A Hybrid Level Set Optimization Design Method of Functionally Graded Cellular Structures Considering Connectivity

With the continuous advancement in topology optimization and additive manufacturing(AM)technology,the capability to fabricate functionally graded materials and intricate cellular structures with spatially varying microstructures has grown significantly.However,a critical challenge is encountered in the design of these structures–the absence of robust interface connections between adjacent microstructures,potentially resulting in diminished efficiency or macroscopic failure.A Hybrid Level Set Method(HLSM)is proposed,specifically designed to enhance connectivity among non-uniform microstructures,contributing to the design of functionally graded cellular structures.The HLSM introduces a pioneering algorithm for effectively blending heterogeneous microstructure interfaces.Initially,an interpolation algorithm is presented to construct transition microstructures seamlessly connected on both sides.Subsequently,the algorithm enables the morphing of non-uniform unit cells to seamlessly adapt to interconnected adjacent microstructures.The method,seamlessly integrated into a multi-scale topology optimization framework using the level set method,exhibits its efficacy through numerical examples,showcasing its prowess in optimizing 2D and 3D functionally graded materials(FGM)and multi-scale topology optimization.In essence,the pressing issue of interface connections in complex structure design is not only addressed but also a robust methodology is introduced,substantiated by numerical evidence,advancing optimization capabilities in the realm of functionally graded materials and cellular structures.

Full-Scale Isogeometric Topology Optimization of Cellular Structures Based on Kirchhoff-Love Shells

Cellular thin-shell structures are widely applied in ultralightweight designs due to their high bearing capacity and strength-to-weight ratio.In this paper,a full-scale isogeometric topology optimization(ITO)method based on Kirchhoff-Love shells for designing cellular tshin-shell structures with excellent damage tolerance ability is proposed.This method utilizes high-order continuous nonuniform rational B-splines(NURBS)as basis functions for Kirchhoff-Love shell elements.The geometric and analysis models of thin shells are unified by isogeometric analysis(IGA)to avoid geometric approximation error and improve computational accuracy.The topological configurations of thin-shell structures are described by constructing the effective density field on the controlmesh.Local volume constraints are imposed in the proximity of each control point to obtain bone-like cellular structures.To facilitate numerical implementation,the p-norm function is used to aggregate local volume constraints into an equivalent global constraint.Several numerical examples are provided to demonstrate the effectiveness of the proposed method.After simulation and comparative analysis,the results indicate that the cellular thin-shell structures optimized by the proposed method exhibit great load-carrying behavior and high damage robustness.

Symplectic analysis for elastic wave propagation in two-dimensional cellular structures

On the basis of the finite element analysis, the elastic wave propagation in cellular structures is investigated using the symplectic algorithm. The variation principle is first applied to obtain the dual variables and the wave propagation problem is then transformed into two-dimensional （2D） symplectic eigenvalue problems, where the extended Wittrick-Williams algorithm is used to ensure that no phase propagation eigenvalues are missed during computation. Three typical cellular structures, square, triangle and hexagon, are introduced to illustrate the unique feature of the symplectic algorithm in higher-frequency calculation, which is due to the conserved properties of the structure-preserving symplectic algorithm. On the basis of the dispersion relations and phase constant surface analysis, the band structure is shown to be insensitive to the material type at lower frequencies, however, much more related at higher frequencies. This paper also demonstrates how the boundary conditions adopted in the finite element modeling process and the structures＇ configurations affect the band structures. The hexagonal cells are demonstrated to be more efficient for sound insulation at higher frequencies, while the triangular cells are preferred at lower frequencies. No complete band gaps are observed for the square cells with fixed-end boundary conditions. The analysis of phase constant surfaces guides the design of 2D cellular structures where waves at certain frequencies do not propagate in specified directions. The findings from the present study will provide invaluable guidelines for the future application of cellular structures in sound insulation.

In-Plane and Out-of-Plane Mechanical Properties of Zero Poisson’s Ratio Cellular Structures for Morphing Application

Intelligent structures like zero Poisson’s ratio(ZPR)cellular structures have been widely applied to the engineering fields such as morphing wings in recent decades,owing to their outstanding characteristics including light weight and low effective modulus. In-plane and out-of-plane mechanical properties of ZPR cellular structures are investigated in this paper. A theoretical method for calculating in-plane tensile modulus,in-plane shear modulus and out-of-plane bending modulus of ZPR cellular structures is proposed,and the impacts of the unit cell geometrical configurations on in-plane tensile modulus,in-plane shear modulus and out-of-plane bending modulus are studied systematically based on finite element(FE)simulation. Experimental tests validate the feasibility and effectiveness of the theoretical and FE analysis. And the results show that the in-plane and out-of-plane mechanical properties of ZPR cellular structures can be manipulated by designing cell geometrical parameters.

