Gyroid Surface Research Articles

Manufacturability and Performance Study of Triply Periodic Minimal Surface Air-to-Air Heat Exchanger

Abstract The study tests 3D printability, heat transfer characteristics and pressure drop of two types of triply periodic minimal surface heat exchanger in order to develop new flow principles for compact heat exchanger design. Various generic plate heat exchanger designs are also tested to compare to the printed alternatives. Geometry variations for heat exchangers and laboratory testing air recuperators are modelled in SolidWorks software and manufactured mostly by UV LCD and FDM additive manufacturing methods. Digital light processing printing method has been found to be most successful in printing the TPMS structures, while using photopolymer materials. Literature studies conclude that the most promising structures are Schoen’s gyroid and Schwarz-diamond surfaces, which have been modelled and tested in several variations. Using these results, full size gyroid and Schwarz-D structure heat exchangers have been modelled, manufactured and tested. The results are compared and analysed to study the effect of advanced surface designs in heat transfer efficiency. The obtained results can be used in compact air-to-air thermal recuperator development as well as other low pressure heat exchanger applications, as the printed TPME heat exchangers outperform the plate heat exchangers in similar dimensions.

In Vivo Assessment of a Triple Periodic Minimal Surface Based Biomimmetic Gyroid as an Implant Material in a Rabbit Tibia Model.

Biomimetic approaches to implant construction are a rising frontier in implantology. Triple Periodic Minimal Surface (TPMS)-based additively manufactured gyroid structures offer a mean curvature of zero, rendering this structure an ideal porous architecture. Previous studies have demonstrated the ability of these structures to effectively mimic the mechanical cues required for optimal implant construction. The porous nature of gyroid materials enhances bone ingrowth, thereby improving implant stability within the body. This enhancement is attributed to the increased surface area of the gyroid structure, which is approximately 185% higher than that of a dense material of the same form factor. This larger surface area allows for enhanced cellular attachment and nutrient circulation facilitated by the porous channels. This study aims to evaluate the biological performance of a gyroid-based Ti6Al-4V implant material compared to a dense alloy counterpart. Cellular viability was assessed using the lactate dehydrogenase (LDH) assay, which demonstrated that the gyroid surface allowed marginally higher viability than dense material. The in vivo integration was studied over 6 weeks using a rabbit tibia model and characterized using X-ray, micro-CT, and histopathological examination. With a metal volume of 8.1%, the gyroid exhibited a bone volume/total volume (BV/TV) ratio of 9.6%, which is 11-fold higher than that of dense metal (0.8%). Histological assessments revealed neovascularization, in-bone growth, and the presence of a Haversian system in the gyroid structure, hinting at superior osteointegration.

Investigations on the mechanical properties of multi-directional graded cellular structures based on gyroid surface

A novel multi-directional graded cellular structure based on gyroid surface is designed and additively manufactured in this work. Through quasi-static compression tests, their mechanical characteristics were assessed. The results revealed that cellular structures featuring bidirectional and three-directional gradients exhibit notably enhanced mechanical performance compared to unidirectional gradients (8.8% for energy absorption, 89.7% for compressive strength, 53.9% and 66.3% for elastic modulus and yield strength, respectively). Moreover, the mechanical properties of structures with three-directional gradients can be finely tuned by adjusting gradient variation. Consequently, these innovative multi-directional graded cellular structures offer promising potential across diverse applications as efficient energy absorbers.

Effect of Lattice Structure on Mechanical Properties of Ti-6Al-4V-Ta Alloy for Improved Antibacterial Properties

This study investigates the effect of a tantalum addition and lattice structure design on the mechanical and antibacterial properties of Ti-6Al-4V alloys. TPMS lattice structures, such as Diamond, Gyroid, and Primitive, were generated by MSLattice 1.0 software and manufactured using laser powder bed fusion (LPBF). The results indicate that Gyroid and Primitive structures at a 40% density exhibit superior ultimate compressive strength, which closely emulates bone’s biomechanical properties. To be precise, adding 8% tantalum (Ta) significantly increases the material’s elastic modulus and energy absorption, enhancing the material’s suitability for dynamic load-bearing implants. Nevertheless, the Ta treatment reduces bacterial biofilm formation, especially on Gyroid surfaces, suggesting its potential for infection management. Overall, all findings provide critical insights into the development of advanced implant materials, contributing to the fields of additive manufacturing, materials science, and biomedical engineering and paving the way for improved patient outcomes in orthopedic applications.

