Triply Periodic Minimal Surface Structures Research Articles

Design of nonlinear gradient sheet-based TPMS-lattice using artificial neural networks

Gradient triply periodic minimal surface (TPMS) structures are renowned for lightweight design and enhanced performance, but their complex and nonlinear configurations pose challenges in achieving targeted design goals. A new design methodology for the nonlinear gradient structure was proposed in this study, with the aim of achieving efficient and accurate modeling of complex and gradient sheet-based TPMS structures under specific performance objectives. This method utilized automated finite element (FE) simulations to obtain structure topology element densities under various boundary conditions. An artificial neural network (ANN) was then employed to efficiently predict the correspondence between these boundary conditions and topology element densities. A mapping was established between topology element densities and TPMS structural parameters, and the gradient structure was accurately constructed by using the voxel modeling technique. Taking a typical cantilever beam TPMS structure as an example of nonlinear gradient design, the results indicate that the error between the ANN-predicted and FE-simulated structure topology element densities is only 2.73 %, with prediction time being only 0.15 % of the simulation time. The thin regions of the gradient structure align with those geometrically removed in regular topology optimization scheme, achieving up to 65.45 % weight reduction, a 28.72 % improvement over the regular scheme, along with uniform structural stress transition and maximum stress reduction. TC4 alloy nonlinear gradient TPMS structures, printed by metal selective laser melting (SLM) technique, confirm the practical application value of this design method.

Enhancing tensile properties of polymer‐based triply periodic minimal surface metamaterial structures: Investigating the impact of post‐curing time and layer thickness via response surface methodology

AbstractThis research aims to explore the influence of post‐curing time and layer thickness on the tensile characteristics of various triply periodic minimal surface (TPMS) structures produced by mask stereolithography (MSLA). The study determined the best post‐curing duration, layer thickness, and TPMS lattice type to improve ultimate tensile strength (UTS) and absorbed energy. To experimentally evaluate the tensile characteristics, a dog bone‐shaped specimen was utilized. Three distinct TPMS structures, Gyroid (G), Neovius (N), and Diamond (D), were present in the test region. After investigating many process factors with response surface methodology (RSM), optimization methods are applied to find their best printing procedure. The work shows the novel use of RSM to optimize post‐curing and printing parameters on TPMS structure mechanical properties during manufacturing. According to the optimization results, the biggest factor affecting UTS is layer thickness, while the most significant factor increasing energy is curing time. The optimal operating parameters for MSLA printing based on the optimization results are a layer thickness of 0.05 mm, a post‐curing period of 40 min, and a lattice type of N. The optimum responses corresponding to the optimum parameters were determined as 7.16 MPa for UTS and 18.16 J for energy.Highlights Optimized the production process parameters of TPMS geometries. Compared TPMS structures for mechanical performance. Identified optimal input parameters to improve UTS and energy absorption. Conducted comprehensive experimental evaluations to validate the optimization.

Crack propagation in TPMS scaffolds under monotonic axial load: Effect of morphology

In this paper, the mechanical behaviour and failure of porous additively manufactured (AM) polylactide (PLA) scaffolds based on the triply periodic minimal surfaces (TPMS) is investigated using numerical calculations of their unit cells and representative volumes. The strain-amplification factor is chosen as the main parameter, and the most critical locations for failure of different types of scaffold structures are evaluated. The results obtained are presented in comparison with a multiple-crack-growth algorithm using the extended finite element method (XFEM), underpinned by the experimentally obtained fracture properties of PLA. The effect of morphology of TPMS structures on the pre-critical, critical and post-critical behaviours of scaffolds under monotonic loading regimes is assessed. The results provide an understanding of the fracture behaviour and main risk points for crack initiation in structures of AM-PLA scaffolds based on typical commonly used types of TPMS, as well as the influence of structure type and external load on this behaviour.

