Enhanced energy-absorbing and sound-absorbing capability of functionally graded and helicoidal lattice structures with triply periodic minimal surfaces

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.

A novel triple periodic minimal surface-like plate lattice and its data-driven optimization method for superior mechanical properties

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.

Adaptive enhancement design of triply periodic minimal surface lattice structure based on non-uniform stress distribution

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.

Triply periodic minimal surface(TPMS)porous structures:from multi-scale design,precise additive manufacturing to multidisciplinary applications

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.

The effect of porosity on the mechanical properties of 3D-printed triplyperiodic minimal surface (TPMS) bioscaffold

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.

TPMS骨组织多孔结构参数化设计方法研究

三周期极小曲面(Triply Periodic Minimal Surface,TPMS)曲率为零,具有相连通的高孔隙率结构,能够更好地适应细胞增长、营养物输送和代谢物排出。基于传统CAD的TPMS多孔结构设计,孔隙率、孔径大小与TPMS曲面参数未建立明确的对应关系,设计缺乏灵活性。通过探究阈值和周期对孔隙率的影响关系,提出一种TPMS多孔结构参数化设计方法。基于TPMS设计孔单元,研究发现阈值与孔隙率基本呈线性关系,周期与孔隙率无关,但周期的改变会显著影响模型的孔径大小。由此将阈值和周期作为参数化设计的主要参数输入,可自动生成孔隙率和孔径大小可控的多孔结构。该方法实现于Rhinoceros的Grasshopper(GH)插件,并进行实例验证。

Innovative Design and Additive Manufacturing of Regenerative Cooling Thermal Protection System Based on the Triply Periodic Minimal Surface Porous Structure

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.

TPMS点阵结构的密度梯度杂交优化设计

三周期极小曲面(triply periodic minimal surface,TPMS)点阵结构因其优异的综合性能受到中外学者的广泛关注。在点阵结构实际应用过程中,常常需要对其进行优化设计以兼顾轻量化与承载性能两方面的要求。目前,对TPMS点阵结构的优化设计主要集中于密度梯度层面,未综合考虑载荷方向对其力学性能的影响。为此,首先研究了TPMS点阵结构的各向异性特征。基于平均场均匀化方法求解了不同类型TPMS点阵结构的等效弹性矩阵,通过Matlab插值计算,绘制了其在三维空间范围内的杨氏模量图。发现不同类型的TPMS点阵结构呈现出不同的各向异性特征,其中W点阵结构在[100]等轴线方向上性能较强,在[111]等斜向对角方向上性能较弱,而P点阵结构则刚好相反。根据TPMS点阵结构的各向异性,同时考虑主应力方向以及相对密度分布对其性能的影响,提出了TPMS点阵结构的密度梯度杂交优化设计方法。以悬臂梁模型为基础,基于载荷边界条件对其进行拓扑优化设计,并将拓扑优化密度云映射为点阵结构的相对密度分布,从而实现密度梯度设计。根据TPMS点阵结构的各向异性特征以及单元主应力方向分别选择W和P点阵单胞填充悬臂梁,使主应力方向位于点阵结构性能较强的方向,避免点阵结构在性能薄弱的方向承受较大的应力。将不同类型的TPMS点阵单元合理分布后,利用激活函数将它们进行杂交连接,实现结构梯度设计。综合相对密度分布和单元结构分布,生成密度梯度杂交点阵结构。采用有限元仿真方法对比分析优化设计前后点阵结构的承载性能,结果表明密度梯度W和P点阵结构的刚度与对应的均质点阵结构相比都有明显提高,而由W和P两种点阵单胞组成的密度梯度杂交点阵结构刚度最大,比密度梯度W和P点阵结构分别提高4.63%和33.63%。该结果表明在密度优化的基础上,根据承载时单元主应力方向将不同类型的点阵结构进行合理分布以及混合杂交设计能够进一步提高结构的整体刚度。建立的TPMS点阵结构密度梯度杂交优化方法为其在轻量化设计等方面的应用提供了一定的指导。

Gyroid Triply Periodic Minimal Surface Lattice Structure Enables Improved Superelasticity of CuAlMn Shape Memory Alloy

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.