Air Flow Analysis for Triply Periodic Minimal Surface Heat Exchangers

Due to the increasing popularity of additive manufacturing technologies, more varied and complex shapes of heat exchangers can be produced, that can be optimized to be more compact and efficient. In this paper a triply minimal periodic surface – gyroid structure is designed to study the applicability of such structures in air-to-air heat exchangers used in residential ventilation recuperation systems. Gyroid surface structures are useful to decrease overall heat exchanger size, pressure and increase heat transfer. Several geometry variations with different flow rate values were analysed to compare the efficiency of heat exchanger designs, as well as basic counterflow plate heat exchanger arrangement was analysed, to compare the gyroid designs to conventional methods. To calculate the pressure difference, temperature and heat transfer in each variation, SolidWorks Flow Simulation was used. The results showed that by using gyroid structures, heat exchanger energy transfer can be optimised for required back pressure and heat transfer, while reducing the overall dimensions, compared to conventional heat exchangers. By incorporating low cost, printed thermal recuperators, thermal efficiency of residential buildings can be improved. Suitable materials, manufacturing methods and application limitations are discussed.

Mechanical performance of interpenetrating phase composites with multi-sheet lattice structures

Interpenetrating phase composites (IPCs), as a novel type of composite material, offer advantages such as lightweight, high strength, and superior energy absorption. This study proposed a multi-sheet lattice structure based on the Gyroid surface, which was initially designed and then fabricated via TC4 laser powder bed fusion (LPBF). Through the infiltration of epoxy resin, a composite material with interpenetrating phases was achieved. Subsequently, the mechanical properties of the IPCs were comprehensively investigated using experimental and numerical simulation methods. In quasi-static compression tests, the IPCs demonstrated higher strength and improved energy absorption characteristics compared to original lattice structures. However, under dynamic loading conditions, while the strength of the IPCs showed significant enhancement, the improvement in energy absorption characteristics of the composite structures was constrained by temperature rise, thermal softening effects, and the glass transition of the epoxy resin induced by elevated temperatures. Thus, while the proposed IPCs exhibited high strength under both quasi-static and dynamic loads, it is imperative to consider material properties and the influence of temperature on energy absorption to prevent overestimation of performance under dynamic loading conditions. Therefore, this study not only highlights the novelty of utilizing a multi-sheet lattice structure based on the Gyroid surface for creating IPCs, but also underscores the importance of carefully considering temperature effects on material properties when evaluating their performance under dynamic conditions.

Numerical investigation of gyroid heat exchanger

A novel cylindrical gyroid surface-based tube is designed to investigate fluid flow and heat transfer characteristics numerically. The simulations are carried out using finite volume based CFD software Ansys Fluent. The numerical validation is performed to verify the robustness of the solver and grid independence study are also carried out to compute the simulations using optimum mesh. The heat exchanger (HX) tubes with gyroid surfaces are manufactured using additive manufacturing and a crossflow HX is fabricated with a bank of gyroid tubes where the experiments were conducted. The numerical results of the Realizable k-ε turbulence model with enhanced wall treatment is validated with in-house experimental data. The thermal performance of the gyroid tube HX is also compared with a conventional circular tube (CCT). Parametric analysis is also carried out by varying the gyroid design parameter and an optimum HX design is proposed. The results show that due to larger surface area and enhanced fluid mixing, the gyroid tube-based HXs show better thermal performance compared to CCT-based HX.

Parametric design and performance evaluation of gyroid triply periodic minimal surface preparation by LCD photopolymerization

In this paper, the Gyroid triply periodic minimal surface is prepared by liquid crystal display photopolymerization technology, and 10 models of the periodic parameter T in [1/5, 2] are designed. Using the method of finite element method and experimental verification, when T = 1/3, there are fewer stress concentration areas on the Gyroid surface, the number of grids is moderate, the compression crush rate is the smallest, and the porosity error is reasonable. Through the microscopic morphology, it is found that the surface, after printing, forms gear shape and resin residue so that the actual volume is larger than the theoretical volume, and the porosity is minor. Keeping periodic parameter T = 1/3 and porosity of 50%, four kinds of Gyroid surface structures were designed by changing the parameter surface offset, wall thickness, offset thickness, and gradient arrangement. The effects of different loading directions on its mechanical properties, deformation behavior, and energy absorption were discussed through compression experiments. The results show that the vertical load is applied to form a fault zone from the upper left angle to the lower right angle of 45°, and the parallel load is applied to create a fault zone from the upper right angle to the lower left grade of 45°. When the load is used in the vertical direction, the energy absorption and energy efficiency of the surface offset Gyroid surface are the largest. When the load is applied in the parallel order, the energy absorption curves of the four structures change similarly, and the deformation amplitude of the wall thickness Gyroid surface during the compression process is relatively stable. The energy efficiency of gradient arrangement Gyroid surface increases fastest in the compaction stage.