Lightweight and large-scale rGO reinforced SiBCN aerogels with hierarchical cellular structures exposed to high-temperature environments

SiBCN ceramic aerogel is an ideal potential candidate for ultra-high temperature thermal insulation due to its unique microscopic pore structure combined with the excellent thermal stability of SiBCN ce-ramic.Here,reduced graphene oxide(rGO)modified SiBCN aerogels(rGO/SiBCN)were prepared through solvothermal,freeze-casting and pyrolysis,and the dimension of the aerogel is up toΦ130 mm×28 mm.The density of the rGO/SiBCN aerogel is as low as 0.024 g/cm^(3) and the microstructural regulation is achieved by controlling the rGO content in the aerogel.The hierarchical cellular structure endows the aerogel with a high specific surface area(148.6 m^(2)/g)and low thermal conductivity(0.057 W m^(-1) K^(-1)).The 10 mm-thick sample exhibits excellent thermal insulation and ablation resistance,as evidenced by its ability to reduce the temperature from~1100℃to~180℃under the intense heat of a butane flame.Moreover,benefiting from the ultrahigh-temperature stability of SiBCN,the rGO/SiBCN aerogel exhibits good thermal stability up to 1200℃in argon and short-oxidation resistance at 800℃in air.There-fore,the rGO/SiBCN aerogel with superior overall performance could expand its practical application in high-temperature thermal insulation under extreme environments.

Mechanical properties and shape memory behavior of 4D printed functionally graded cellular structures

The properties of functionally graded(FG) cellular structures vary spatially, and the varying properties can meet the requirements of different working environments. In this study, we fabricated FG cellular structures with shape memory effect by 4D printing and evaluated the compressive performance and shape memory behavior of these structures with temperature through experimental analysis and finite element simulations. The results show that the maximum energy absorption gradually decreases but the compressive modulus gradually increases with increasing gradient parameters. Moreover, the finite element simulations also show that the compressive deformation mode of the structure shifts from uniform to non-uniform deformation with increasing gradient parameters. The compressive modulus and compressive strength of 4D printed FG structures decrease with increasing temperature due to the influence of the shape memory polymer, and they exhibit outstanding shape recovery capability under high-temperature stimulus. The proposed 4D printed FG structures with such responsiveness to stimulus shed light on the design of intelligent energy-absorbing devices that meet specific functional requirements.

Review of Crashworthiness Studies on Cellular Structures

The application of lightweight structures with excellent energy absorption performance is crucial for enhancing vehicle safety and energy efficiency.Cellular structures,inspired by the characteristics observed in natural organisms,have exhibited exceptional structural utilization in terms of energy absorption compared with traditional structures.In recent years,various innovative cellular structures have been proposed to meet different engineering needs,resulting in significant performance improvements.This paper provides a comprehensive overview of novel cellular structures for energy absorption applications.In particular,it outlines the application forms and design concepts of cellular structures under typical loading conditions in vehicle collisions,including axial loading,oblique loading,bending loading,and blast loading.Cellular structures have evolved to meet the demands of complex loading conditions and diverse research methods,focusing on achieving high-performance characteristics across multiple load cases.Moreover,this review discusses manufacturing techniques and strate-gies for enhancing the manufacturing performance of cellular structures.Finally,current key challenges and future research directions for cellular structures are discussed.The aim of this study is to provide valuable guidelines for researchers and engineers in the development of next-generation lightweight cellular structures.