Vat photopolymerization 3D printing of glass microballoon-reinforced TPMS meta-structures

Advancements in additive manufacturing coincide with the influx of assiduous research in realizing complex structures using printable composite materials with tunable properties. In this research study, photocurable resins with a broad range of mechanical properties were hybridized with ceramic particles to engineer the overall mechanical response. The newly formulated printable resins comprised up to 20 wt.% glass microballoons, balancing the tunability of the composite properties and manufacturability by overcoming light-reinforcement challenges. The compressive and tensile bulk properties were first assessed using additively manufactured samples tested under quasi-static loading. Complementary digital image correlation (DIC) was used to resolve the strain fields, revealing insights about the mechanical behavior and failure modes as a function of reinforcement weight ratio. Despite the expected hyperelastic constitutive behavior and shared macromolecular composition, the neat and hybridized photocurable resins exhibited distinctive mechanical behavior, leading to the characterization of the dynamic properties as a function of temperature to ascertain the underpinnings of respective responses. Triply periodic minimal surface (TPMS) structures were also manufactured using the vat photopolymerization approach to demonstrate the utility of newly formulated printable composite resins. The printed structures were tested under compression at a quasi-static loading rate. The DIC-resolved strains revealed the underlying structural mechanics as a function of the material properties. This case study correlates the mechanics governing particulate-reinforced elastomers with the observed variations in strain development, stiffness, load-bearing capacity, and specific energy absorption for TPMS structures. Finite element analysis (FEA) based on hyperelastic potential and using the properties of the bulk resin closely matched the deformation patterns from the experimental DIC results. The outcomes of this research reveal the potential for tunable, 3D printed sports gear for impact mitigation in various biomechanical loading conditions.

Effect of residual stress on mechanical properties of Triply periodic minimal surface lattice structures in Additive manufacturing

Due to its special porous structure with smooth continuous surface and high specific surface area, the triply periodic minimal surface (TPMS) lattice structure exhibits excellent properties such as strong bearing capacity, high energy absorption rate and good fatigue performance. The residual stresses generated during the additive manufacturing (AM) process can have a significant impact on the mechanical properties of the TPMS structure. In this paper, the AM process of four typical TPMS structures are investigated by the thermal–mechanical coupling model. The mechanism of residual stress generation is analyzed, and an optimized preparation process scheme is proposed to reduce the residual stress. Furthermore, the effects of residual stresses on the mechanical properties of TPMS structures are investigated for different types, volume fractions and compression directions. Results show that the influences of scanning speed and hatch spacing on the residual stress are not significant with constant laser power, but the deposition thickness should be adjusted according to the characteristics of the structure. The residual stress will reduce the elastic modulus and yield strength, while no obvious effect on the plastic behavior is observed. Importantly, the residual stress has the greatest influence on the mechanical properties of I-WP-type among the four investigated types, which becomes more pronounced with the increase of volume fraction. Moreover, the influence of residual stress on the mechanical properties of TPMS structures depends on the compression direction. Our results give a comprehensive understanding of the residual stress distribution and impact on the mechanical properties of TPMS structures, providing guidance to the rational design and optimization of TPMS structures in engineering applications.

Investigations on the heat transfer performance of phase change material (PCM)-based heat sink with triply periodic minimal surfaces (TPMS)

During the operational process of electronic components, excessive heat generation results in significant temperature elevation. This elevated temperature poses a significant risk to their service life. Regarding the issue of efficient thermal management of electronic devices in enclosed spaces experiencing high heat flow, a thermal management scheme for electronic equipment using TPMS and a PCM-based heat sink is proposed. The apparent heat capacity method is employed to simulate the melting process of the PCM-based heat sink. The effects of structural parameters w1, w3, and C of TPMS structures on the heat transfer characteristics (including base temperature, liquid fraction, average cell temperature, and average heat transfer coefficient) of the PCM-based heat sink during the melting process are discussed. A temperature testing platform is established. Experimental research is performed to investigate the effect of TPMS structures with two different printing prototypes (Sample 1, and Sample 2) on the heat sink during the intermittent cycle. The results indicate that increasing the parameters C and w1 significantly improves the average heat transfer coefficient (HTC) of the heat sink. When C increases from 0.3 to 0.7, the average HTC increases from 307 W/(m2·K) to 358 W/(m2·K). When w1 increases from 1 to 3, the average HTC increases from 284.5 W/(m2·K) to 321.3 W/(m2·K). Sample 1, possessing superior thermal conductivity, exhibits better heat transfer performance. When the temperature achieves a stable periodic variation, the base temperature of Sample 1 stabilizes within the range of 310 K-340 K. And Sample 2 stabilizes within the range of 315 K-350 K.