Design, Stereolithographic 3D Printing, and Characterization of TPMS Scaffolds.

Anatomical and functional tissue loss is one of the most debilitating problems and involves a great cost to the international health-care sector. In the field of bone tissue, the use of scaffolds to promote tissue regeneration is a topic of great interest. In this study, a combination of additive manufacturing and computational methods led to creating porous scaffolds with complex microstructure and mechanical behavior comparable to those of cancellous bone. Specifically, some representative models of triply periodic minimal surfaces (TPMSs) were 3D-printed through a stereolithographic technique using a dental resin. Schwarz primitive and gyroid surfaces were created computationally: they are characterized by a complex geometry and a high pore interconnectivity, which play a key role in the mechanism of cell proliferation. Several design parameters can be varied in these structures that can affect the performance of the scaffold: for example, the larger the wall thickness, the lower the elastic modulus and compressive strength. Morphological and mechanical analyses were performed to experimentally assess the properties of the scaffolds. The relationship between relative density and elastic modulus has been analyzed by applying different models, and a power-law equation was found suitable to describe the trend in both structures.

Tetragonal gyroid structure from symmetry manipulation: A brand-new member of the gyroid surface family

Tetragonal gyroid structure from symmetry manipulation: A brand-new member of the gyroid surface family

COMMERCIALLY PURE (CP-TI) TITANIUM MEDICAL IMPLANT PRODUCTION USING LASER POWDER BED FUSION (L-PBF) TECHNOLOGY

Decreasing the bulk weight without losing the biomechanical properties of commercial pure titanium (Cp-Ti) medical implants is now possible by using Laser Powder Bed Fusion (L-PBF) technology. Gyroid lattice structures that have precious mechanical and biological advantages because of similarity to trabecular bone. The aim of the study was to design and develop L-PBF process parameter optimization for manufacturing gyroid lattice Cp-Ti structures. The cleaning process was then optimized to remove the non-melted powder from the gyroid surface without mechanical loss.Gyroid cubic designs were created with various relative densities by nTopology. L-PBF process parameter optimization was progressed using with Cp-Ti (EOS TiCP Grade2) powder in the EOS M290 machine to achieve parts that have almost full dense and dimensional accuracy. The metallography method was made for density. Dimensional accuracy at gyroid wall thicknesses was investigated between designed and manufactured via stereomicroscope, also mechanical tests were applied with real time experiment and numerical analysis (ANSYS). Mass loss and strut thickness loss were investigated for chemical etching cleaning process.Gyroid parts had 99,5% density. High dimensional accuracy was achieved during L-PBF process parameters optimization. Final L-PBF parameters gave the highest 19% elongation and 427 MPa yield strength values at tensile test. Mechanical properties of gyroid were controlled with changing relative density. A minute chemical etching provided to remove non-melted powders.Compression test results of gyroids at numerical and real-time analysis gave unrelated while deformation behaviors were compatible with each other. Gyroid Cp-Ti osteosynthesis mini plates will be produced with final L-PBF process parameters. MTT cytotoxicity test will be characterized for cell viability.Acknowledgements This project is granted by TUBITAK (120N943). Feza Korkusuz MD is a member of the Turkish Academy of Sciences (TÜBA).

Fabrication of Ceramic-Polymer Piezo-Composites with Triply Periodic Minimal Interfaces via Digital Light Processing

The geometry of the phase interface in co-continuous piezoelectric composites is critical in improving their piezoelectric properties. However, conventional co-continuous piezoelectric composites are mostly simple structures such as wood stacks or honeycombs, which are prone to stress concentrations at the joints, thus reducing the fatigue service performance and force–electric conversion efficiency of piezoelectric composites. Such simple structures limit further improvements in the overall performance of co-continuous piezoelectric composites. In this study, based on the digital light processing 3D printing method, we investigated the influence of three different structures–the gyroid, diamond, and woodpile interfaces–on the piezoelectric and mechanical properties of co-continuous ceramic/polymer piezoelectric composites. These findings demonstrate that the gyroid and diamond interfaces outperformed the ceramic skeleton of the woodpile interface in terms of both mechanical and electrical properties. When the ceramic volume percentage was 50%, the piezo-composite of the gyroid surface exhibited the greatest hydrostatic figure of merit (HFOM), reaching 4.23×10−12 Pa−1, and its piezoelectric coefficient (d33) and relative dielectric constant (εr) reached 115 pC/N and 748, respectively. The research results lay the foundation for the application of co-continuous piezoelectric composites in underwater communication and detection.

