Triply periodic minimal surface(TPMS)-based bone implants are an innovative approach in orthopedic implantology,offering customized solutions for bone defect repair and regeneration.This review comprehensively examine...Triply periodic minimal surface(TPMS)-based bone implants are an innovative approach in orthopedic implantology,offering customized solutions for bone defect repair and regeneration.This review comprehensively examines the current research landscape of TPMS-based bone implants,addressing key challenges and proposing future directions.It explores design strategies aimed at optimizing mechanical strength and enhancing biological integration,with a particular emphasis on TPMS structures.These design strategies include graded,hierarchical,and hybrid designs,each contributing to the overall functionality and performance of the implants.This review also highlights state-of-the-art fabrication technologies,particularly advancements in additive manufacturing(AM)techniques for creating metal-based,polymer-based,and ceramic-based bone implants.The ability to precisely control the architecture of TPMS structures using AM techniques is crucial for tailoring the mechanical and biological properties of such implants.Furthermore,this review critically evaluates the biological performance of TPMS implants,focusing on their potential to promote bone ingrowth and regeneration.Key factors,such as mechanical properties,permeability,and biocompatibility,are examined to determine the effectiveness of these implants in clinical applications.By synthesizing existing knowledge and proposing innovative research directions,this review underscores the transformative potential of TPMS-based bone implants in orthopedic surgery.The objective is to improve clinical outcomes and enhance patient care through advanced implant designs and manufacturing techniques.展开更多
Magnesium(Mg)-based materials are promising for lightweight structural applications.However,their widespread adoption is significantly constrained by inherent limitations in mechanical properties.To address this chall...Magnesium(Mg)-based materials are promising for lightweight structural applications.However,their widespread adoption is significantly constrained by inherent limitations in mechanical properties.To address this challenge,this study introduces a novel Mg-based interpenetratingphase composite reinforced with a nickel-titanium(NiTi)scaffold featuring a triply periodic minimal surface(TPMS)configuration.By combining experimental investigations with finite element simulations,we systematically elucidate the dual impact of the scaffold’s unit cell size(a)on manufacturing viability and mechanical enhancement.To compensate for compromised infiltration dynamics induced by decreasing a,a critical permeability threshold of 1×10^(-8) m^(2) is proposed for achieving successful composite fabrication.Mechanically,reducing a strengthens the interaction between the scaffold and matrix:the TPMS-configured NiTi scaffolds improve stress transfer,deflect crack propagation,and facilitate damage delocalization,whereas the Mg matrix preserves structural integrity and enables load redistribution.Consequently,the composites significantly outperform pure Mg,and lowering a leads to more substantial enhancements in compressive strength,energy dissipation,and deformation recoverability.This study offers valuable insight into the design and fabrication of highperformance Mg-based materials for structural and biomedical applications.展开更多
The pore structure of porous scaffolds plays a crucial role in bone repair.The prevalent bone implant structure in clinical practice is the traditional cubic structure.However,the traditional cubic structure exhibits ...The pore structure of porous scaffolds plays a crucial role in bone repair.The prevalent bone implant structure in clinical practice is the traditional cubic structure.However,the traditional cubic structure exhibits sharp edges and junctions that are not conducive to cell adhesion or growth.In this study,a double gyroid(DG)Ti6Al4V scaffold based on a triply periodic minimal surface(TPMS)structure was devised,and the osseointegration performance of DG structural scaffolds with varying porosities was investigated.Compression tests revealed that the elastic modulus and compressive strength of DG structural scaffolds were sufficient for orthopedic implants.In vitro cellular experiments demonstrated that the DG structure significantly enhanced cell proliferation,vascularization,and osteogenic differentiation compared to the cubic structure.The DG structure with 55%porosity exhibited the most favorable outcomes.In vivo experiments in rabbits further demonstrated that DG scaffolds could promote neovascularization and bone regeneration and maturation;those with 55%porosity performed best.Comparing the surface area,specific surface area per unit volume,and internal flow distribution characteristics of gyroid and DG structure scaffolds,the latter are more conducive to cell adhesion and growth within scaffolds.This study underscored the potential of DG scaffolds based on the TPMS structure in optimizing the pore structure design of titanium scaffolds,inducing angiogenesis,and advancing the clinical application of titanium scaffolds for repairing bone defects.展开更多
Triply periodic minimal surface(TPMS)structures,characterized by special repeating 3D surface periodically with an average curvature of zero in threedimensional directions,have a wide range of applications.Laser powde...Triply periodic minimal surface(TPMS)structures,characterized by special repeating 3D surface periodically with an average curvature of zero in threedimensional directions,have a wide range of applications.Laser powder bed fusion(LPBF)technique,as a type of additive manufacturing techniques,provides the capability to fabricate such complex-shaped porous TPMS structures.In this study,Ti6Al4V G-sheet TPMS structures with various unit cell sizes were fabricated using LPBF to investigate the structural and material anisotropy and their effects on the anisotropy in energy absorption capacity by combining the finite element simulations and experimental analysis.The results showed that the TPMS structures can be successfully fabricated using LPBF,although the sheet thickness exceeds the designed values,with deviation decreasing as the unit cell size increases from 2 to 4 mm.The inherent anisotropy during the LPBF process results in variations in structural dimension,materials characteristics,and energy absorption capacity between directions parallel and perpendicular to the build direction.The anisotropic ratio of the LPBFed Ti6Al4V G-sheet TPMS structures increases from 1.5 to 2.2 in the structural dimension and from 2.8 to 3.3 in specific energy absorption per unit mass(SEA_(m))respectively with decreasing the unit cell size from 4 to 2 mm.The anisotropy of SEA_(m) primarily originates from the coupling effects of anisotropic dimensions and material properties in the LPBFed G-sheet TPMS structure.Among these factors,anisotropic material properties play a more significant role compared to dimensional anisotropy.展开更多