Design and performance assessment of a triply-periodic-minimal-surface structures-enhanced gallium heat sink for high heat flux dissipation: A numerical study

This study numerically investigates a phase-change material heat sink using gallium and Primitive Triply Periodic Minimal Surface (TPMS) cells structure as in-fill for applications requiring high heat-flux dissipation, e.g., electronics. Initially, we used only gallium without thermal conductivity enhancers, relying solely on buoyancy-driven circulations of melted gallium for the convective cooling of a hot sink base. However, this study aims to surpass gallium’s innate heat-dissipation capability. Therefore, the sink is enhanced with a high conductivity Primitive TPMS cells structure. Hybridization of conduction and convection heat dissipation enhancements is accomplished by using only one layer of the TPMS cells installed at the hot sink base. Comparison with the full TPMS structure filling option is made. In the full TPMS structure filling option, the sink relies mainly on conduction through the TPMS structure’s body and less on natural convection. However, equipping the sink with TPMS structures reduces the overall latent heat storage capacity. Therefore, additional gallium is added to the sink to match the overall gallium content in the baseline case without TPMS structures. Furthermore, the effect of the boundary conditions applied at the wall is explored. The results show considerable improvements in heat dissipation and peak temperatures with the TPMS cells, where by the time 100 s (about 20 s post complete melting) peak temperatures are about 13 percent lower than in the case without TPMS structures. Furthermore, the full structure filling option demonstrates superior performance over the partially filled ones, highlighting the importance of conduction through TPMS cells over convection in the free gallium space. Unlike the partial filling option, conduction in the full filling option has a continuous favorable impact on heat dissipation from the onset of the heating process.

Bending performance and failure mechanisms of composite sandwich structures with 3D printed hybrid triply periodic minimal surface cores

In this paper, a novel hybrid triply periodic minimal surface (TPMS) core with a nonlinear transition region was designed by combining two types of TPMS (Diamond and Schwarz P) structures using the sigmoid function. The width of the transition region was precisely regulated by adjusting the gradient control parameter r in the sigmoid function. Composite sandwich structures (CSS) were fabricated by bonding two carbon fiber reinforced polymer (CFRP) face sheets to a 3D printed polylactic acid (PLA) core. The bending performance and failure mechanisms of the CSSs with the hybrid TPMS cores were analyzed through three-point bending tests and finite element analysis (FEA). The results indicate that as r increases, the transition region of the hybrid TPMS cores becomes narrower, leading to a gradual decrease in bending strength, bending stiffness, and core shear stress. The failure process of the CSSs in the experiment aligns well with the FEA results. Through comparative analysis of the stiffness-to-weight and strength-to-weight ratios of the CSSs with the native TPMS cores, the hybrid TPMS cores with a wider transition region enhance the structural efficiency of the CSSs, while those with a narrower transition region negatively impact the performance of the CSSs.

Multi-morphological design of TPMS-based microchannels for thermal performance optimization

Higher heat flux density in more compact and powerful electronic systems calls for further innovative solutions. Microchannel heat sinks based on triply periodic minimal surface (TPMS) can help dissipate highly concentrated heat, ensuring the system’s safety and longevity. Some researches indicate that compared to traditional TPMS structures, multi-morphology TPMS structures can further improve performances and adapt to local functional requirements. However, the morphology distribution has not been analyzed from a thermal performance perspective. In this study, a multi-morphological TPMS-based microchannel design method for thermal performance optimization is proposed. Firstly, the thermal properties of different TPMS structures are analyzed using the homogenization method, which provides a theoretical basis for TPMS distributions and their transition boundaries. Then, a beta growth algorithm is proposed to smoothly transition these regions with complex transition boundaries. A series of designed microchannels show that this method can not only greatly increase design freedom but also automatically guarantee the geometric continuity of heterogeneous TPMS structures. Finally, the optimized microchannel and the traditional gradient microchannel are compared in a finite element analysis simulation. And the results show that the optimized structure’s cooling efficiency increased by 4.4%, and its cooling uniformity improved by 15%, proving that properly arranging the TPMS morphology can further enhance thermal performance.