Design and mechanical properties analysis of a cellular Waterbomb origami structure

Cellular structures are commonly used to design energy-absorbing structures,and origami structures are becominga prevalent method of cellular structure design.This paper proposes a foldable cellular structure based on theWaterbomb origami pattern.The geometrical configuration of this structure is described.Quasi-static compressiontests of the origami tube cell of this cellular structure are conducted,and load-displacement relationship curvesare obtained.Numerical simulations are carried out to analyze the effects of aspect ratio,folding angle,thicknessand number of layers of origami tubes on initial peak force and specific energy absorption(SEA).Calculationformulas for initial peak force and SEA are obtained by the multiple linear regression method.The degree ofinfluence of each parameter on the mechanical properties of the single-layer tube cell is compared.The resultsshow that the cellular structure exhibits negative stiffness and periodic load-bearing capacity,as well as foldingangle has the most significant effect on the load-bearing and energy-absorbing capacity.By adjusting the designparameters,the stiffness,load-bearing capacity and energy absorption capacity of this cellular structure can beadjusted,which shows the programmable mechanical properties of this cellular structure.The foldability andthe smooth periodic load-bearing capacity give the structure potential for application as an energy-absorbing structure.

Direct design to stress mapping for cellular structures

This paper aims to instantly predict within any accuracy the stress distribution of cellular structures under parametric design,including the shapes or distributions of the cell geometries,or the magnitudes of external loadings.A classical model reduction technique has to balance the simulation accuracy and interaction speed,and has difficulty achieving this goal.We achieve this by computing offline a design-to-stress mapping that ultimately expresses the stress distribution as an explicit function in terms of its design parameters.The mapping is determined as a solution to an extended finite element analysis problem in a high-dimension space,including both the spatial coordinates and the design parameters.The well-known curse of dimensionality intrinsic to the high-dimension problem is(partly)resolved through a spatial separation using two main techniques.First,the target mapping takes a reduced form as a sum of the products of separated one-variable functions,extending the proper generalized decomposition technique.Second,the simulation problem in a varied computation domain is reformulated as that in a fixed-domain,taking an integration function as the sum of the products of separated one-variable functions,in combination with high-order singular value decomposition.Extensive 2D and 3D examples are shown to demonstrate the approach’s performance.

Corrosion behaviour of PEEK or β-TCP-impregnated Ti6Al4V SLM structures targeting biomedical applications

Ti6Al4V cellular structures were produced by selective laser melting(SLM)and then filled either with beta-tricalcium phosphate(β-TCP)or PEEK(poly-ether-ether-ketone)through powder metallurgy techniques,to improve osteoconductivity and wear resistance.The corrosion behavior of these structures was explored considering its importance for the long-term performance of implants.Results revealed that the incorporation of open cellular pores induced higher electrochemical kinetics when being compared with dense structures.The impregnation ofβ-TCP and PEEK led to the creation of voids or gaps between the metallic matrix and the impregnated material which also influenced the corrosion behavior of the cellular structures.

Design Optimization of Irregular Cellular Structure for Additive Manufacturing

Irregularcellular structurehas great potential to be considered in light-weight design field. However, the research on optimizing irregular cellular structures has not yet been reporteddue to the difficulties in their modeling technology. Based on the variable density topology opti- mization theory, an efficient method for optimizing the topology of irregular cellular structures fabricated through additive manufacturing processes is proposed. The pro- posed method utilizes tangent circles to automatically generate the main outline of irregular cellular structure. The topological layoutof each cellstructure is optimized using the relative density informationobtained from the proposed modified SIMP method. A mapping relationship between cell structure and relative densityelement is builtto determine the diameter of each cell structure. The results show that the irregular cellular structure can be optimized with the proposed method. The results of simulation and experimental test are similar for irregular cellular structure, which indicate that the maximum deformation value obtained using the modified Solid Isotropic Microstructures with Penalization （SIMP） approach is lower 5.4× 10-5 mm than that using the SIMP approach under the same under the same external load. The proposed research provides the instruction to design the other irregular cellular structure.

Functionally Graded Cellular Structure Design Using the Subdomain Level Set Method with Local Volume Constraints

Functional graded cellular structure(FGCS)usually shows superiormechanical behaviorwith lowdensity and high stiffness.With the development of additivemanufacturing,functional graded cellular structure gains its popularity in industries.In this paper,a novel approach for designing functionally graded cellular structure is proposed based on a subdomain parameterized level set method(PLSM)under local volume constraints(LVC).In this method,a subdomain level set function is defined,parameterized and updated on each subdomain independently making the proposed approach much faster and more cost-effective.Additionally,the microstructures on arbitrary two adjacent subdomains can be connected perfectly without any additional constraint.Furthermore,the local volume constraint for each subdomain is applied by virtue of the augmented Lagrange multiplier method.Finally,several numerical examples are given to verify the correctness and effectiveness of the proposed approach in designing the functionally graded cellular structure.From the optimized results,it is also found that the number of local volume constraints has little influence on the convergence speed of the developed approach.