Lattice structures can be designed to achieve unique mechanical properties and have attracted increasing attention for applications in high-end industrial equipment,along with the advances in additive manufacturing(AM...Lattice structures can be designed to achieve unique mechanical properties and have attracted increasing attention for applications in high-end industrial equipment,along with the advances in additive manufacturing(AM)technologies.In this work,a novel design of plate lattice structures described by a parametric model is proposed to enrich the design space of plate lattice structures with high connectivity suitable for AM processes.The parametric model takes the basic unit of the triple periodic minimal surface(TPMS)lattice as a skeleton and adopts a set of generation parameters to determine the plate lattice structure with different topologies,which takes the advantages of both plate lattices for superior specific mechanical properties and TPMS lattices for high connectivity,and therefore is referred to as a TPMS-like plate lattice(TLPL).Furthermore,a data-driven shape optimization method is proposed to optimize the TLPL structure for maximum mechanical properties with or without the isotropic constraints.In this method,the genetic algorithm for the optimization is utilized for global search capability,and an artificial neural network(ANN)model for individual fitness estimation is integrated for high efficiency.A set of optimized TLPLs at different relative densities are experimentally validated by the selective laser melting(SLM)fabricated samples.It is confirmed that the optimized TLPLs could achieve elastic isotropy and have superior stiffness over other isotropic lattice structures.展开更多
With the rapid development of additive manufacturing(AM),scaffold architectures based on triply periodic minimal surfaces(TPMS)have attracted increasing interest in various engineering fields.Nevertheless,they are lim...With the rapid development of additive manufacturing(AM),scaffold architectures based on triply periodic minimal surfaces(TPMS)have attracted increasing interest in various engineering fields.Nevertheless,they are limited because of the complexity of the design process when adopted in different research and engineer-ing fields.In this work,we present a free and easy-to-use software package called TPMS_Scaffold_Generator,which is coded using MATLAB(Mathworks,Inc.,USA).It offers three function tabs which are homogeneous tab,heterogeneous tab and multisymmetrical tab,respectively.Variables of the tabs include the volume frac-tion,topology type,unit cell size,the length of architecture in X,Y,Z direction,accuracy,and the style of gradient and so forth.TPMS_Scaffold_Generator can generate various TPMS scaffolds,especially ultralight and multisymmetrical scaffolds.The latest version of the TPMS_Scaffold_Generator is freely available at:https://github.com/LeveeLin/TPMS_Scaffold_Generator.git.展开更多
Improving the shape memory effect and superelasticity of Cu-based shape memory alloys(SMAs)has always been a research hotspot in many countries.This work systematically investigates the effects of Gyroid triply period...Improving the shape memory effect and superelasticity of Cu-based shape memory alloys(SMAs)has always been a research hotspot in many countries.This work systematically investigates the effects of Gyroid triply periodic minimal surface(TPMS)lattice structures with different unit sizes and volume fractions on the manufacturing viability,compressive mechanical response,superelasticity and heating recovery properties of CuAlMn SMAs.The results show that the increased specific surface area of the lattice structure leads to increased powder adhesion,making the manufacturability proportional to the unit size and volume fraction.The compressive response of the CuAlMn SMAs Gyroid TPMS lattice structure is negatively correlated with the unit size and positively correlated with the volume fraction.The superelastic recovery of all CuAlMn SMAs with Gyroid TPMS lattice structures is within 5%when the cyclic cumulative strain is set to be 10%.The lattice structure shows the maximum superelasticity when the unit size is 3.00 mm and the volume fraction is 12%,and after heating recovery,the total recovery strain increases as the volume fraction increases.This study introduces a new strategy to enhance the superelastic properties and expand the applications of CuAlMn SMAs in soft robotics,medical equipment,aerospace and other fields.展开更多
Inspired by natural porous architectures,numerous attempts have been made to generate porous structures.Owing to the smooth surfaces,highly interconnected porous architectures,and mathematical controllable geometry fe...Inspired by natural porous architectures,numerous attempts have been made to generate porous structures.Owing to the smooth surfaces,highly interconnected porous architectures,and mathematical controllable geometry features,triply periodic minimal surface(TPMS)is emerging as an outstanding solution to constructing porous structures in recent years.However,many advantages of TPMS are not fully utilized in current research.Critical problems of the process from design,manufacturing to applications need further systematic and integrated discussions.In this work,a comprehensive overview of TPMS porous structures is provided.In order to generate the digital models of TPMS,the geometry design algorithms and performance control strategies are introduced according to diverse requirements.Based on that,precise additive manufacturing methods are summarized for fabricating physical TPMS products.Furthermore,actual multidisciplinary applications are presented to clarify the advantages and further potential of TPMS porous structures.Eventually,the existing problems and further research outlooks are discussed.展开更多
Minimal surface is extensively employed in many areas. In this paper, we propose a control mesh representation of a class of minimal surfaces, called generalized helicoid minimal surfaces, which contain the right heli...Minimal surface is extensively employed in many areas. In this paper, we propose a control mesh representation of a class of minimal surfaces, called generalized helicoid minimal surfaces, which contain the right helicoid and catenoid as special examples. We firstly construct the Bézier-like basis called AHT Bézier basis in the space spanned by {1, t, sint, cost, sinht, cosht}, t∈[0,α], α∈[0,5π/2]. Then we propose the control mesh representation of the generalized helicoid using the AHT Bézier basis. This kind of representation enables generating the minimal surfaces using the de Casteljau-like algorithm in CAD/CAGD mod- elling systems.展开更多