3D-printed triply periodic minimal surface (TPMS) structures as catalyst carriers

The flow and forced convection heat transfer properties of triply periodic minimal surface (TPMS) lattices were investigated both experimentally and numerically. The TPMS structures consist of periodically arranged Gyroid (G) unit cells of 81 % porosity and different unit cell sizes (2–4 mm). This is the first study to evaluate the effect of cell diameter on pressure drop and heat transfer characteristics of solid-gyroid structures prepared by selective laser melting (SLM) technique. Moreover, the range of pore-based Reynolds number covered the laminar and turbulent regimes (Rep=11–1700). The results shown that larger cell diameter provides higher heat transfer coefficients and unit pressure drop. An increase of cell diameter from 2 mm to 4 mm can enhance heat transfer coefficient and unit pressure drop of 39 % and 85 %, respectively. New correlations for flow resistance and heat transfer of solid-gyroid structures were developed. It was confirmed that TPMS lattices can be an alternative to conventional catalytic supports, because they provide comparable thermal efficiency index as foam and packed bed.

Fabrication characterization and compression failure analysis of Ni-based alloy ABD-900AM TMPS structures via laser powder bed fusion

The novel high-strength and high-temperature nickel-based alloy developed for additive manufacturing, i.e., ABD-900AM, shows great potential in next-generation aircraft engines. However, there are limited investigations about the printing capability of ABD-900AM with complex structure as well as compression behaviors of this new alloy system. To meet the lightweight requirement, ABD-900AM with triply periodic minimal surface (TPMS) is fabricated by selective laser melting (SLM) in the present work, and the printing quality and compression performance of different TPMS structures are analyzed utilizing both experimental and computational methods. First, six types of TPMS structures are designed, and the external contours fabricated by SLMed ABD-900AM are detected through 3D optical scanning. In general, high fabrication quality is achieved with the proper process parameters, while the positive deviations are observed at the lateral surfaces and edges, and the negative deviations are observed at the upper regions of the cellular structures. Further, compression tests of SLMed ABD-900AM TPMS structures are conducted, and the failure mechanisms are evaluated. The equivalent elastic modulus is ranked as Diamond > Split-P > Primitive > Gyroid > I-WP > Lidinoid. The SLMed ABD-900AM TPMS structures shows advantages compared to these TPMS structures fabricated using typical metal alloys. Finally, the computational models of SLMed ABD-900AM TPMS structures are built up in the commercial software ABAQUS. The stress-strain behaviors and the failure process of different SLMed ABD-900AM TPMS structures are successfully reproduced.

Mechanical properties and energy absorption of medium-entropy alloy triply periodic minimal surface cellular structures fabricated via selective laser melting

Triply periodic minimal surfaces (TPMSs) are extensively used as effective tools for the microarchitectural designing of cellular structures. CoCrNi medium-entropy alloy, known for its high strength and high ductility, is an ideal candidate for fabricating TPMS-based structures. However, few studies have focused on this topic. This study investigated the compressive mechanical and energy absorption properties of CoCrNi D-sheet TPMS cellular structures fabricated via selective laser melting (SLM). The surface morphology of the fabricated D-sheet TPMS structure was observed through scanning electron microscopy, and the deformation and failure mechanisms of the structure were analyzed by the quasi-static compression test. The results indicated that the SLM-ed CoCrNi D-sheet TPMS structure exhibited stable collapse mechanisms compared to other metal-based TPMS structures. Meanwhile, the energy absorption characteristics of the modified finite element (FE) model agreed well with the experimental results. Furthermore, the impact of the level constant on the energy absorption performance of the D-sheet TPMS structure was investigated using the FE model. Thus, an optimal D-sheet (OD-sheet) TPMS structure with lower density and higher energy absorption capacity was obtained. Additionally, the Gibson–Ashby prediction model was established to aid in selecting CoCrNi OD-sheet TPMS structures with controlled relative densities for energy absorption applications.