熔融沉积成型TPMS多孔结构的孔隙特征和力学性能

基于三周期极小曲面(TPMS)设计了孔隙率为40%(P40)、50%(P50)、60%(P60)的均质和平均孔隙率为50%(ZP50)的梯度Primitive多孔结构,并采用熔融沉积技术(FDM)打印成型,研究了不同孔隙率下多孔结构的孔隙特征、力学性能和吸能特性。结果表明,均质和梯度TPMS结构的实际孔隙率均小于设计孔隙率,偏差均在1.5%~4%之间;均质多孔结构的抗压强度随着孔隙率的增加而升高,P40均质结构的抗压强度最大为8.644 MPa;相同孔隙率下,ZP50的抗压强度比P50高15.54%,并且ZP50结构在应变为28%前要比P50具有较优良的吸能特性。研究结果丰富了增材制造成型极小曲面多孔结构力学内涵,为工程应用提供了相关依据。

孔隙表征参数驱动的TPMS多孔结构建模

为了设计符合工程设计参数要求的多孔结构模型,提出一种孔隙表征参数驱动的多孔结构建模思路,并以增材制造制备成形.首先,针对三周期极小化曲面(TPMS)的4种常用类型(P/D/G/I-WP),研究了TPMS数学参数对各类孔隙表征参数(孔隙率、比表面积和孔径大小)的影响,并建立了相关参数之间的映射关系模型;接着,提出了若干基于孔隙表征参数的TPMS多孔结构设计方法,包括单设计参数法、多设计参数法、嵌套设计法;最后,给出了相关的工程应用案例并进行Micro-CT测试实验.实验结果表明,所设计模型的孔隙表征参数可控,增材制造成形的模型样件受工艺影响,其精度存在一定偏差.

面向组织工程的松质骨微观结构TPMS建模方法

骨支架作为种子细胞和生长因子的载体,在骨组织工程中处于核心地位.从骨支架结构设计的角度出发,提出一种松质骨微观结构的建模方法.该方法结合三周期极小化曲面(TPMS)和分形几何理论,在对骨骼微孔表面分析的基础上建立具有分形特征的造孔单元;然后采用双重轮廓线方法对解剖骨骼外表面模型进行六面体网格划分,并依据孔径分布规律调整网格顶点的位置;最后利用等参变换将分形造孔单元映射到每一个六面体中,得到骨支架孔隙微观结构的整体模型.实例分析结果表明,文中方法是可行和有效的.该方法有望提供与增材制造技术相适应的骨支架数字化模型.

径向梯度三周期极小曲面骨小梁支架结构设计与力学性能分析

背景:传统骨植入物的弹性模量较大,与人体骨弹性模量不匹配,会引起应力遮挡效应,从而导致骨吸收。径向梯度三周期极小曲面骨小梁支架具有与人体松质骨匹配的弹性模量,且屈服强度大于人体皮质骨屈服强度,为骨支架设计提供了一种新的选择。目的:通过隐式曲面法构建径向梯度三周期极小曲面结构,采用激光选区熔化技术制备样件,进行准静态压缩实验,得到力学性能与人体骨骼匹配的骨小梁支架。方法:通过隐式曲面法,建立G型、Ⅰ型、P型和D型4种径向梯度三周期极小曲面骨小梁支架;采用激光选区熔化技术制备样件,观测成型样件的表面形貌,评估成型质量,进行准静态压缩实验,评估样件的力学性能。结果与结论:准静态压缩实验结果表明,对比4种径向梯度三周期极小曲面支架,G支架平台应力波动小,没有出现失效断裂,塑性最好;对45%,55%和65%3种孔隙率G支架的力学性能进行分析,发现55%孔隙率G支架的弹性模量在人体松质骨的弹性模量范围内(0.022-3.7 GPa),屈服强度接近人体皮质骨最大屈服强度(187.7-222.3 MPa)。结果显示,55%孔隙率的G型径向梯度三周期极小曲面骨小梁支架能够降低应力遮挡效应,承受较高人体载荷,提高植入物的稳定性,延长植入物的使用寿命。

