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.

Ballistic performances of the hourglass lattice sandwich structures under high-velocity fragments

In this paper,the numerical simulation method is used to study the ballistic performances of hourglass lattice sandwich structures with the same mass under the vertical incidence of fragments.Attention is paid to elucidating the influences of rod cross-section dimensions,structure height,structure layer,and rod inclination angle on the deformation mode,ballistic performances,and ability to change the ballistic direction of fragments.The results show that the ballistic performances of hourglass lattice sandwich structures are mainly affected by their structural parameters.In this respect,structural parameters optimization of the hourglass lattice sandwich structures enable one to effectively improve their ballistic limit velocity and,consequently,ballistic performances.

Valley transport in Kekulé structures of graphene

Valleytronics is an emergent discipline in condensed matter physics and offers a new way to encode and manipulate information based on the valley degree of freedom in materials. Among the various materials being studied, Kekulé distorted graphene has emerged as a promising material for valleytronics applications. Graphene can be artificially distorted to form the Kekulé structures rendering the valley-related interaction. In this work, we review the recent progress of research on Kekulé structures of graphene and focus on the modified electronic bands due to different Kekulé distortions as well as their effects on the transport properties of electrons. We systematically discuss how the valley-related interaction in the Kekulé structures was used to control and affect the valley transport including the valley generation, manipulation, and detection. This article summarizes the current challenges and prospects for further research on Kekulé distorted graphene and its potential applications in valleytronics.

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.

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.

Skeleton-Based Volumetric Parameterizations for Lattice Structures

Lattice structures with excellent physical properties have attracted great research interest.In this paper,a novel volume parametric modeling method based on the skeleton model is proposed for the construction of threedimensional lattice structures.The skeleton model is divided into three types of nodes.And the corresponding algorithms are utilized to construct diverse types of volume parametric nodes.The unit-cell is assembled with distinct nodes according to the geometric features.The final lattice structure is created by the periodic arrangement of unit-cells.Several different types of volume parametric lattice structures are constructed to prove the stability and applicability of the proposed method.The quality is assessed in terms of the value of the Jacobian matrix.Moreover,the volume parametric lattice structures are tested with the isogeometric analysis to verify the feasibility of integration of modeling and simulation.

Strength failure of spatial reticulated structures under multi-support excitation

Under strong earthquakes, long-span spatial latticed structures may collapse due to dynamic instability or strength failure. The elasto-plastic dynamic behaviors of three spatial latticed structures, including two double-layer cylindrical shells and one spherical shell constructed for the 2008 Olympic Games in Beijing, were quantitatively examined under multi-support excitation （MSE） and uniform support excitation （USE）. In the numerical analyses, several important parameters were investigated such as the peak acceleration and displacement responses at key joints, the number and distribution of plastic members, and the deformation of the shell at the moment of collapse. Analysis results reveal the features and the failure mechanism of the spatial latticed structures under MSE and USE. In both scenarios, the double-layer reticulated shell collapses in the ＂overflow＂ mode, and the collapse is governed by the number of invalid plastic members rather than the total number of plastic members, beginning with damage to some of the local regions near the supports. By comparing the numbers and distributions of the plastic members under MSE to those under USE, it was observed that the plastic members spread more sufficiently and the internal forces are more uniform under MSE, especially in cases of lower apparent velocities in soils. Due to the effects of pseudo-static displacement, the stresses in the members near the supports under MSE are higher than those under USE.

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.

Assessment of Similitude Behavior in Natural Frequencies of Printed Turbine Blade

Improving structures involves comparing old and new designs on a key parameter.Calculating the percent change in performance is a method to assess.This paper proposes a cost-effective analogy by generating replicas of additive manufactured aluminum alloy(Al Si10Mg)body-centered cubic lattice(BCC)based turbine blade(T106C)with the same in poly-lactic acid(PLA)material and their comparison in the context of percent change for natural frequencies.Initially,a cavity is created inside the turbine blade(hollow blade).Natural frequencies are obtained experimentally and numerically by incorporating BCC at 50%and 80%of the cavity length into the hollow blade for both materials.The cost of manufacturing the metal blades is 90%more than that of the PLA blades.The two material blade designs show a similar percentage variation,as the first-order mode enhancs more than 5%and the second-order mode more than 4%.To observe the behavior in another material,both blades are analyzed numerically with a nickel-based U-500 material,and the same result is achieved,describing that percent change between designs can be verified using the PLA material.

