Influence of manufacturing process-induced geometrical defects on the energy absorption capacity of polymer lattice structures

Modern additive manufacturing processes enable fabricating architected cellular materials of complex shape,which can be used for different purposes.Among them,lattice structures are increasingly used in applications requiring a compromise among lightness and suited mechanical properties,like improved energy absorption capacity and specific stiffness-to-weight and strength-to-weight ratios.A dedicated modeling strategy to assess the energy absorption capacity of lattice structures under uni-axial compression loading is presented in this work.The numerical model is developed in a non-linear framework accounting for the strain rate effect on the mechanical responses of the lattice structure.Four geometries,i.e.,cubic body centered cell,octet cell,rhombic-dodecahedron and truncated cuboctahedron 2+,are investigated.Specifically,the influence of the relative density of the representative volume element of each geometry,the strain-rate dependency of the bulk material and of the presence of the manufacturing process-induced geometrical imperfections on the energy absorption capacity of the lattice structure is investigated.The main outcome of this study points out the importance of correctly integrating geometrical imperfections into the modeling strategy when shock absorption applications are aimed for.

Compression behavior of 316L lattice structures produced by indirect additive manufacturing

As a new type of lightweight structure,metallic lattice structure has higher stiffness and strength to weight ratio.To freely obtain 316L lattice structures with designed cell structure and adjustable porosity,additive manufacturing combined with investment casting was conducted to fabricate the 316L lattice structures with Kelvin cell.The compression simulation of 316L lattice structures with different porosities was carried out by using the finite element method.The numerical simulation results were verified by compression experiment,and the simulated results were consistent with the compression tests.The compressive mechanical properties of 316L lattice structures are directly related to porosity and independent of strut diameters.The 316L lattice structures with Kelvin cell have a smooth stress-strain curve and obvious plastic platform,and the hump stress-strain curves are avoided.

Mechanical property and biological behaviour of additive manufactured TiNi functionally graded lattice structure

Bio-inspired porous metallic scaffolds have tremendous potential to be used as artificial bone substitutes.In this work,a radially graded lattice structure (RGLS),which mimics the structures of natural human bones,was designed and processed by laser powder bed fusion of martensitic Ti-rich TiNi powder.The asymmetric tension-compression behaviour,where the compressive strength is significantly higher than the tensile strength,is observed in this Ti-rich TiNi material,which echoes the mechanical behaviour of bones.The morphologies,mechanical properties,deformation behaviour,and biological compatibility of RGLS samples were characterised and compared with those in the uniform lattice structure.Both the uniform and RGLS samples achieve a relative density higher than 99%.The graded porosities and pore sizes in the RGLS range from 40%-80% and 330-805 µm,respectively,from the centre to the edge.The chemical etching has significantly removed the harmful partially-melted residual powder particles on the lattice struts.The compressive yield strength of RGLS is 71.5 MPa,much higher than that of the uniform sample (46.5 MPa),despite having a similar relative density of about 46%.The calculated Gibson-Ashby equation and the deformation behaviour simulation by finite element suggest that the dense outer regions with high load-bearing capability could sustain high applied stress,improving the overall strength of RGLS significantly.The cell proliferation study suggests better biological compatibility of the RGLS than the uniform structures.The findings highlight a novel strategy to improve the performance of additively manufactured artificial implants by bio-inspiration.

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.

Blade Segment with a 3D Lattice of Diamond Grits Fabricated via an Additive Manufacturing Process

Diamond tools with orderly arrangements of diamond grits have drawn considerable attention in the machining field owing to their outstanding advantages of high sharpness and long service life.This diamond super tool,as well as the manufacturing equipment,has been unavailable to Chinese enterprises for a long time due to patents.In this paper,a diamond blade segment with a 3D lattice of diamond grits was additively manufactured using a new type of cold pressing equipment(AME100).The equipment,designed with a rotary working platform and 16 molding stations,can be used to additively manufacture segments with diamond grits arranged in an orderly fashion,layer by layer;under this additive manufacturing process,at least 216000 pcs of diamond green segments with five orderly arranged grit layers can be produced per month.The microstructure of the segment was observed via SEM and the diamond blade fabricated using these segments was compared to other commercial cutting tools.The experimental results showed that the 3D lattice of diamond grits was formed in the green segment.The filling rate of diamond grits in the lattice could be guaranteed to be above 95%;this is much higher than the 90%filling rate of the automatic array system(ARIX).When used to cut stone,the cutting amount of the blade with segments made by AME100 is two times that of ordinary tools,with the same diamond concentration.When used to dry cut reinforced concrete,its cutting speed is 10%faster than that of ARIX.Under wet cutting conditions,its service life is twice that of ARIX.By applying the machine vision online inspection system and a special needle jig with a negative pressure system,this study developed a piece of additive manufacturing equipment for efficiently fabricating blade segments with a 3D lattice of diamond grits.