The new regenerative cooling thermal protection system exhibits the multifunctional characteristics of load-carrying and heat exchange cooling,which are fundamental for the lightweight design and thermal protection of...The new regenerative cooling thermal protection system exhibits the multifunctional characteristics of load-carrying and heat exchange cooling,which are fundamental for the lightweight design and thermal protection of hypersonic vehicles.Triply periodic minimal surface(TPMS)is especially suitable for the structural design of the internal cavity of regenerative cooling structures owing to its excellent structural characteristics.In this study,test pieces were manufactured using Ti6Al4V lightweight material.We designed three types of porous test pieces,and the interior was filled with a TPMS lattice(Gyroid,Primitive,I-WP)with a porosity of 30%.All porous test pieces were manufactured via selective laser melting technology.A combination of experiments and finite element simulations were performed to study the selection of the internal cavity structure of the regenerative cooling thermal protection system.Hence,the relationship between the geometry and mechanical properties of a unit cell is established,and the deformation mechanism of the porous unit cell is clarified.Among the three types of porous test pieces,the weight of the test piece filled with the Gyroid unit cell was reduced by 8.21%,the average tensile strength was reduced by 17.7%compared to the solid test piece,while the average tensile strength of the Primitive and I-WP porous test pieces were decreased by 30.5%and 33.3%,respectively.Compared with the other two types of unit cells,Gyroid exhibited better mechanical conductivity characteristics.Its deformation process was characterised by stretching,shearing,and twisting,while the Primitive and I-WP unit cells underwent tensile deformation and tensile and shear deformation,respectively.The finite element predictions in the study agree well with the experimental results.The results can provide a basis for the design of regenerative cooling thermal protection system.展开更多
Lattice structures have drawn much attention in engineering applications due to their lightweight and multi-functional properties.In this work,a mathematical design approach for functionally graded(FG)and helicoidal l...Lattice structures have drawn much attention in engineering applications due to their lightweight and multi-functional properties.In this work,a mathematical design approach for functionally graded(FG)and helicoidal lattice structures with triply periodic minimal surfaces is proposed.Four types of lattice structures including uniform,helicoidal,FG,and combined FG and helicoidal are fabricated by the additive manufacturing technology.The deformation behaviors,mechanical properties,energy absorption,and acoustic properties of lattice samples are thoroughly investigated.The load-bearing capability of helicoidal lattice samples is gradually improved in the plateau stage,leading to the plateau stress and total energy absorption improved by over 26.9%and 21.2%compared to the uniform sample,respectively.This phenomenon was attributed to the helicoidal design reduces the gap in unit cells and enhances fracture resistance.For acoustic properties,the design of helicoidal reduces the resonance frequency and improves the peak of absorption coefficient,while the FG design mainly influences the peak of absorption coefficient.Across broad range of frequency from 1000 to 6300 Hz,the maximum value of absorption coefficient is improved by18.6%-30%,and the number of points higher than 0.6 increased by 55.2%-61.7%by combining the FG and helicoidal designs.This study provides a novel strategy to simultaneously improve energy absorption and sound absorption properties by controlling the internal architecture of lattice structures.展开更多
Prevailing tissue degeneration caused by musculoskeletal maladies poses a great demand on bioscaffolds,which are artificial,biocompatible structures implanted into human bodies with appropriate mechanical properties.R...Prevailing tissue degeneration caused by musculoskeletal maladies poses a great demand on bioscaffolds,which are artificial,biocompatible structures implanted into human bodies with appropriate mechanical properties.Recent advances in additive manufacturing,i.e.,3D printing,facilitated the fabrication of bioscaffolds with unprecedented geometrical complexity and size flexibility and allowed for the fabrication of topologies that would not have been achieved otherwise.In our work,we explored the effect of porosity on themechanical properties of a periodic cellular structure.The structure was derived from the mathematically created triply periodic minimal surface(TPMS),namely the Sheet-Diamond topology.First,we employed a series of software including MathMod,Meshmixer,Netfabb and Cura to design the model.Then,we utilized additive manufacturing technology to fabricate the cellular structures with designated scale.Finally,we performed compressive testing to deduce the mechanical properties of each cellular structure.Results showed that,in comparison with the highporosity group,the yield strength of the low-porosity group was 3 times higher,and the modulus was 2.5 times larger.Our experiments revealed a specific relationship between porosity and Young’s modulus of PLA-made Sheet-Diamond TPMS structure.Moreover,it was observed that the high-and low-porosity structures failed through distinctive mechanisms,with the former breaking down via buckling and the latter via micro-fracturing.展开更多
The Schwarz primitive triply periodic minimal surface(P-type TPMS)lattice structures are widely used.However,these lattice structures have weak load-bearing capacity compared with other cellular structures.In this pap...The Schwarz primitive triply periodic minimal surface(P-type TPMS)lattice structures are widely used.However,these lattice structures have weak load-bearing capacity compared with other cellular structures.In this paper,an adaptive enhancement design method based on the non-uniform stress distribution in structures with uniform thickness is proposed to design the P-type TPMS lattice structures with higher mechanical properties.Two types of structures are designed by adjusting the adaptive thickness distribution in the TPMS.One keeps the same relative density,and the other keeps the same of non-enhanced region thickness.Compared with the uniform lattice structure,the elastic modulus for the structure with the same relative density increases by more than 17%,and the yield strength increases by more than 10.2%.Three kinds of TPMS lattice structures are fabricated by laser powder bed fusion(L-PBF)with 316L stainless steel to verify the proposed enhanced design.The manufacture-induced geometric deviation between the as-design and as-printed models is measured by micro X-ray computed tomography(μ-CT)scans.The quasi-static compression experimental results of P-type TPMS lattice structures show that the reinforced structures have stronger elastic moduli,ultimate strengths,and energy absorption capabilities than the homogeneous P-TPMS lattice structure.展开更多