Programmable Self-Assembly of Nanoplates into Bicontinuous Nanostructures.

Self-assembly is the process by which individual components arrange themselves into an ordered structure by changing the shapes, components, and interactions. It has enabled us to construct an extensive range of geometric forms on many length scales. Nevertheless, the potential of two-dimensional polygonal nanoplates to self-assemble into extended three-dimensional structures with compartments and corridors has remained unexplored. In this paper, we show coarse-grained Monte Carlo simulations demonstrating self-assembly of hexagonal/triangular nanoplates via complementary interactions into faceted, sponge-like "bicontinuous polyhedra" (or infinite polyhedra) whose flat walls partition space into a pair of mutually interpenetrating labyrinths. Two bicontinuous polyhedra can be self-assembled: the regular (or Platonic) Petrie-Coxeter infinite polyhedron (denoted {6,4|4}) and the semi-regular Hart "gyrangle". The latter structure is chiral, with both left- and right-handed versions. We show that the Petrie-Coxeter assembly is constructed from two complementary populations of hexagonal nanoplates. Furthermore, we find that the 3D chiral Hart gyrangle can be assembled from identical achiral triangular nanoplates decorated with regioselective complementary interaction sites. The assembled Petrie-Coxeter and Hart polyhedra are faceted versions of two of the simplest triply periodic minimal surfaces, namely, Schwarz's primitive and Schoen's gyroid surfaces, respectively, offering alternative routes to those bicontinuous nanostructures, which are widespread in synthetic and biological materials.

Methodology for modelling and simulation of tailored 3D functionally graded auxetic metamaterials

The description of methodologies for modelling auxetic structures with functional gradient and simulating their behaviour under loading is lacking in the literature, despite an increase of the interest in auxetics and the quantity of experimental data on these structures. This work proposes a method that allows modelling of tailored complex functionally graded auxetic structures, achieved through modifications in the equations defining the basic surfaces that characterize the aforementioned structures. In this method, the simulation studies were performed by means of the finite element method. To showcase the capabilities of this method with complex geometries, the gyroid surface was the chosen example from which to form the auxetic structures. The study was performed on geometries with different gradient types and steepness’s to obtain comprehensive data that allows to infer on the accuracy of the method. The obtained results demonstrate that even for large deformations (> 10%), the simulations concur with the experimental results. The good agreement between computational and experimental results points out the validation of the proposed methodology and the further application for various auxetic structures.

Microrobot with Gyroid Surface and Gold Nanostar for High Drug Loading and Near-Infrared-Triggered Chemo-Photothermal Therapy.

The use of untethered microrobots for precise synergistic anticancer drug delivery and controlled release has attracted attention over the past decade. A high surface area of the microrobot is desirable to achieve greater therapeutic effect by increasing the drug load. Therefore, various nano- or microporous microrobot structures have been developed to load more drugs. However, as most porous structures are not interconnected deep inside, the drug-loading efficiency may be reduced. Here, we propose a magnetically guided helical microrobot with a Gyroid surface for high drug-loading efficiency and precise drug delivery. All spaces inside the proposed microrobot are interconnected, thereby enabling drug loading deep inside the structure. Moreover, we introduce gold nanostars on the microrobot structure for near-infrared-induced photothermal therapy and triggering drug release. The results of this study encourage further exploration of a high loading efficiency in cell-based therapeutics, such as stem cells or immune cells, for microrobot-based drug-delivery systems.

Interface contact behavior of 3D printed porous surfaces

When a 3D printed implant integrates a thin surface lattice, the geometry of this porous region controls the bone-implant interface, affecting both short-term implant stability and long-term osseointegration. In intervertebral devices, for example, high expulsion resistance and propensity to subside are imperative in reducing implant migration and loss of disc height. Moreover, the shear strength of the porous-solid metal interface is critical to prevent metal-to-metal decohesion prior to and after osseointegration. While lap shear and subsidence tests are both governed by ASTM standards, expulsion testing is not standardized, and the tradeoffs in the potential implant failure modes have not been thoroughly investigated to find an optimal porosity satisfactory in all three performance tests. In this multi parameter study, we perform a series of experiments on 3D printed porous gyroid surfaces to understand the interplays and inherent tradeoffs between porosity, expulsion resistance, propensity to subside, and porous layer strength. Porosity was the only significant factor affecting expulsion, subsidence, and ultimate shear strength. As porosity increased, expulsion resistance of the surface porosity sample increased, resulting in samples that are harder to push out of a constrained bony cavity; however, shear strength and propensity to subside both decreased, resulting in a weaker metal-to-metal porous layer adhesion and equivalent penetration into the Sawbone surface at lower forces. Within the error of the measurements, the 6 × 6 × 6 0.75 mm wall thickness gyroid (65% modeled porosity and 62% measured porosity) design presented the best overall performance characteristics.

