoparticles, then tripods and branched tripods, and finally an ordered network. Each stage in the development of the network phase could then be examined by combining real-space transmission electron microscopy observations with reciprocal-space small-angle X-ray scattering results. The fingerprint scattering profile of the building block for the network (i.e. the tripod of the gyroid) could be well fitted with the form factor of an effective sphere, and the diffraction results from the ordered network could thus be reasonably addressed. As a result, the examination of well ordered network materials can be simplified as the scattering from the form factor of a sphere convoluted with the nodes of its structure factor, providing a facile method of identifying the network phases from X-ray scattering data.

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Jin, Hongyu, Yue Zhuo, Yang Sun, Hongya Fu, and Zhenyu Han. "Microstructure design and degradation performance in vitro of three-dimensional printed bioscaffold for bone tissue engineering." Advances in Mechanical Engineering 11, no. 10 (October 2019): 168781401988378. http://dx.doi.org/10.1177/1687814019883784.

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In bone tissue engineering, three-dimensional printed biological scaffolds play an important role in the development of bone regeneration. The ideal scaffolds should have the ability to match the bone degradation rate and osteogenic ability. This article optimizes the unit cell model of the microstructure including spherical pore, gyroid, and topology to explore degradation performance of scaffolds. Boolean operation of array microstructure unit cells and selected part of a computer-aided design (CAD) femur model are adopted to create a reconstructed scaffold model. Polylactic acid/[Formula: see text]-tricalcium phosphate/hydroxyapatite scaffolds with spherical pore, gyroid, and topology-optimized structures are manufactured by three-dimensional printing utilizing the composition of bio-ink including polylactic acid, [Formula: see text]-tricalcium phosphate, and hydroxyapatite. After degradation of the scaffolds in vitro for several days, the mechanical properties are analyzed to study the effects of different microstructures on the degradation properties. The results show that the gyroid scaffolds with favorable degradability still maintain excellent mechanical properties after degradation. Mechanical properties of the scaffolds with topology-optimized structure and spherical pore microstructure scaffolds have a significant decrease after degradation.

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Gawronska, Elzbieta, Robert Dyja, Andrzej Grosser, and Jerzy Winczek. "Engineering calculations for complex geometric domains." MATEC Web of Conferences 157 (2018): 02009. http://dx.doi.org/10.1051/matecconf/201815702009.

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The paper aims to present the possibility of performing engineering calculations in domains of complex shapes expressed by mathematical descriptions. We focus on calculations done with the use of the Finite Element Method. An example of the compound structure is gyroid, which is a periodic structure representing an area close to the porous structure. The presented gyroid structure exhibits circular struts and a spherical core and spatially occupies a cube. The side length of the cube is defined as unit cell size, and the volume percentage of the struts inside the cube is referred to as volume fraction. The periodic cellular lattice structures are generated by our own software module. One of the uses of such structures is their employment in additive manufacturing (AM) of the so-called 3D printing (layer-by-layer AM technique), where they can contribute reducing the weight of an item and limiting the material consumption. It is important to answer the question of what effect does an element with a gyroid structure have on the thermal properties (e.g. the heat flow versus the volume fraction) compared to an element with full structure. The paper will show the results of such a comparison.

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Sasaki, Haruna, Yoichi Takanishi, Jun Yamamoto, and Atsushi Yoshizawa. "Achiral flexible liquid crystal trimers exhibiting gyroid-like surfaces in chiral conglomerate phases." Soft Matter 13, no. 37 (2017): 6521–28. http://dx.doi.org/10.1039/c7sm01499f.

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Hsueh, Han-Yu, Cheng-Thai Yao, and Rong-Ming Ho. "Well-ordered nanohybrids and nanoporous materials from gyroid block copolymer templates." Chemical Society Reviews 44, no. 7 (2015): 1974–2018. http://dx.doi.org/10.1039/c4cs00424h.

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Prasad, Ishan, Hiroshi Jinnai, Rong-Ming Ho, Edwin L. Thomas, and Gregory M. Grason. "Anatomy of triply-periodic network assemblies: characterizing skeletal and inter-domain surface geometry of block copolymer gyroids." Soft Matter 14, no. 18 (2018): 3612–23. http://dx.doi.org/10.1039/c8sm00078f.

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Garcia, Adrian E., Chen Santillan Wang, Robert N. Sanderson, Kyle M. McDevitt, Yunfei Zhang, Lorenzo Valdevit, Daniel R. Mumm, Ali Mohraz, and Regina Ragan. "Scalable synthesis of gyroid-inspired freestanding three-dimensional graphene architectures." Nanoscale Advances 1, no. 10 (2019): 3870–82. http://dx.doi.org/10.1039/c9na00358d.

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Saranathan, Vinodkumar, Suresh Narayanan, Alec Sandy, Eric R. Dufresne, and Richard O. Prum. "Evolution of single gyroid photonic crystals in bird feathers." Proceedings of the National Academy of Sciences 118, no. 23 (June 1, 2021): e2101357118. http://dx.doi.org/10.1073/pnas.2101357118.

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Vivid, saturated structural colors are conspicuous and important features of many animals. A rich diversity of three-dimensional periodic photonic nanostructures is found in the chitinaceous exoskeletons of invertebrates. Three-dimensional photonic nanostructures have been described in bird feathers, but they are typically quasi-ordered. Here, we report bicontinuous single gyroid β-keratin and air photonic crystal networks in the feather barbs of blue-winged leafbirds (Chloropsis cochinchinensis sensu lato), which have evolved from ancestral quasi-ordered channel-type nanostructures. Self-assembled avian photonic crystals may serve as inspiration for multifunctional applications, as they suggest efficient, alternative routes to single gyroid synthesis at optical length scales, which has been experimentally elusive.

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Journal articles on the topic 'Gyroid'

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