It is of significance but remains a pivotal challenge to simultaneously enhance the strength and lightweight levels of porous structures.We provide an innovative strategy to improve the strength of porous structures w...It is of significance but remains a pivotal challenge to simultaneously enhance the strength and lightweight levels of porous structures.We provide an innovative strategy to improve the strength of porous structures with unchanged lightweight levels by applied composite materials.Selective laser melting(SLM)is convenient for integral forming of materials and structures.Hence,in this study,the research about the mechanical response of triply periodic minimal surfaces(TPMS)porous structures with 316 L and composites fabricated by SLM was conducted.The compression test and finite element method(FEM)were used to characterize mechanical properties.The composite structures exhibit enhanced elastic modulus,yield strength,unvaried lightweight level and refined grain microstructure,which are difficult to realize for porous structures made by pure 316 L materials.The elastic modulus,yield strength,plateau stress and energy absorption of composites were 3187.50,67.73,15.24 and 17.09 MJ/m^(3),respectively.展开更多
We give a local analytic characterization that a minimal surface in the 3-sphere S3 C R4 defined by an irreducible cubic polynomial is one of the Lawson＇s minimal tori. This provides an alternative proof of the resul...We give a local analytic characterization that a minimal surface in the 3-sphere S3 C R4 defined by an irreducible cubic polynomial is one of the Lawson＇s minimal tori. This provides an alternative proof of the result by Perdomo （Characterization of order 3 algebraic immersed minimal surfaces of S3, Geom. Dedicata 129 （2007）, 23 34）.展开更多
Let M be a closed surface with positive Gauss curvature minimally immersed in a standard Euclidean unit sphere Sn. In this paper, we choose a local orthonormal frame field on M, under which the shape operators have ve...Let M be a closed surface with positive Gauss curvature minimally immersed in a standard Euclidean unit sphere Sn. In this paper, we choose a local orthonormal frame field on M, under which the shape operators have very convenient form. We also give some applications of this kind of frame field.展开更多
We analyze three commonly used energy functions in solving Plateau-Mesh Prob- lem, that is, Dirichlet, area, and the discrete mean curvature（DMC）. They all possess unique advantages compared to others, but their dra...We analyze three commonly used energy functions in solving Plateau-Mesh Prob- lem, that is, Dirichlet, area, and the discrete mean curvature（DMC）. They all possess unique advantages compared to others, but their drawbacks restrict their usages individually. Our algo- rithm combines the three steps together to make full use of their features. At first the Dirichlet energy is optimized for faster approximation with better topology. Then the area energy is used to come close to the constrained domain. Finally the DMC energy is engaged to achieve a better converging step. Results show that our method can work under a rather noisy initial mesh, which is even topologically different from the final result.展开更多
In 1980,Simon proposed a quantization conjecture about the Gaussian curvature K of closed minimal surfaces in unit spheres:if K(s+1)≤K≤K(s)(K(s):=2/(s(s+1)),s∈N),then either K=K(s)or K=K(s+1).Notice that the surfac...In 1980,Simon proposed a quantization conjecture about the Gaussian curvature K of closed minimal surfaces in unit spheres:if K(s+1)≤K≤K(s)(K(s):=2/(s(s+1)),s∈N),then either K=K(s)or K=K(s+1).Notice that the surface must be one of Calabi’s standard minimal 2-spheres if the curvature is a positive constant.The cases s=1 and s=2 were proven in the 1980s by Simon and others.In this paper,we give a pinching theorem of the Simon conjecture in the case s=3 and also give a new proof of the cases s=1 and s=2 by some Simons-type integral inequalities.展开更多
This study uses numerical and analytical schemes to consider the wave propagation behavior of a triply periodic minimal surface sandwich cylindrical system(TPMS-SCS)for the first time.Although these structures exhibit...This study uses numerical and analytical schemes to consider the wave propagation behavior of a triply periodic minimal surface sandwich cylindrical system(TPMS-SCS)for the first time.Although these structures exhibit outstanding physical and mechanical properties,their dynamic and acoustic features have not been reported yet.This study addresses this gap by calculating the sound transmission loss(STL)coefficient within the framework of the wave approach across various architectures,including the primitive(P),Schoen gyroid(G),and wrapped package-graph(IWP)of a TPMS lattice structure.To determine an analytical STL,a third-order approach is used to precisely capture the stress-strain distribution based on the thickness coordinate,thereby providing a simultaneous solution to the general characteristic relations along with fluid-structure coupling.Given the lack of studies for frequency and STL comparisons,the structure is modeled considering a finite element(FE)design,which is a challenging and time-consuming process because of the complex topological TPMS configurations incorporated within a sandwich cylinder.In fact,achieving convincing computational accuracy requires fine mesh discretization,which significantly increases computational costs during vibroacoustic analysis.Using the numerical results from the COMSOL software Multiphysics,the accuracy of the analytical STL spectrum is verified for different configurations,including P,G,and IWP.The effective acoustic specifications of a TPMS-SCS in the frequency domain are examined by the comparison of the STL with that of a simple cylinder of the same mass.In this context,it would also be beneficial to examine the effect of TPMS thickness,which can demonstrate the importance of the present results.The findings of this approach can be beneficial for scholars working on the numerical and analytical sound insulation characteristics of metamaterial-based cylindrical systems.展开更多
Costa first constructed a family of complete minimal surfaces which have genus 1 and 4 planar ends by use of Weierstrass-g functions.They are Willmore tori of Willmore energy 16π.In this paper,the authors consider th...Costa first constructed a family of complete minimal surfaces which have genus 1 and 4 planar ends by use of Weierstrass-g functions.They are Willmore tori of Willmore energy 16π.In this paper,the authors consider the geometry of conjugate surfaces of these surfaces.It turns out that these conjugate surfaces are doubly periodic minimal surfaces with fat ends in R^(3).Moreover,the authors can also perform a Lorentzian deformation on these Costa's minimal tori,which produce a family of complete space-like stationary surfaces(i.e.,of zero mean curvature)with genus 1 and 4 planar ends in 4-dimensional Lorentz-Minkowski space R_(1)^(4).展开更多
基金funded by the National Natural Science Foundation of China(No.52275343)the Natural Science Foundation of Zhejiang Province(No.LY23E050003)+1 种基金Ningbo Youth Science and Technology Innovation Leading Talent Project(No.2023QL021)Smart Medicine and Engineering Interdisciplinary Innovation Project of Ningbo University(No.ZHYG001).