Design exploration of staggered hybrid minimal surface magnesium alloy bone scaffolds

Bone implant design faces multifaceted challenges, requiring the simultaneous optimization of hierarchical porous structures, large surface areas, and appropriate elastic moduli. Triply Periodic Minimal Surface (TPMS) structures show promise but are limited in their design space, making it difficult to comprehensively and precisely control these properties. This study introduces a novel implicit modeling method for reconstructing TPMS structures, breaking longstanding limitations of design freedom in bone implant design. This innovative approach uses an offset function to precisely manipulate discrete points on the isosurface, achieving unprecedented controllable freeform deformation while avoiding errors in conventional Boolean operations. Building on this breakthrough, new staggered hybrid TPMS (SH-TPMS) porous structures are developed that effectively balance and optimize volume fraction and surface area. Subsequently, magnesium alloy SH-TPMS bone scaffolds have been successfully fabricated using laser powder bed fusion (LPBF) technology. The resulting SH-TPMS structures feature multi-level controllable channel architectures. Compared to conventional TPMS structures, these staggered hybrid designs maintain consistent elastic modulus and deformation patterns through optimized mass distribution while achieving an average increase of 50 % in specific surface area at equivalent volume fractions. Mechanical performance tests confirm that the elastic moduli of the SH-Gyroid and SH-Diamond scaffolds are 4.56 GPa and 8.40 GPa, respectively, comparable to that of human bone. This work presents a promising new strategy for fabricating optimized bone implants, offering a balance between enhanced surface area and tailored mechanical properties.

Sandwich structures with TPMS core and printed circuit board faces

Sandwich structures are widely used in the aerospace industries due to their mechanical properties that give them high energy absorption, low density, and high mechanical strength. These structures are composed of two faces interspersed by a core that can have various geometric configurations. One of the most widely used geometric cells are honeycomb structures, highly used in structural applications since the early 20th century. However, new geometric core configurations, as well as alternative materials and manufacturing processes, are being studied for space applications. Triply Periodic Minimal Surfaces (TPMS) are lattice structures composed of periodic surface structures in three independent directions. Among the available models, the most notable TPMS structures are Schwartz-type, Diamond-type, and Gyroid-type. Since the structures are too complex to be manufactured by subtractive manufacturing, additive manufacturing is excellent, being able to produce complex structures much faster and easier. One of the most common types of 3D printing is Fused Deposition Modeling (FDM), which is based on the fusion and deposition of various materials, such as thermoplastic materials. To save space and improve the mechanical strength of Cubesats, sandwich structures are being produced using printed circuit boards (PCB) of electrical and electronic components as outer faces. These faces are called laminates and are made of thermosetting materials such as fiberglass and epoxy resin, composites, or ceramic materials. The objective of this paper is to produce sandwich panels, with a core based on the TPMS architecture. They will be printed in thermoplastic material with laminated faces used in printed circuit boards. A numerical analysis using the finite element method was performed and its testing according to ASTM C393, furthermore, this paper aims to realize an optimized TPMS core with mass distribution based on the stress profile and compare them.

Study on the Energy Absorption Performance of Triply Periodic Minimal Surface (TPMS) Structures at Different Load-Bearing Angles.