Effect of Cellular Structure on Mechanical Properties of Polyurethane Foam Curing Materials

Based on the mechanical properties and microstructure of polyurethane foam solidified material, a two-dimensional model of polyurethane foam solidified material was constructed. Polyurethane foam was obtained by fully and uniformly mixing the two components. The research was carried out through the combination of experimental test and finite element simulation. The experimental results show that when the pore density is constant, the size of the bubble hole is an important factor affecting the mechanical properties of the model. The smaller the size of the bubble hole, the less likely it is to produce stress concentration inside the model, and the stronger the resistance to material deformation. Under the random distribution, the lower the density of the polyurethane cured material, the higher the probability of damage between the adjacent bubbles, which is not conducive to the stability of the material. The density of the cured material should not be lower than 199 kg/m^3.

Design and Mechanical Characterization of an S-Based TPMS Hollow Isotropic Cellular Structure

Cellular structures are regarded as excellent candidates for lightweight-design,load-bearing,and energy-absorbing applications.In this paper,a novel S-based TPMS hollow isotropic cellular structure is proposed with both superior load-bearing and energy-absorbing performances.The hollow cellular structure is designed with Boolean operation based on the Fischer-Koch(S)implicit triply periodic minimal surfaces(TPMS)with different level parameters.The anisotropy and effective elasticity properties of cellular structures are evaluated with the numerical homogenization method.The finite element method is further conducted to analyze the static mechanical performance of hollow cellular structure considering the size effect.The compression experiments are finally carried out to reveal the compression properties and energy-absorption characteristics.Numerical results of the Zener ratio proved that the S-based hollow cellular structure tends to be isotropic,even better than the sheet-based Gyroid TPMS.Compared with the solid counterpart,the S-based hollow cellular structure has a higher elastic modulus,better load-bearing and energy absorption characteristics.

Impact Performance of 3D Integrated Cellular Woven Composite Panel

This paper studied the impact resistance of 3D integrated cellular woven composite panel under persudo-static impact, comprised the test result with property of typical 3D woven composites, analyzed some parameters that maybe affect composites＇ impact resistance and at last used SEM to observe the damage process and mechanism of samples. The result shows that the impact resistance of 3D integrated cellular woven composites is much better than the performance of typical 3D woven composites; it is an active method to improve the impact resistance of composites that developing preform with cellular on the basis of typical 3D woven structure; for different 3D integrated cellular woven structure, the value of absorbed-energy is increasing with the hollow percentage; tiny deformatlen will not emerge on samples until the acting force gets to 85% of the maximum; similar with typical 3D woven composites, the delaminated phenomenon of 3D integrated cellular woven composites is also unapparent during impact process.

Multifunctional cellular carbon foams derived from chitosan toward self-cleaning, thermal insulation, and highly efficient microwave absorption properties

To adapt the practical demand,designing and constructing the multifunctional microwave absorbers(MAs)is the key future direction of research and development.However,effective integrating the multiple functions into a single material remains a huge challenge.Herein,cellular carbon foams(CCFs)with different porous structures were elaborately designed and fabricated in high efficiency through a facile continuous freeze-drying and carbonization processes using a sustainable biomass chitosan as the precursor.The obtained results revealed that the thermal treated temperature and g-C_(3)N_(4) amount played a great impact on the carbonization degrees,pore sizes,and morphologies of CCFs,which led to their tunable electromagnetic(EM)parameters,improved conduction loss,and polarization loss abilities.Owing to the special cellular structure,the designed CCFs samples simultaneously displayed the strong absorption capabilities,broad absorption bandwidths,and thin matching thicknesses.Meanwhile,the as-prepared CCFs exhibited the strong hydrophobicity and good thermal insulation,endowing its attractive functions of self-cleaning and thermal insulation.Therefore,our findings not only presented a facile approach to produce different porous structures of CCFs,but also provided an effective strategy to develop multifunctional high-performance MAs on basis of three-dimensional CCFs.

Hall-Petch relationship in selective laser melting additively manufactured metals:using grain or cell size?