文摘Triply periodic minimal surface(TPMS)-based bone implants are an innovative approach in orthopedic implantology,offering customized solutions for bone defect repair and regeneration.This review comprehensively examines the current research landscape of TPMS-based bone implants,addressing key challenges and proposing future directions.It explores design strategies aimed at optimizing mechanical strength and enhancing biological integration,with a particular emphasis on TPMS structures.These design strategies include graded,hierarchical,and hybrid designs,each contributing to the overall functionality and performance of the implants.This review also highlights state-of-the-art fabrication technologies,particularly advancements in additive manufacturing(AM)techniques for creating metal-based,polymer-based,and ceramic-based bone implants.The ability to precisely control the architecture of TPMS structures using AM techniques is crucial for tailoring the mechanical and biological properties of such implants.Furthermore,this review critically evaluates the biological performance of TPMS implants,focusing on their potential to promote bone ingrowth and regeneration.Key factors,such as mechanical properties,permeability,and biocompatibility,are examined to determine the effectiveness of these implants in clinical applications.By synthesizing existing knowledge and proposing innovative research directions,this review underscores the transformative potential of TPMS-based bone implants in orthopedic surgery.The objective is to improve clinical outcomes and enhance patient care through advanced implant designs and manufacturing techniques.
基金supported by the Mainland-Hong Kong Joint Funding Scheme(MHKJFS)(Project No:MHP/040/22)RGC Theme-based Research Scheme AoE/M-402/20+1 种基金National Natural Science Foundation of China/Hong Kong Research Grants Council Joint Research Scheme(Project No:N_CityU151/23)Hong Kong Innovation and Technology Commission via the Hong Kong Branch of National Precious Metals Materials Engineering Research Center.
文摘Magnesium(Mg)-based materials are promising for lightweight structural applications.However,their widespread adoption is significantly constrained by inherent limitations in mechanical properties.To address this challenge,this study introduces a novel Mg-based interpenetratingphase composite reinforced with a nickel-titanium(NiTi)scaffold featuring a triply periodic minimal surface(TPMS)configuration.By combining experimental investigations with finite element simulations,we systematically elucidate the dual impact of the scaffold’s unit cell size(a)on manufacturing viability and mechanical enhancement.To compensate for compromised infiltration dynamics induced by decreasing a,a critical permeability threshold of 1×10^(-8) m^(2) is proposed for achieving successful composite fabrication.Mechanically,reducing a strengthens the interaction between the scaffold and matrix:the TPMS-configured NiTi scaffolds improve stress transfer,deflect crack propagation,and facilitate damage delocalization,whereas the Mg matrix preserves structural integrity and enables load redistribution.Consequently,the composites significantly outperform pure Mg,and lowering a leads to more substantial enhancements in compressive strength,energy dissipation,and deformation recoverability.This study offers valuable insight into the design and fabrication of highperformance Mg-based materials for structural and biomedical applications.
基金supported bythe National Natural Science Foundation of China(Nos.U23A20523,82272504,and 82072456)the Department of Science and Technology of Jilin Province,China(Nos.20210101439JC,20210101321JC,20220204119YY,202201ZYTS131,202201ZYTS129,20230204114YY,YDZJ202201ZYTS505,and YDZJ202301ZYTS076)+4 种基金the Special Program for Science and Technology Personnel of Changchun(No.ZKICKJJ2023015)the Key Training Plan for Outstanding Youth of Jilin University(No.419070623036)the Research Fund of the First Hospital of Jilin University(No.2021-zl-01)the Graduate Innovation Fund of Jilin University(No.2024CX125)the Foun-dation of National Center for Translational Medicine(Shanghai)SHU Branch,China(No.SUITM-202405).
文摘The pore structure of porous scaffolds plays a crucial role in bone repair.The prevalent bone implant structure in clinical practice is the traditional cubic structure.However,the traditional cubic structure exhibits sharp edges and junctions that are not conducive to cell adhesion or growth.In this study,a double gyroid(DG)Ti6Al4V scaffold based on a triply periodic minimal surface(TPMS)structure was devised,and the osseointegration performance of DG structural scaffolds with varying porosities was investigated.Compression tests revealed that the elastic modulus and compressive strength of DG structural scaffolds were sufficient for orthopedic implants.In vitro cellular experiments demonstrated that the DG structure significantly enhanced cell proliferation,vascularization,and osteogenic differentiation compared to the cubic structure.The DG structure with 55%porosity exhibited the most favorable outcomes.In vivo experiments in rabbits further demonstrated that DG scaffolds could promote neovascularization and bone regeneration and maturation;those with 55%porosity performed best.Comparing the surface area,specific surface area per unit volume,and internal flow distribution characteristics of gyroid and DG structure scaffolds,the latter are more conducive to cell adhesion and growth within scaffolds.This study underscored the potential of DG scaffolds based on the TPMS structure in optimizing the pore structure design of titanium scaffolds,inducing angiogenesis,and advancing the clinical application of titanium scaffolds for repairing bone defects.
基金financially supported by the Open Project Program of Chinese Scholar Tree Ridge State Key Laboratory(No.AF20240023)
文摘Triply periodic minimal surface(TPMS)structures,characterized by special repeating 3D surface periodically with an average curvature of zero in threedimensional directions,have a wide range of applications.Laser powder bed fusion(LPBF)technique,as a type of additive manufacturing techniques,provides the capability to fabricate such complex-shaped porous TPMS structures.In this study,Ti6Al4V G-sheet TPMS structures with various unit cell sizes were fabricated using LPBF to investigate the structural and material anisotropy and their effects on the anisotropy in energy absorption capacity by combining the finite element simulations and experimental analysis.The results showed that the TPMS structures can be successfully fabricated using LPBF,although the sheet thickness exceeds the designed values,with deviation decreasing as the unit cell size increases from 2 to 4 mm.The inherent anisotropy during the LPBF process results in variations in structural dimension,materials characteristics,and energy absorption capacity between directions parallel and perpendicular to the build direction.The anisotropic ratio of the LPBFed Ti6Al4V G-sheet TPMS structures increases from 1.5 to 2.2 in the structural dimension and from 2.8 to 3.3 in specific energy absorption per unit mass(SEA_(m))respectively with decreasing the unit cell size from 4 to 2 mm.The anisotropy of SEA_(m) primarily originates from the coupling effects of anisotropic dimensions and material properties in the LPBFed G-sheet TPMS structure.Among these factors,anisotropic material properties play a more significant role compared to dimensional anisotropy.