功能梯度三周期极小曲面静动态力学特性

功能梯度设计能够有效提高结构的力学特性及吸能性能.为探讨功能梯度极小曲面结构在静动态载荷下的力学响应以及梯度壁厚分布方式对其力学特性的影响规律,构建了包含线性梯度和多种非线性梯度(对数梯度、Sigmoid梯度以及指数梯度)Gyroid结构,通过3D打印光敏树脂制备样件开展了准静态压缩试验,采用LS-DYNA构建仿真模型并与试验结果对比,验证了仿真方法的有效性.研究发现,功能梯度壁厚分布方式显著影响结构力学性能及变形模式.在准静态压缩下,功能梯度结构呈现逐层压溃的变形模式,在接触端产生局部的致密化带,这一模式导致梯度结构吸能特性有一定提升.基于准静态测试数据以及试验变形模式分析,构建了Gibson-Ashby模型,揭示了均质结构弹性模量和屈服强度随等效密度的变化规律;利用该Gibson-Ashby模型,预测了功能梯度结构屈服强度,并构建等应力模型预测了梯度结构的弹性模量,预测结果与实验值具有良好的一致性.对于其动态力学性能,构建了4种冲击速度仿真模型,深入探讨不同冲击速度对梯度结构力学性能的影响规律.功能梯度结构在高速冲击下,由于其壁厚逐层递增的特性,其局部压溃现象更为明显,导致其在高速冲击下的致密化应变显著增大,其吸能特性也有所提升.其中,对数梯度结构具有最高的屈服强度,而Sigmoid梯度结构具有最高的平均平台应力和吸能特性,其比吸能特性为13.01 J/g,相较于相对密度为45%的均质结构而言提升了45%.此外,基于刚性-完美塑性-锁定模型对梯度结构的动态平台应力进行拟合预测,拟合结果与仿真结果吻合度较高,为预测功能梯度结构的动态力学响应提供了计算方法.

基于增材制造的三周期极小曲面结构关键力学性能研究进展

三周期极小曲面结构是一类具有光滑连续曲面和高比表面积的特殊多孔结构,具有承载能力强、能量吸收率高、疲劳性能好等优异性质,在航空航天、生物医学和隔声吸声等诸多领域有着广泛的应用.增材制造技术在制造复杂拓扑结构方面具有独特优势,为三周期极小曲面结构的制造提供了有力工具.然而增材制造过程中也引入诸多缺陷,对结构的力学性能产生重要影响.全面深入地研究增材制造三周期极小曲面结构的力学性能,对评价和预测结构性能、扩宽其在工程中的应用具有重要意义.首先从结构形式、特点及应用领域等方面对三周期极小曲面结构进行了介绍,重点针对静态压缩吸能、动态抗冲击和疲劳断裂等关键力学性能,综述了近期的重要进展.围绕三周期极小曲面结构的隔声吸声性质和热交换性能,亦进行了讨论.其次,以选区激光熔化与选区激光烧结为例,介绍了增材制造制备三周期极小曲面结构的主要方法.再次,结合增材制造技术,讨论制造过程中引入的缺陷对三周期极小曲面结构力学性能的影响,包括残余应力、表面粗糙度和内部微孔洞等.最后,结合实际应用对该领域面临的主要困难和挑战进行总结,同时展望了未来的研究方向.

电子束增材制造多孔骨支架的选用与疲劳性能研究

增材制造多孔结构具有优良的力学仿生和促骨长入性能,支持骨科植入假体在体内的长期稳定。本研究采用三周期极小曲面(TPMS)法和电子束熔融技术(EBM)设计并制备了仿骨小梁多孔结构,通过微计算机断层扫描技术(Micro-CT)和力学疲劳实验研究它们的孔隙特性、机械力学和疲劳性能,提出了一套新颖的适用于骨科植入假体的选用方法,以满足孔隙连通、力学稳定和高周疲劳寿命的需求。Micro-CT和扫描电镜(SEM)表征发现,单元尺寸≥1.5 mm的多孔支架具有仿生的孔径(748μm)和良好的孔隙连通性;TPMS-Gyroid支架的力学稳定性和可靠性优于TPMS-Diamond支架,所建立的Gibson-Ashby方程可为钛合金多孔支架的设计提供力学性能预测;支架在应力水平为0.2时的疲劳寿命>106次,满足植入材料的长期安全使用要求,其弹性模量与人体松质骨的弹性模量相似(0.1~1.1 GPa)。疲劳行为的研究还发现,疲劳棘轮和疲劳损伤是引发多孔支架失效的主要原因。在设计金属多孔支架结构时,可通过增大支架单元尺寸来减少裂纹萌生的缺口数量,有助于提高支架的疲劳寿命。