Additional Twists of Yarn Produced by System of Compact Spinning with Lattice Apron

Based on the flow simulation in the condensing zone of compact spinning with lattice apron and a bead-elastic rod dynamic model of the flexible fiber,trajectories of fibers with different negative pressure are simulated by specially designed Matlab procedure.Then displacement components of fibers at YZ profile under different negative pressure conditions are extracted and compared.The results show that the fibers of different initial positions gradually converge,and are interlaced for position change in yarn cross-section,caused by the airflow in the condensing zone.Finally,compact-spun yarn with different negative pressure and conventional ring spun yarn are produced and their twists are tested.Both the results of simulation and experiments illustrate the existence of additional twists.Also the relationship between additional twists and negative pressure is verified.

A new design of dual-constituent triangular lattice metamaterial with unbounded thermal expansion

Triangular lattice metamaterials composed of bi-layer curved rib elements (called the Lehman-Lakes lattice) possess unbounded thermal expansion, high stiffness and impossibility of thermal buckling, which are highly desirable in many engineering structural applications subjected to large fluctuations in temperature. However, the requirement of such lattice metamaterial is that it must be a hinged joint in order to achieve the bending deformation upon heating freely, which directly leads to poor manufacturability, especially in small dimensions. In this study, a new design of dual-constituent triangular lattice metamaterial (DTLM) with good manufacturability is proposed to achieve the identical unbounded thermal expansion. In this lattice, a special bi-layer curved rib element where layer one is partially covered by layer two is presented, where the hinge joints are not necessary because the flexural rigidity in the single-layer part is much smaller than that in the bi-layer part, and the desirable thermal bending deformation can be achieved. A sample fabricated by additive manufacturing is given in order to show the good manufacturability;simultaneously, the multifunctional performance of the tailored DTLM with zero, large positive or negative coefficient of thermal expansion (CTE) can remain excellent, as well as the Lehman-Lakes lattice. Examples illustrate that the DTLM with zero CTE has about 34.2% improvement in stiffness and meanwhile has 17% reduction in weight compared with the Lehman-Lakes lattice. The stiffness of the DTLM has a moderate reduction when achieving the same large positive or negative CTE. In addition, the thermomechanical properties of the DTLM are given by the closed-form analytical solution and their effectiveness is verified by the detailed numerical simulation.

Compressive mechanical properties and shape memory effect of NiTi gradient lattice structures fabricated by laser powder bed fusion

Laser additive manufacturing (AM) of lattice structures with light weight, excellent impact resistance, and energy absorption performance is receiving considerable attention in aerospace, transportation, and mechanical equipment application fields. In this study, we designed four gradient lattice structures (GLSs) using the topology optimization method, including the unidirectional GLS, the bi-directional increasing GLS, the bi-directional decreasing GLS and the none-GLS. All GLSs were manufactureed by laser powder bed fusion (LPBF). The uniaxial compression tests and finite element analysis were conducted to investigate the influence of gradient distribution features on deformation modes and energy absorption performance of GLSs. The results showed that, compared with the 45° shear fracture characteristic of the none-GLS, the unidirectional GLS, the bi-directional increasing GLS and the bi-directional decreasing GLS had the characteristics of the layer-by-layer fracture, showing considerably improved energy absorption capacity. The bi-directional increasing GLS showed a unique combination of shear fracture and layer-by-layer fracture, having the optimal energy absorption performance with energy absorption and specific energy absorption of 235.6 J and 9.5 J g-1 at 0.5 strain, respectively. Combined with the shape memory effect of NiTi alloy, multiple compression-heat recovery experiments were carried out to verify the shape memory function of LPBF-processed NiTi GLSs. These findings have potential value for the future design of GLSs and the realization of shape memory function of NiTi components through laser AM.