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.

Fabrication of silica-based ceramic cores with internal lattice structures by stereolithography

Ceramic cores are widely used in investment casting,and ideal properties of cores are essential for high-quality castings.Under the circumstances requiring thick cores,solid cores are likely to encounter deformation and cracking defects due to the accumulation of shrinkage.Therefore,with the superiority of ceramic stereolithography in producing complex ceramic parts,hollow cores with lattice structures were designed and fabricated.The dimensional accuracy and properties of the green and sintered bodies were evaluated.Results show the dimensional accuracy of sintered cores is controlled within±0.25 mm benefited from the precise green bodies.The mechanical properties are not obviously deteriorated.The bending strength reaches 11.94 MPa at room temperature and 12.87 MPa at 1,500℃ with a creep deformation of 0.345 mm.Furthermore,casting verifications prove that the hollow cores meet the requirements of investment casting.Smooth casting surfaces are obtained,at the same time,the core-removal efficiency is improved by over 3 times.

Numerical simulation and experimental validation on fabrication of nickel-based superalloy Kagome lattice sandwich structures

Nickel-based superalloy lattice sandwich structures present higher stiffness,higher strength and higher temperature resistance in comparison with other metals.In this study,the Kagome unit was adopted to design the lattice sandwich structure and ProCAST software was used to simulate the filling and solidification processes of the nickel-based superalloy.Grain morphology and sizes of the nickel-based superalloy lattice sandwich structures were simulated by using of cellular automaton coupled with finite element model(CAFE),and indirect additive manufacture combining with investment casting were carried out to fabricate the nickel-based superalloy lattice sandwich structures.The calculated grain morphology and sizes are in good agreement with the experimental results.The grains are mainly equiaxed with an average size of about 500µm.The simulated results also show that the superheat of melting and the mold preheated temperature have significant influence on the grain size of the Kagome lattice sandwich structures,lower superheat of melting and mold preheated temperatures are encouraged to obtain the fine grains while assuring the integrity of the Kagome lattice sandwich structures for industrial application.

Deformation mode and energy absorption of polycrystal-inspired square-cell lattice structures

Lattice structures are widely used in many engineering fields due to their excellent mechanical properties such as high specific strength and high specific energy absorption(SEA)capacity.In this paper,square-cell lattice structures with different lattice orientations are investigated in terms of the deformation modes and the energy absorption(EA)performance.Finite element(FE)simulations of in-plane compression are carried out,and the theoretical models from the energy balance principle are developed for calculating the EA of these lattice structures.Satisfactory agreement is achieved between the FE simulation results and the theoretical results.It indicates that the 30◦oriented lattice has the largest EA capacity.Furthermore,inspired by the polycrystal microstructure of metals,novel structures of bi-crystal lattices and quad-crystal lattices are developed through combining multiple singly oriented lattices together.The results of FE simulations of compression indicate that the EA performances of symmetric lattice bi-crystals and quad-crystals are better than those of the identical lattice polycrystal counterparts.This work confirms the feasibility of designing superior energy absorbers with architected meso-structures from the inspiration of metallurgical concepts and microstructures.

Short beam shear properties and failure modes of the wood-based X-type lattice sandwich structure

A wood-based X-type lattice sandwich structure was manufactured by insertion-glue method.The birch was used as core,and Oriented Strand Board was used as panel of the sandwich structure.The short beam shear properties and the failure modes of the wood-based X-type lattice sandwich structure with different core direction(vertical and parallel),unit specification(120 mm×60 mm and 60 mm×60 mm),core size(50 mm and 60 mm),and drilling depth(9 mm and 12 mm)were investigated by a short beam shear test and the establishment of a theoretical model to study the equivalent shear modulus and deflection response of the X-type lattice sandwich structure.Results from the short beam shear test and the theoretical model showed that the failure modes of the wood-based X-type lattice sandwich structure were mainly the wrinkling and crushing of the panels under three-point bending load.The experimental values of deflection response of various type specimens were higher than the theoretical values of them.For the core direction of parallel,the smaller the unit specification is,the shorter the core size is,and the deeper the drilling depth is,the greater the short beam shear properties of the wood-based X-type lattice sandwich structure is.