基金Project supported by the National Natural Science Foundation of China (No.11972086)。
文摘Lattice structures can be designed to achieve unique mechanical properties and have attracted increasing attention for applications in high-end industrial equipment,along with the advances in additive manufacturing(AM)technologies.In this work,a novel design of plate lattice structures described by a parametric model is proposed to enrich the design space of plate lattice structures with high connectivity suitable for AM processes.The parametric model takes the basic unit of the triple periodic minimal surface(TPMS)lattice as a skeleton and adopts a set of generation parameters to determine the plate lattice structure with different topologies,which takes the advantages of both plate lattices for superior specific mechanical properties and TPMS lattices for high connectivity,and therefore is referred to as a TPMS-like plate lattice(TLPL).Furthermore,a data-driven shape optimization method is proposed to optimize the TLPL structure for maximum mechanical properties with or without the isotropic constraints.In this method,the genetic algorithm for the optimization is utilized for global search capability,and an artificial neural network(ANN)model for individual fitness estimation is integrated for high efficiency.A set of optimized TLPLs at different relative densities are experimentally validated by the selective laser melting(SLM)fabricated samples.It is confirmed that the optimized TLPLs could achieve elastic isotropy and have superior stiffness over other isotropic lattice structures.
基金supported by National Natural Science Foundation of China(Grant Nos.52105396,52235008,and U2341270)Natural Sci-ence Foundation of Hubei Province of China(Grant No.2021CFB003)+1 种基金Open Foundation of Guangxi Key Laboratory of Processing for Non-ferrous Metals and Featured Materials,Guangxi University,China(Grant No.2022GXYSOF17)Fundamental Research Funds for the Central Universities of China(Grant No.2022IVA138).
文摘With the rapid development of additive manufacturing(AM),scaffold architectures based on triply periodic minimal surfaces(TPMS)have attracted increasing interest in various engineering fields.Nevertheless,they are limited because of the complexity of the design process when adopted in different research and engineer-ing fields.In this work,we present a free and easy-to-use software package called TPMS_Scaffold_Generator,which is coded using MATLAB(Mathworks,Inc.,USA).It offers three function tabs which are homogeneous tab,heterogeneous tab and multisymmetrical tab,respectively.Variables of the tabs include the volume frac-tion,topology type,unit cell size,the length of architecture in X,Y,Z direction,accuracy,and the style of gradient and so forth.TPMS_Scaffold_Generator can generate various TPMS scaffolds,especially ultralight and multisymmetrical scaffolds.The latest version of the TPMS_Scaffold_Generator is freely available at:https://github.com/LeveeLin/TPMS_Scaffold_Generator.git.
基金supported by the National Natural Science Foundation of China(No.51974028)the Fundamental Research Funds for the Central Universities(No.2021JCCXJD01)the Key R&D and transformation projects in Qinghai Province(No.2023-HZ-801).
文摘Improving the shape memory effect and superelasticity of Cu-based shape memory alloys(SMAs)has always been a research hotspot in many countries.This work systematically investigates the effects of Gyroid triply periodic minimal surface(TPMS)lattice structures with different unit sizes and volume fractions on the manufacturing viability,compressive mechanical response,superelasticity and heating recovery properties of CuAlMn SMAs.The results show that the increased specific surface area of the lattice structure leads to increased powder adhesion,making the manufacturability proportional to the unit size and volume fraction.The compressive response of the CuAlMn SMAs Gyroid TPMS lattice structure is negatively correlated with the unit size and positively correlated with the volume fraction.The superelastic recovery of all CuAlMn SMAs with Gyroid TPMS lattice structures is within 5%when the cyclic cumulative strain is set to be 10%.The lattice structure shows the maximum superelasticity when the unit size is 3.00 mm and the volume fraction is 12%,and after heating recovery,the total recovery strain increases as the volume fraction increases.This study introduces a new strategy to enhance the superelastic properties and expand the applications of CuAlMn SMAs in soft robotics,medical equipment,aerospace and other fields.
基金financially supported by National Key R&D Program of China(No.2020YFC1107103)Key Research and Development Program of Zhejiang Province(No.2021C01107)+1 种基金China Postdoctoral Science Foundation(No.2020M681846)Science Fund for Creative Research Groups of National Natural Science Foundation of China(No.51821093).
文摘Inspired by natural porous architectures,numerous attempts have been made to generate porous structures.Owing to the smooth surfaces,highly interconnected porous architectures,and mathematical controllable geometry features,triply periodic minimal surface(TPMS)is emerging as an outstanding solution to constructing porous structures in recent years.However,many advantages of TPMS are not fully utilized in current research.Critical problems of the process from design,manufacturing to applications need further systematic and integrated discussions.In this work,a comprehensive overview of TPMS porous structures is provided.In order to generate the digital models of TPMS,the geometry design algorithms and performance control strategies are introduced according to diverse requirements.Based on that,precise additive manufacturing methods are summarized for fabricating physical TPMS products.Furthermore,actual multidisciplinary applications are presented to clarify the advantages and further potential of TPMS porous structures.Eventually,the existing problems and further research outlooks are discussed.
基金Project supported by the National Natural Science Foundation of China (No. 60473130) and the National Basic Research Program (973) of China (No. 2004CB318000)
文摘Minimal surface is extensively employed in many areas. In this paper, we propose a control mesh representation of a class of minimal surfaces, called generalized helicoid minimal surfaces, which contain the right helicoid and catenoid as special examples. We firstly construct the Bézier-like basis called AHT Bézier basis in the space spanned by {1, t, sint, cost, sinht, cosht}, t∈[0,α], α∈[0,5π/2]. Then we propose the control mesh representation of the generalized helicoid using the AHT Bézier basis. This kind of representation enables generating the minimal surfaces using the de Casteljau-like algorithm in CAD/CAGD mod- elling systems.