As engineering demands for structural energy absorption intensify, triply periodic minimal surface (TPMS) structures, known for their light weight and exceptional energy absorption, are increasingly valued in aerospace, automotive, and shipping engineering. In this study, the energy absorption performance of three typical TPMS structures was evaluated (i.e., Gyroid, Diamond, and IWP) using quasi-static compression tests at various load-bearing angles. The results showed that while there is little influence of load-bearing angles on the energy absorption performance of Gyroid structures, its energy absorption is the least of the three structures. In contrast, Diamond structures have notable fluctuation in energy absorption at certain angles. Moreover, IWP (I-graph and Wrapped Package-graph) structures, though highly angle-sensitive, achieve the highest energy absorption. Further analysis of deformation behaviors revealed that structures dominated by bending deformation are stable under multi-directional loads but less efficient in energy absorption. Conversely, structures exhibiting mainly tensile deformation, despite their load direction sensitivity, perform best in energy absorption. By integrating bending and tensile deformations, energy absorption was enhanced through a multi-stage platform response. The data and conclusions revealed in the present study can provide valuable insights for future applications of TPMS structures.

An isogeometric analysis of solar panels with a bio-inspired substrate

We in this paper propose a high-performance design using bio-inspired metamaterials for multilayered perovskite solar cell (MPSC) plates. The static bending and free vibrational responses of the newly designed MPSC panels with the presence of the triply periodic minimal surface (TPMS) substrate are subsequently investigated numerically. The displacements of the present plate model are then approximated by five-variable higher-order shear deformation theories (HSDTs). The weak forms are established for both the static bending and free vibration problems and subsequently derive the discrete forms using the NURBS-based isogeometric approach. To enhance the operational efficiency of solar panels in challenging environments, we integrate advanced lightweight architectures based on bio-inspired TPMS structures as a substrate layer into the original solar panel design. In this research, three widely employed TPMS structures: Primitive, Gyroid, and I-graph and Wrapped Package-graph (IWP), are examined in conjunction with two functional grading patterns implemented through the thickness direction. For the first time, the static bending performance of MPSC plates integrated into a TPMS-based substrate layer and subjected to wind pressure as well as thermal conditions is comprehensively studied. In addition, the influence of several significant factors on the free vibration behavior of MPSC plates is also elucidated. The findings show a promising and intriguing design avenue, particularly in the application of high-performance metamaterials to address contemporary challenges in renewable energy usage and environmental protection.

Enhancing mechanical properties and damage tolerance of additive manufactured ceramic TPMS lattices by hybrid design

AbstractMany studies have reported that additive manufactured ceramic lattices with microarchitectures often exhibit low‐strain brittle fracture behavior. In this work, the fracture behavior of ceramic triply periodic minimal surface (TPMS) lattices was optimized by introducing a hybrid design strategy that utilizes different microarchitectures. Hybrid ceramic TPMS structures incorporating Gyroid and Primitive unit cells were successfully fabricated using the Lithography‐based ceramics manufacturing (LCM) technique, and their mechanical properties were evaluated under both quasistatic and dynamic compression. The hybrid designs exhibited improved damage tolerance and fracture strength compared to their normal counterparts. Compared to normal Gyroid and Primitive structures, the G2P2 structure exhibits the best energy absorption capacity of 12.5 × 104 J/m3, demonstrating a 13% and 217% increase in energy absorption capacity under quasistatic loading, respectively. Additionally, compared with other normal and hybrid designs, the G2P2 structure exhibits the highest fracture strength of 13.03 MPa under quasistatic loading conditions. Moreover, the P2G hybrid structure displayed a distinct deformation pattern characterized by a smoother stress decrease under quasistatic loading, enhancing damage tolerance. The order of Young's modulus under quasistatic loading was Normal Gyroid ≈ G2P2 > G2P1 > Normal Primitive > P2G. Fracture strength follows the order of G2P2 ≈ Normal Gyroid > Normal Primitive > G2P1 > P2G. The mechanical properties of hybrid TPMS structures suggest that the hybrid design strategy can broaden the achievable range of mechanical properties among ceramic TPMS structures.