Multi-Material and Multiscale Topology Design Optimization of Thermoelastic Lattice Structures

This study establishes amultiscale andmulti-material topology optimization model for thermoelastic lattice structures(TLSs)consideringmechanical and thermal loading based on the ExtendedMultiscale Finite ElementMethod(EMsFEM).The corresponding multi-material and multiscale mathematical formulation have been established with minimizing strain energy and structural mass as the objective function and constraint,respectively.The Solid Isotropic Material with Penalization(SIMP)interpolation scheme has been adopted to realize micro-scale multi-material selection of truss microstructure.The modified volume preserving Heaviside function(VPHF)is utilized to obtain a clear 0/1 material of truss microstructure.Compared with the classic topology optimization of single-material TLSs,multi-material topology optimization can get a better structural design of the TLS.The effects of temperatures,size factor,and mass fraction on optimization results have been presented and discussed in the numerical examples.

Structures and electrical properties of pure and vacancy-included ZnO NWs of different sizes

The structures and electronic properties of ZnO nanowires（NWs） of different diameters are investigated by employing the first-principles density functional theory. The results indicate that the oxygen vacancy（VO） exerts a more evident influence on the band gap of the ZnO NWs. However, the effect will be weakened with the increase of the diameter. In addition, the energy band shifts downward due to the existence of VOand the offset decreases with the reduction of the VOconcentration. As the concentration of surface Zn atoms decreases, the conduction band shifts downward, while 2p electrons are lost in the oxygen vacancy, resulting in the split of valence band and the formation of an impurity level. Our findings agree well with the previous observations and will be of great importance for theoretical research based on ZnO NWs.

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.

Zero-field splitting parameters and local structures for tetragonal Cr^(2+) centers in Cr^(2+)-doped ZnSe semiconductors

The inter-relation between zero-field splitting （ZFS） parameters and local lattice structures of the （CrSe4）6 clusters in ZnSe semiconductors has been established by using the complete diagonalization （of the energy matrix） method. On the basis of this, the local lattice distortions, the ZFS parameters D, a, F and the optical spectrum for Cr2＋ ions doped into ZnSe are theoretically investigated, and the contributions of the spin singlets have been taken into account. The calculated ZFS parameters are in good agreement with the experimental values. From our calculations, the tetragonal distortion parameters AR = 0.091A and Aθ = 4.28° of Cr2＋ in ZnSe are acquired, and the results suggest that there exists a tetragonal expansion distortion for the local lattice structure of （CrSe4）6- clusters in ZnSe crystals. The influence of the spin singlets on ZFS parameters is also discussed, indicating that the contributions to ZFS parameters a and F cannot be ignored.

Plasmonic emission and plasma lattice structures induced by pulsed laser in Purcell cavity on silicon

The lattice structure image of a plasma standing wave in a Purcell cavity of silicon is observed. The plasma wave produced by the pulsed laser could be used to fabricate the micro-nanostructure of silicon. The plasma lattice structures induced by the nanosecond pulsed laser in the cavity may be similar to the Wigner crystal structure. It is interesting that the beautiful diffraction pattern could be observed in the plasma lattice structure. The radiation lifetime could be shortened to the nanosecond range throughout the entire spectral range and the relaxation time could be lengthened for higher emission efficiency in the Purcell cavity, which results in the fact that the plasmonic emission is stronger and its threshold is lower.

Periodic Lattice Porous Structure Produced by Selective Laser Melting:Process,Experiment and Numerical Simulation Analysis

To accurately perform the coupled simulation of temperature field and stress field of complex parts and porous structures under the optimal manufacturing process parameters,three kinds of porous structures with different complexity were designed in this paper.Firstly,ANSYS additive software was used to conduct the stress/deformation simulation of the whole structure under different scanning strategies.Secondly,the optimal scanning strategy for different porous structures was determined,then the experimental preparation was performed,and mechanical properties of compression were tested and studied.The results show that the elastic modulus and yield strength increase with the increase of pole diameter/wall thickness.In addition,the quasi-static compression simulation of different structures was performed,and the compression performance was analyzed based on the experimental data.Finally,the stress concentration region of different structures was obtained.