基金support from the National Natural Science Foundation of China(NSFC,Project Nos.91860136 and 51801231)the Key R&D Plan of Guangdong Province(Grant No.2018B090905001)the Key Science and Technology project of Shaanxi Province(Grant No.2018zdzx01-04-01).
文摘The new regenerative cooling thermal protection system exhibits the multifunctional characteristics of load-carrying and heat exchange cooling,which are fundamental for the lightweight design and thermal protection of hypersonic vehicles.Triply periodic minimal surface(TPMS)is especially suitable for the structural design of the internal cavity of regenerative cooling structures owing to its excellent structural characteristics.In this study,test pieces were manufactured using Ti6Al4V lightweight material.We designed three types of porous test pieces,and the interior was filled with a TPMS lattice(Gyroid,Primitive,I-WP)with a porosity of 30%.All porous test pieces were manufactured via selective laser melting technology.A combination of experiments and finite element simulations were performed to study the selection of the internal cavity structure of the regenerative cooling thermal protection system.Hence,the relationship between the geometry and mechanical properties of a unit cell is established,and the deformation mechanism of the porous unit cell is clarified.Among the three types of porous test pieces,the weight of the test piece filled with the Gyroid unit cell was reduced by 8.21%,the average tensile strength was reduced by 17.7%compared to the solid test piece,while the average tensile strength of the Primitive and I-WP porous test pieces were decreased by 30.5%and 33.3%,respectively.Compared with the other two types of unit cells,Gyroid exhibited better mechanical conductivity characteristics.Its deformation process was characterised by stretching,shearing,and twisting,while the Primitive and I-WP unit cells underwent tensile deformation and tensile and shear deformation,respectively.The finite element predictions in the study agree well with the experimental results.The results can provide a basis for the design of regenerative cooling thermal protection system.
基金supported by the NUS R&G Postdoc Fellowship Program (No.A-0000065-76-00)the China Scholarship Council (No.202006050088)。
文摘Lattice structures have drawn much attention in engineering applications due to their lightweight and multi-functional properties.In this work,a mathematical design approach for functionally graded(FG)and helicoidal lattice structures with triply periodic minimal surfaces is proposed.Four types of lattice structures including uniform,helicoidal,FG,and combined FG and helicoidal are fabricated by the additive manufacturing technology.The deformation behaviors,mechanical properties,energy absorption,and acoustic properties of lattice samples are thoroughly investigated.The load-bearing capability of helicoidal lattice samples is gradually improved in the plateau stage,leading to the plateau stress and total energy absorption improved by over 26.9%and 21.2%compared to the uniform sample,respectively.This phenomenon was attributed to the helicoidal design reduces the gap in unit cells and enhances fracture resistance.For acoustic properties,the design of helicoidal reduces the resonance frequency and improves the peak of absorption coefficient,while the FG design mainly influences the peak of absorption coefficient.Across broad range of frequency from 1000 to 6300 Hz,the maximum value of absorption coefficient is improved by18.6%-30%,and the number of points higher than 0.6 increased by 55.2%-61.7%by combining the FG and helicoidal designs.This study provides a novel strategy to simultaneously improve energy absorption and sound absorption properties by controlling the internal architecture of lattice structures.
文摘Prevailing tissue degeneration caused by musculoskeletal maladies poses a great demand on bioscaffolds,which are artificial,biocompatible structures implanted into human bodies with appropriate mechanical properties.Recent advances in additive manufacturing,i.e.,3D printing,facilitated the fabrication of bioscaffolds with unprecedented geometrical complexity and size flexibility and allowed for the fabrication of topologies that would not have been achieved otherwise.In our work,we explored the effect of porosity on themechanical properties of a periodic cellular structure.The structure was derived from the mathematically created triply periodic minimal surface(TPMS),namely the Sheet-Diamond topology.First,we employed a series of software including MathMod,Meshmixer,Netfabb and Cura to design the model.Then,we utilized additive manufacturing technology to fabricate the cellular structures with designated scale.Finally,we performed compressive testing to deduce the mechanical properties of each cellular structure.Results showed that,in comparison with the highporosity group,the yield strength of the low-porosity group was 3 times higher,and the modulus was 2.5 times larger.Our experiments revealed a specific relationship between porosity and Young’s modulus of PLA-made Sheet-Diamond TPMS structure.Moreover,it was observed that the high-and low-porosity structures failed through distinctive mechanisms,with the former breaking down via buckling and the latter via micro-fracturing.
基金supported by the National Natural Science Foundation of China(Nos.12002031,12122202U22B2083)+1 种基金the China Postdoctoral Science Foundation(Nos.BX2021038 and 2021M700428)the National Key Research and Development of China(No.2022YFB4601901)。
文摘The Schwarz primitive triply periodic minimal surface(P-type TPMS)lattice structures are widely used.However,these lattice structures have weak load-bearing capacity compared with other cellular structures.In this paper,an adaptive enhancement design method based on the non-uniform stress distribution in structures with uniform thickness is proposed to design the P-type TPMS lattice structures with higher mechanical properties.Two types of structures are designed by adjusting the adaptive thickness distribution in the TPMS.One keeps the same relative density,and the other keeps the same of non-enhanced region thickness.Compared with the uniform lattice structure,the elastic modulus for the structure with the same relative density increases by more than 17%,and the yield strength increases by more than 10.2%.Three kinds of TPMS lattice structures are fabricated by laser powder bed fusion(L-PBF)with 316L stainless steel to verify the proposed enhanced design.The manufacture-induced geometric deviation between the as-design and as-printed models is measured by micro X-ray computed tomography(μ-CT)scans.The quasi-static compression experimental results of P-type TPMS lattice structures show that the reinforced structures have stronger elastic moduli,ultimate strengths,and energy absorption capabilities than the homogeneous P-TPMS lattice structure.