Ti6Al4V有序多孔Diamond夹芯结构隔声性能研究

基于三周期极小曲面(TPMS)的Ti6Al4V有序多孔夹芯结构具有轻质、高强以及可设计性好等优点,在航空航天、生物医学等领域具有广阔的应用前景,而其隔声性能还没有得到充分的研究。基于此,通过TPMS隐函数法设计了Ti6Al4V有序多孔Diamond夹芯结构,研究了胞元层数、面板厚度、体积分数3个参数对其隔声性能的影响。结果表明,体积分数对钛合金有序多孔Diamond夹芯结构的隔声性能影响最大,胞元层数次之,面板厚度影响较小。增大体积分数和调节胞元层数都可以有效的提升夹芯结构的隔声性能。在Diamond夹芯结构具备轻质高强的基础上研究其隔声性能,扩展了Ti6Al4V有序多孔夹芯结构的多功能性。

基于三周期极小曲面的多孔结构力学性能研究

针对设计多孔结构时难以直接预测其力学性能的问题,选取三周期极小曲面中的Schwarz_P曲面,采用选区激光熔化技术制备不同结构参数的Schwarz_P结构;通过压缩试验研究其力学性能,建立Schwarz_P结构的结构参数与力学性能之间的关系模型。试验结果表明:建立的模型拟合优度在98%以上,采用该模型预测的力学性能与实测值基本一致,在设计多孔结构时可直观地预估其力学性能。

3D-printed strontium-incorporatedβ-TCP bioceramic triply periodic minimal surface scaffolds with simultaneous high porosity,enhanced strength,and excellent bioactivity

In bone tissue engineering,scaffolds with excellent mechanical and bioactive properties play prominent roles in space maintaining and bone regeneration,attracting increasingly interests in clinical practice.In this study,strontium-incorporatedβ-tricalcium phosphate(β-TCP),named Sr-TCP,bioceramic triply periodic minimal surface(TPMS)structured scaffolds were successfully fabricated by digital light processing(DLP)-based 3D printing technique,achieving high porosity,enhanced strength,and excellent bioactivity.The Sr-TCP scaffolds were first characterized by element distribution,macrostructure and microstructure,and mechanical properties.Notably,the compressive strength of the scaffolds reached 1.44 MPa with porosity of 80%,bringing a great mechanical breakthrough to porous scaffolds.Furthermore,the Sr-TCP scaffolds also facilitated osteogenic differentiation of mouse osteoblastic cell line(MC3T3-E1)cells in both gene and protein aspects,verified by alkaline phosphatase(ALP)activity and polymerase chain reaction(PCR)assays.Overall,the 3D-printed Sr-TCP bioceramic TPMS structured scaffolds obtained high porosity,boosted strength,and superior bioactivity at the same time,serving as a promising approach for bone regeneration.

Bioceramic scaffolds with triply periodic minimal surface architectures guide early-stage bone regeneration

The pore architecture of porous scaffolds is a critical factor in osteogenesis,but it is a challenge to precisely configure strut-based scaffolds because of the inevitable filament corner and pore geometry deformation.This study provides a pore architecture tailoring strategy in which a series of Mg-doped wollastonite scaffolds with fully interconnected pore networks and curved pore architectures called triply periodic minimal surfaces(TPMS),which are similar to cancellous bone,are fabricated by a digital light processing technique.The sheet-TPMS pore geometries(s-Diamond,s-Gyroid)contribute to a 3‒4-fold higher initial compressive strength and 20%-40%faster Mg-ion-release rate compared to the other-TPMS scaffolds,including Diamond,Gyroid,and the Schoen’s I-graph-Wrapped Package(IWP)in vitro.However,we found that Gyroid and Diamond pore scaffolds can significantly induce osteogenic differentiation of bone marrow mesenchymal stem cells(BMSCs).Analyses of rabbit experiments in vivo show that the regeneration of bone tissue in the sheet-TPMS pore geometry is delayed;on the other hand,Diamond and Gyroid pore scaffolds show notable neo-bone tissue in the center pore regions during the early stages(3-5 weeks)and the bone tissue uniformly fills the whole porous network after 7 weeks.Collectively,the design methods in this study provide an important perspective for optimizing the pore architecture design of bioceramic scaffolds to accelerate the rate of osteogenesis and promote the clinical translation of bioceramic scaffolds in the repair of bone defects.