THE LARGEST SOLUTION OF LINEAR EQUATION OVER THE COMPLETE HEYTING ALGEBRA

Let （L, 〈, V, A） be a complete Heyting algebra. In this article, the linear system Ax = b over a complete Heyting algebra, where classical addition and multiplication operations are replaced by V and A respectively, is studied. We obtain： （i） the necessary and sufficient conditions for S（A,b）≠Ф; （ii） the necessary conditions for IS（A,b）｜ = 1. We also obtain the vector x ∈ Ln and prove that it is the largest element of S（A, b） if S（A, b）≠Ф.

CONTACT PROCESS ON HEXAGONAL LATTICE

In this article, we discuss several properties of the basic contact process on hexagonal lattice H, showing that it behaves quite similar to the process on d-dimensional lattice Zd in many aspects. Firstly, we construct a coupling between the contact process on hexagonal lattice and the oriented percolation, and prove an equivalent finite space-time condition for the survival of the process. Secondly, we show the complete convergence theorem and the polynomial growth hold for the contact process on hexagonal lattice. Finally, we prove exponential bounds in the supercritical case and exponential decay rates in the subcritical case of the process.

Notes on Preregular Operators in Banach Lattices

Some characterizations of preregular operators between two Banach lattices are presented. Then several sufficient conditions for preregular operators being regular are given, and some related results are also obtained.

Delamination Testing of AlSi10Mg Sandwich Structures with Pyramidal Lattice Truss Core made by Laser Powder Bed Fusion

Sandwich structures possess a high bending stiffness compared to monolithic structures with a similar weight.This makes them very suitable for lightweight applications,where high stiffness to weight ratios are needed.Most common manufacturing methods of sandwich structures involve adhesive bonding of the core material with the sheets.However,adhesive bonding is prone to delamination,a failure mode that is often difficult to detect.This paper presents the results of delamination testing of fully additive manufactured(AM)AlSi10Mg sandwich structures with pyramidal lattice truss core using Laser Powder Bed Fusion(LPBF).The faces and struts are 0.5 mm thick,while the core is 2 mm thick.The inclination of the struts is 45°.To characterise the bonding strength,climbing drum peel tests and out-of-plane tensile tests are performed.Analytical formulas are derived to predict the expected failure loads and modes.The analytics and tests are supported by finite element(FE)calculations.From the analytic approach,design guidelines to avoid delamination in AM sandwich structures are derived.The study presents a critical face sheet thickness to strut diameter ratio for which the structure can delaminate.This ratio is mainly influenced by the inclination of the struts.The peel tests resulted in face yielding,which can also be inferred from the analytics and numerics.The out-of-plane tensile tests didn’t damage the structure.

Design of Lattice Structures Using Local Relative Density Mapping Method

In order to solve the problem of substantial computational resources of lattice structure during optimization, a local relative density mapping(LRDM) method is proposed. The proposed method uses solid isotropic microstructures with penalization to optimize a model at the macroscopic scale. The local relative density information is obtained from the topology optimization result. The contour lines of an optimized model are extracted using a density contour approach, and the triangular mesh is generated using a mesh generator. A local mapping relationship between the elements’ relative density and the struts’ relative cross?sectional area is established to automatically determine the diameter of each individual strut in the lattice structures. The proposed LRDM method can be applied to local finite element meshes and local density elements, but it is also suitable for global ones. In addition, some cases are con?sidered in order to test the e ectiveness of the LRDM method. The results show that the solution time of the LRDM is lower than the RDM method by approximately 50%. The proposed method provides instructions for the design of more complex lattice structures.

The Lattice of Fully Invariant Subgroups of the Cotorsion Hull

The paper considers the lattice of fully invariant subgroups of the cotorsion hull ?when a separable primary group T?is an arbitrary direct sum of torsion-complete groups.The investigation of this problem in the case of a cotorsion hull is important because endomorphisms in this class of groups are completely defined by their action on the torsion part and for mixed groups the ring of endomorphisms is isomorphic to the ring of endomorphisms of the torsion part if and only if the group is a fully invariant subgroup of the cotorsion hull of its torsion part. In the considered case, the cotorsion hull is not fully transitive and hence it is necessary to introduce a new function which differs from an indicator and assigns an infinite matrix to each element of the cotorsion hull. The relation ?difined on the set ?of these matrices is different from the relation proposed by the autor in the countable case and better discribes the lower semilattice. The use of the relation ?essentially simplifies the verification of the required properties. It is proved that the lattice of fully invariant subgroups of the group is isomorphic to the lattice of filters of the lower semilattice.