Expanding manufacturability of sheet-based triply periodic minimal surfaces by electron beam powder bed fusion in Wafer theme

Porous biomaterials based on triply periodic minimal surfaces (TPMS) are intensely studied and discussed in the literature. Manufacturing of these structures with a complex geometry became possible using additive manufacturing methods, having their own specifics and challenges. Previously, we demonstrated that sheet-based gyroids, one of TPMS structures, manufactured by electron beam powder bed fusion in Melt and Wafer themes could possess identical mechanical properties (quasi-elastic gradient). In the current research sheet-based gyroids were produced using Wafer Theme with five different settings, including electron beam current and scan speed variation with MultiBeam turned on and off, in attempt to obtain thin walls without losing mechanical performance. Mechanical tests revealed that the specimens manufactured with higher beam line energy on average show better mechanical properties. The specimens produced with MultiBeam showed slightly lower mechanical properties, and do not demonstrate significant improvement in the TPMS surface roughness. According to SEM studies, the average wall thickness was about 0.4 mm for specimens with high line energy, and 0.3 mm for low line energy. Through-hole defects on the horizontal surfaces, noticed and discussed by us previously, have larger average area of the hole and more irregular shape for increased beam line energy. TPMS surface morphology of the specimens produced with higher beam energy and no MultiBeam was on average more even. According to EBSD, α/α` martensite with laths oriented in a Widmanstätten basket-weave pattern was observed with no β phase in the resulting material. No significant differences in microstructure between specimens produced with different beam energy was detected. FEA modeling revealed the impact of the wall thickness, through holes size and orientation on quasi-elastic gradient of a gyroid. It was demonstrated that, through holes with small size located on the horizontal surfaces (layer plane) have only a minor impact on the mechanical properties of the samples if they are not extremely abundant.

Multifunctional Design of Triply Periodic Minimal Surface Structures for Temporary Pediatric Fixation Devices

Fracture fixation and limb deformity correction in pediatric orthopedics often use temporary metallic fixation devices. These devices’ higher stiffness compared to cortical bone leads to stress shielding, causing significant bone density reduction, periprosthetic loosening, and bone growth interference. The 3D‐printed triply periodic minimal surface (TPMS) structures present a promising engineering solution to match bone stiffness while ensuring reliable implant strength. In this study, finite‐element modeling and experimental testing are employed to identify optimal multifunctional TPMS‐based lattices that meet the required design constraints of 1) stiffness in the range of cortical bone, 2) strength in the range of cortical bone, 3) minimum osteointegration to facilitate the implant removal after healing, and 4) manufacturability with limited defect sensitivity. Six different types of TPMS structures in Ti–6Al–4V material manufactured via laser powder bed fusion are evaluated for their ability to target the lower and upper bounds of pediatric cortical bone stiffness. Lattices based on the Primitive unit cell design are superior, demonstrating the highest strength/stiffness ratio, best manufacturability, and potentially reduced osteointegration due to larger pore size, smaller surface area, and smallest negative Gaussian curvature compared to other investigated TPMS types.

Study on isotropic design of triply periodic minimal surface structures under an elastic modulus compensation mechanism

The energy absorption characteristics of the triply periodic minimal surfaces (TPMS) structure may vary significantly due to the anisotropy under multi-directional loading conditions. To address this issue effectively, an isotropic design strategy based on a precise elastic modulus compensation mechanism for different TPMS lattices is proposed. This strategy involves combining a TPMS lattice with a high elastic modulus in the axial direction with another TPMS lattice featuring a low elastic modulus in the same direction, leveraging the complementary effects of elastic modulus to achieve isotropy. The relationship between the relative density and the elastic modulus of six types of TPMS lattices is analyzed through homogenization simulation and finite element analysis. Mathematical expressions are then fitted using the Gibson-Ashby model. Additionally, a Kriging model is employed to establish the relationship between the Zener anisotropy values of hybrid TPMS structures and the relative density of their component lattices. This enables the precise complementary effect of elastic modulus in different TPMS lattice structures, providing a widely applicable selection rule for achieving isotropy. Using the Primitive-Diamond hybrid lattice as an example, the Zener anisotropy index after hybridization is reduced by 65.2 % and 31.37 % compared to single Primitive and Diamond lattices, respectively.