Mechanical behaviors regulation of triply periodic minimal surface structures with crystal twinning

Triply periodic minimal surface (TPMS) structures have been realized as excellent mechanical materials with high specific strength, energy absorption, and unique layered deformation mechanism due to their saddle shape-surface with non-positive Gaussian curvature. However, the performance of TPMS structures is limited by anisotropic mechanical behavior owing to the oblique shear band with stress concentration when the load beyond the yield stress, resulting in structural catastrophic failure. Herein, a strategy is proposed to manipulating the path of stress transfer by introducing crystal twinning to achieve a designable deformation behavior of the TPMS structures. Various contact reflection twin boundaries for the gyroid (G) and diamond (D) surface structures have been introduced by connecting the ideal structures by mirror-symmetry while maintaining the structural integrity. Compression tests were carried out from various directions of perfect and twinned- G and D surface scaffolds after 3D printing. It was found that the twin boundary can effectively protect the structure from catastrophic failure by deflecting the cracks under compressive loads, and regulate the deformation behavior by various structural design. This study provides new insights in applying the microscopic crystal defects to macroscopic architectural materials, which also contributes to the understanding of these unique microscopic structures. Graphical abstract • Inspired by crystal twinning, deformation programmable TPMS structures were constructed. • Effects of the number, location and orientation of twin boundaries on TPMS structures were investigated. • FE simulations reveal that twin boundaries effectively manipulate the direction and path of stress transfer. • This method can be extended to other type of crystal defects and may yield different phenomena.

Helical Microdomains with Homochirality Trapped in a Gyroid Network from Symmetric AB1CB2D Pentablock Quaterpolymer Melt Studied by Monte Carlo Simulation

Front Cover: Phase behavior of symmetric ABCBD pentablock quarterpolymers has been investigated by Monte-Carlo simulation. Two alternating helices of red(A) and blue(B)) domains are trapped in {100} large homochiral holes of the level surface for the Schoen's Gyroid surface indicated in green. The red and blue helices are naturally packed tetragonally with the same helical sense, i.e., they keep homochirality. This is reported by Jiro Suzuki, Atsushi Takano, and Yushu Matsushita in article number 2200015.

Design and 3D printing manufacturing of complex structures for airflow evaluation

ABSTRACT 3D printing has been established as a versatile option for obtaining complex structures useful in diverse science or technology fields. Heterogeneous photocatalysis is one of the fields where complex geometries are needed to generate parameters such as great surface area and better residence times inside the structures. This research focuses on the design and manufacturing of 3D printed filters as part of a photocatalytic system. The first stage presented here consists of design, manufacturing, and evaluating different structures that could favor specifically our designed reaction system and the mentioned parameters useful for heterogeneous photocatalysis in airflow with polluted gaseous currents. Thus, six different filters were designed based on gyroid surfaces, zeolite (mordenite), and sinusoidal function. Accordingly results of easily manufacturing by 3D printing (SLA and FDM) and the finishing of the pieces, three filters were elected to evaluate airflow on their structures employing simulation of a wind tunnel with the software Autodesk Flow Design and RWIND Simulation of Dlubal, both in 2D and 3D diagrams. Thus, the filters with the most adequate geometries for specific parameters in our system will be probed in future stage as supports or components to assist adequality the toxic gases degradation in the photocatalytic process.

Polarization-dependent reflection of I-WP minimal-surface-based photonic crystal.

Brilliantly colored butterflies and weevils are known to utilize photonic crystals for their coloration. Interestingly, the morphology of such crystals made of cuticle is based on triply periodic minimal surfaces such as gyroid and diamond surfaces. Recently, a different minimal-surface-based photonic crystal, the I-WP surface, was discovered inside the scale of a longhorn beetle. The letter I is derived from expressing the body center symmetry and WP is derived from a wrapped package. It was reported that the brilliant green color is produced by the photonic band gap existing along the [110] direction of this crystal. In this study, the polarization dependence of the reflection from this photonic crystal was investigated. A peculiar reflectance spectrum with two peaks was observed under the crossed polarizers. This characteristic is theoretically reproduced by calculating the reflectance from a finite-sized photonic crystal, and the spectral shape is explained based on the symmetry of the electromagnetic modes. In addition, inspired by this longhorn beetle, a photonic crystal structure consisting of colloidal particles is proposed, which has a similar polarization effect.