Nikodým-Type Theorems for Lattice Group-Valued Measures with Respect to Filter Convergence

We present some convergence and boundedness theorems with respect to filter convergence for lattice group-valued measures. We give a direct proof, based on the sliding hump argument. Furthermore we pose some open problems.

增材制造点阵夹芯混合结构的振动特性

采用增材制造(additive anufacturing,AM)技术制备了钛合金点阵夹芯梁,使用硅橡胶作为阻尼材料对点阵空隙进行了填充。测试对比了有/无填充的点阵夹芯悬臂梁的模态振型,并对其进行了扫频振动激励。试验结果表明:填充阻尼材料不会改变结构振型,但可显著降低振动响应幅值。开展了硅橡胶的动态力学分析试验(dynamic mechanical analysis,DMA),结合广义麦克斯韦(generalized Maxwell model,GMM)粘弹性模型,标定了频域粘弹性模型参数。通过硅橡胶单轴拉伸试验标定了多项式型超弹性模型参数。基于粘超弹性模型及标定参数,对有填充的点阵夹芯悬臂梁进行了振动响应有限元模拟,与试验结果相符,证明本文采用的粘超弹性模型和其参数标定方法可有效用于混合结构的振动特性计算。

增材制造钛基金字塔点阵结构对镁/钛双金属复合材料界面强化的优化

采用超声辅助固-液复合铸造的方法,通过在界面处采用增材制造的钛基金字塔型点阵材料制备镁/钛异种双金属复合材料。采用正交法对点阵结构参数进行优化。结果表明,优化后的点阵结构参数为:杆直径(d)1 mm,杆长与杆直径比(l/d)3,上节点和下节点直径与杆直径比(d_(1)/d,d_(2)/d)均为2.5,其中l/dd是影响接头失效强度的最显著因素,最优点阵结构参数下镁/钛双金属接头的失效强度为77.3 MPa。实验结果和有限元分析表明:随着点阵结构长径比的增加,镁/钛双金属接头的失效强度先增加后减小,当长径比为3时,失效强度达到最大。

增材制造金属晶格夹层结构研究现状与应用

金属晶格夹层结构具有优异的力、声、电、热综合性能。增材制造基于“离散+堆积”思想,层层堆叠制造,能够解放复杂金属晶格结构设计思路,为仿生设计和拓扑优化提供了更高的自由度,为后续开发出超轻、超强多功能晶格夹层结构提供了更多的可能。本文综述了增材制造金属晶格夹层结构的工艺,深入分析讨论了其结构设计、工艺优化、缺陷控制、性能调控和应用背景,总结了研究现状并展望了未来的发展前景。

基于一般二元关系粗糙近似算子的格结构研究

刻画了基于一般二元关系及悲观多粒度粗糙近似算子的完备格结构,证明了在选取蕴涵算子之后,基于一般二元关系的粗糙近似算子构成MV、R0与布尔代数。

基于校准窗口集成与耦合市场特征的可解释双层日前电价预测

随着电力市场之间耦合程度不断加深,只局限于单个市场内部的传统特征集不足以支撑高精度预测的需求。而且模型预测性能对校准窗口的选择敏感,而传统电价预测仅使用一个固定时间长度的数据集,同时预测模型的“黑盒”结构导致预测结果在工程应用中可信度偏低。针对上述问题,该文提出一种考虑校准窗口集成与耦合市场特征的可解释双层日前电价预测框架。内层框架为基于改进自适应噪声完备集合经验模态分解(improved complete ensemble empirical mode decomposition,ICEEMDAN)的择优预测,首先分解原始电价序列,然后应用Lasso估计回归(lassoestimated autoregressive,LEAR)、长期和短期时间序列网络(long-term and short-term time-series networks,LSTNet)、卷积神经网络-长短记忆神经网络(convolutionalneuralnetworks-longshort termmemory,CNN-LSTM)、移动平均(autoregressive integrated moving average,ARIMA)和核极限学习机(kernel extreme learning machines,KELM)模型预测子序列并选择最优预测算法。外层框架为基于贝叶斯模型平均(bayes modelaveraging,BMA)的校准窗口集成预测,针对每个不同校准窗口长度数据集下的预测分配权重并集成得到预测电价。最后,通过可解释方法沙普利加性解释模型(shapley additiveexplanations,SHAP)分析耦合市场特征如何影响预测电价。该文通过北欧电力市场数据集的算例分析证明了所提算法的优越性和校准窗口集成方案的有效性。