The mechanical properties of many materials prepared by additive manufacturing technology have been greatly improved.High strength is attributed to grain refinement,formation of high density dislocation and existence of cellular structures with nanoscale during manufacturing.In addition,the super-saturated solid solution of elements in the matrix and the solid solution segregation along the wall of the cellular structures also promote the improvement of strength by enhancing dislocation pinning.Hence,the existence of cellular structure in grains leads to differences in the prediction of material strength by Hall-Petch relationship,and there is no unified calculation method to determine the d value as grain size or cell size.In this work,representative materials including austenite 316L SS were printed by selective laser melting(SLM),and the strength was predicted.The values of cell size and grain size were substituted into Hall-Petch formula,and the results showed that the calculation error for 316L is increased from 4.1%to 11.9%.Therefore,it is concluded that the strength predicted by grain size is more accurate than that predicted by cell size in additive manufacturing materials.When calculating the yield strength of laser additive manufacturing metal materials through the Hall-Petch formula,the grain size should be used as the basis for calculation.

Fabrication and Characterization of Nano-CaCO_3/Polypropylene Foam Sheets

By applying the reinforcing and toughening effect of calcium carbonate （CaCO3） nanoparticles on polypropylene, foam sheets of good performance were successfully fabricated by extrusion. The equipment and conditions of the extrusion were explored. The mechanical properties of the produced foam sheets were tested. The effect of CaCO3 nano-particles on the mechanical properties and the cellular structure of the sheets was comprehensively studied. The experimental results show that the optimum content of CaCO3 nano-particles in the composite material was -4wt%. At this content, the nano-particles were well dispersed in the substrate, and the composite material had maximum tensile strength and impact strength. Surface treatment of the nano-particles only affected the impact strength of the composite material. CaCO3 micro-particles, on the other hand, showed little effect on the properties of the composite material when the micro-particles content was less than 5 wt%. At a content higher than 5wt%, the properties of the composite material significantly worsened.

Selective laser melted near-beta titanium alloy Ti-5Al-5Mo-5V-1Cr-1Fe:Microstructure and mechanical properties

In this work,a near-beta Ti-5Al-5Mo-5V-1Cr-1Fe titanium alloy was fabricated by selective laser melting(SLM),and the microstructure evolution together with the mechanical properties was studied.The as-fabricated alloy showed columnarβgrains spreading over multiple layers and paralleling to the building direction.The distinct microstructure of as-fabricated alloy was composed of near-β(more than 98.1%)with a submicron cellular structure.Different SLM processing parameters such as hatch spacing could affect the microstructure of as-fabricated alloy,which could thus further significantly affect the mechanical properties of as-fabricated alloy.In addition,the as-fabricated alloy with the distinct microstructure exhibits yield strength of 818 MPa combined with elongation of more than 19%,which shows that SLM is a potential technology for manufacturing near-beta titanium components.

Mechanical properties of additively-manufactured cellular ceramic structures:A comprehensive study

Cellular ceramic structures(CCSs)are promising candidates for structural components in aerospace and modern industry because of their extraordinary physical and chemical properties.Herein,the CCSs with different structural parameters,i.e.,relative density,layer,size of unit cells,and structural configuration,were designed and prepared by digital light processing(DLP)-based additive manufacturing(AM)technology to investigate their responses under compressive loading systematically.It was demonstrated that as the relative density increased and the size of the unit cells decreased,the mechanical properties of one-layer CCSs increased.The mechanical properties of three-layer CCSs were more outstanding than those of the CCSs with one and two layers.In addition,structural configurations also played a vital role in the mechanical properties of the CCSs.Overall,the mechanical properties of the CCSs from superior to inferior were that with the structural configurations of modified body-centered cubic(MBCC),Octet,SchwarzP,IWP,and body-centered cubic(BCC).Furthermore,structural parameters also had significant impacts on the failure mode of the CCSs under compressive loading.As the relative density increased,the failure mode of the one-layer CCSs changed from parallel-vertical-inclined mode to parallel-vertical mode.It was worth noting that the size of the unit cells did not alter the failure mode.Inclined fracture took a greater proportion in the failure mode of the multi-layer CCSs.But it could be suppressed by the increased relative density.Similarly,the proportions of the parallel-vertical mode and the fracture along a specific plane always changed with the variation of the structural configurations.This study will serve as the base for investigating the mechanical properties of the CCSs.