基金the Key-Area Research and Development Program of Guangdong Province(No.2020B090923001)the National Natural Science Foundation of China(Grant Nos.51922044,51775208)the Academic Frontier Youth Team(No.2018QYTD04)at Huazhong University of Science and Technology(HUST)。
文摘It is of significance but remains a pivotal challenge to simultaneously enhance the strength and lightweight levels of porous structures.We provide an innovative strategy to improve the strength of porous structures with unchanged lightweight levels by applied composite materials.Selective laser melting(SLM)is convenient for integral forming of materials and structures.Hence,in this study,the research about the mechanical response of triply periodic minimal surfaces(TPMS)porous structures with 316 L and composites fabricated by SLM was conducted.The compression test and finite element method(FEM)were used to characterize mechanical properties.The composite structures exhibit enhanced elastic modulus,yield strength,unvaried lightweight level and refined grain microstructure,which are difficult to realize for porous structures made by pure 316 L materials.The elastic modulus,yield strength,plateau stress and energy absorption of composites were 3187.50,67.73,15.24 and 17.09 MJ/m^(3),respectively.
文摘We give a local analytic characterization that a minimal surface in the 3-sphere S3 C R4 defined by an irreducible cubic polynomial is one of the Lawson＇s minimal tori. This provides an alternative proof of the result by Perdomo （Characterization of order 3 algebraic immersed minimal surfaces of S3, Geom. Dedicata 129 （2007）, 23 34）.
基金Supported by the Fundamental Research Funds for the Central Universities
文摘Let M be a closed surface with positive Gauss curvature minimally immersed in a standard Euclidean unit sphere Sn. In this paper, we choose a local orthonormal frame field on M, under which the shape operators have very convenient form. We also give some applications of this kind of frame field.
基金Supported by the National Natural Science Foundation of China(11371320)Zhejiang Natural Science Foundation(LZ14A010002)+1 种基金Foundation of Science and Technology Department of Zhejiang Province(2013C31084)Scientific Research Fund of Zhejiang Provincial Education Department(Y201431077 and Y201329420)
文摘We analyze three commonly used energy functions in solving Plateau-Mesh Prob- lem, that is, Dirichlet, area, and the discrete mean curvature（DMC）. They all possess unique advantages compared to others, but their drawbacks restrict their usages individually. Our algo- rithm combines the three steps together to make full use of their features. At first the Dirichlet energy is optimized for faster approximation with better topology. Then the area energy is used to come close to the constrained domain. Finally the DMC energy is engaged to achieve a better converging step. Results show that our method can work under a rather noisy initial mesh, which is even topologically different from the final result.
基金supported by National Natural Science Foundation of China(Grant No.12171037)the Fundamental Research Funds for the Central Universities+1 种基金supported by National Natural Science Foundation of China(Grant Nos.12171037 and 12271040)China Postdoctoral Science Foundation(Grant No.2022M720261).
文摘In 1980,Simon proposed a quantization conjecture about the Gaussian curvature K of closed minimal surfaces in unit spheres:if K(s+1)≤K≤K(s)(K(s):=2/(s(s+1)),s∈N),then either K=K(s)or K=K(s+1).Notice that the surface must be one of Calabi’s standard minimal 2-spheres if the curvature is a positive constant.The cases s=1 and s=2 were proven in the 1980s by Simon and others.In this paper,we give a pinching theorem of the Simon conjecture in the case s=3 and also give a new proof of the cases s=1 and s=2 by some Simons-type integral inequalities.
文摘This study uses numerical and analytical schemes to consider the wave propagation behavior of a triply periodic minimal surface sandwich cylindrical system(TPMS-SCS)for the first time.Although these structures exhibit outstanding physical and mechanical properties,their dynamic and acoustic features have not been reported yet.This study addresses this gap by calculating the sound transmission loss(STL)coefficient within the framework of the wave approach across various architectures,including the primitive(P),Schoen gyroid(G),and wrapped package-graph(IWP)of a TPMS lattice structure.To determine an analytical STL,a third-order approach is used to precisely capture the stress-strain distribution based on the thickness coordinate,thereby providing a simultaneous solution to the general characteristic relations along with fluid-structure coupling.Given the lack of studies for frequency and STL comparisons,the structure is modeled considering a finite element(FE)design,which is a challenging and time-consuming process because of the complex topological TPMS configurations incorporated within a sandwich cylinder.In fact,achieving convincing computational accuracy requires fine mesh discretization,which significantly increases computational costs during vibroacoustic analysis.Using the numerical results from the COMSOL software Multiphysics,the accuracy of the analytical STL spectrum is verified for different configurations,including P,G,and IWP.The effective acoustic specifications of a TPMS-SCS in the frequency domain are examined by the comparison of the STL with that of a simple cylinder of the same mass.In this context,it would also be beneficial to examine the effect of TPMS thickness,which can demonstrate the importance of the present results.The findings of this approach can be beneficial for scholars working on the numerical and analytical sound insulation characteristics of metamaterial-based cylindrical systems.
基金supported by the National Natural Science Foundation of China(Nos.12371052,11971107)the National Natural Science Foundation of Fujian Province(Nos.2023J01536,2022J02028,2021J05035).
文摘Costa first constructed a family of complete minimal surfaces which have genus 1 and 4 planar ends by use of Weierstrass-g functions.They are Willmore tori of Willmore energy 16π.In this paper,the authors consider the geometry of conjugate surfaces of these surfaces.It turns out that these conjugate surfaces are doubly periodic minimal surfaces with fat ends in R^(3).Moreover,the authors can also perform a Lorentzian deformation on these Costa's minimal tori,which produce a family of complete space-like stationary surfaces(i.e.,of zero mean curvature)with genus 1 and 4 planar ends in 4-dimensional Lorentz-Minkowski space R_(1)^(4).
