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.

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.

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.

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.

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.

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.

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.

Interfacial Reaction of Ti6Al4V Lattice Structure-Reinforced VW92 Alloy Matrix Composites

A novel melting infiltration by ultrasonic vibration was investigated and applied to fabricate Ti6Al4V(TC4)lattice structure-reinforced Mg-10Gd-2Y-1Zn-xZr(refer to VW92 hereafter,x=0,0.5 wt%)alloy matrix composites.The edge-to-edge matching model indicates that the well-matching and possible orientation relationships(ORs)between theα-Mg andα-Ti,[10-10]_(α-Mg)//[11-23]_(α-Ti) in(0002)_(α-Mg)//(10-10)_(α-Ti) possesses the smallest misfit of 0.4%(f_(r)),and thus theα-Mg grains can nucleate on the TC4 lattice structure.Interfacial reaction occurred in the TC4/VW92+0.5 wt%Zr composites,and the reaction product was confirmed to be Al_(2)Zr_(3),AlZr_(2) andα-Ti(Zr)particles formed by continuous solution of Zr-Ti.Among the interfacial products,the AlZr_(2) phase is a brittle phase with high-volume fraction,which is not conducive to the load transfer.But generally speaking,theα-Ti(Zr)and theα-Mg tend to form a coherent interface,which is beneficial for improving the interfacial bonding strength of composites.

Analytical solutions for equivalent elastic compliance of cubic lattice structures subjected to hypergravity conditions

In order to comprehensively understand the mechanical behavior of biological entities and aerospace applications subjected to hypergravity environments,we delve into the impact of hypergravity on the equivalent compliance of cubic lattice structures.Capitalizing on the periodic spatial distribution,we employ a unit cell methodology to deduce the homogenized stress-strain relationship for the lattice structures,subsequently obtaining the associated equivalent compliance.The equivalent compliance can be conveniently reduced to instances without hypergravity influence.Furthermore,numerical simulations are executed to validate the derivations and to illustrate that hypergravity indeed affects the mechanical properties of lattice structures.We introduce a non-dimensional hypergravity factor,which quantifies the impact of hypergravity magnitude relative to the Young’s modulus of the base material.Our findings reveal that the hypergravity factor influences perpendicular compliance quadratically and parallel compliance linearly.Simultaneously,the perpendicular shear compliance remains unaffected,whereas the parallel shear compliance experiences an inverse effect.Additionally,the lattice structure transforms into a gradient material oriented in the hypergravity direction,consequently generating a scale effect.

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.

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.

A new hybrid lattice structure with improved modulus,strength and energy absorption properties

In this paper,a hybrid octagonal simple-cubic(OSC) lattice structure is obtained by combining the cell configurations of the bending-dominated octagonal lattice and the stretching-dominated SC lattice.Finite element(FE) numerical models of the three lattice structures(octagonal,octet and OSC lattice) are established and the axial quasi-static compression simulations are performed.In addition,a theoretical model is established to predict the plateau stress of the OSC lattice with different volume coefficients k.Satisfactory consistency is achieved between the results of the theoretical model and those from FE numerical simulations.The results show that the elastic modulus,the compression strength and the energy absorption capacity of the proposed OSC lattice are respectively increased by 233%,86%,and 25% compared with the octagonal lattice under the same relative density conditions,while those values are respectively 212%,34%,and 20% compared with the octet lattice,highlighting the superior mechanical properties of the hybrid OSC lattice.The effects of volume coefficient k and loading direction on the compression behavior of the OSC lattice were parametrically analyzed.The results show that the volume coefficient k is inversely related to the mechanical properties,and an anisotropic characteristic is exhibited in terms of the compression behavior of the OSC lattice structures.

Design and Analysis of Energy Absorbent Bioinspired Lattice Structures

The increasing demand for energy absorbent structures,paired with the need for more efficient use of materials in a wide range of engineering fields,has led to an extensive range of designs in the porous forms of sandwiches,honeycomb,and foams.To achieve an even better performance,an ingenious solution is to learn how biological structures adjust their configurations to absorb energy without catastrophic failure.In this study,we have attempted to blend the shape freedom,offered by additive manufacturing techniques,with the biomimetic approach,to propose new lattice structures for energy absorbent applications.To this aim we have combined multiple bio-inspirational sources for the design of optimized configurations under compressive loads.Periodic lattice structures are fabricated based on the designed unit cell geometries and studied using experimental and computational strategies.The individual effect of each bio-inspired feature has been evaluated on the energy absorbance performance of the designed structure.Based on the design parameters of the lattices,a tuning between the strength and energy absorption could be obtained,paving the way for transition within a wide range of real-life applicative scenarios.

A systematic design of multifunctional lattice structures with energy absorption and phononic bandgap by topology and parameter optimization

Lattice structure can realize excellent multifunctional charac-teristics because of its huge design space,and the cellular configuration directly affects the lattice structural performance and lightweight.A novel energy-absorbing multifunctional lat-tice structure with phononic bandgap is presented by topol-ogy and parameter optimization in this paper.First,the two-dimensional(2D)cellular configuration is lightweight designed by using independent continuous mapping(ICM)topology optimization method.The 2D cell is reconstructed by geo-metric parameters and rotated into a three-dimensional(3D)cell by using chiral shape to achieve bandgap.Subsequently,the surrogated model with energy absorption as the object and first-order natural frequency as the constraint is estab-lished to optimize a parametric 3D cell based on the Response Surface Methodology(RSM).Finally,the lattice struc-tures are assembled with dodecagonal staggered arrange-ments to avoid the deformation interference among the adjacent cells.In addition,the lattice structural energy absorp-tion and bandgap characteristics are analyzed and discussed.Compared to Kelvin lattice structure,the optimal lattice struc-ture shows significant improvement in energy absorption effi-ciency.Besides,the proposed design also performs well in damping characteristics of the high-frequency and wide-bandgap.The lattice structural optimization design framework has great meaning to achieve the equipment structural light-weight and multi-function in the aerospace field.

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.

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.

Design and Manufacturing of a Composite Lattice Structure Reinforced by Continuous Carbon Fibers

New techniques have been developed to make materials with a periodic three-dimensional lattice structure. The high stiffness per unit weight and multifunction of such lattice structures make them attractive for use in aeronautic and astronautic structures. In this paper, epoxy-soaked continuous carbon fibres were first introduced to make lattice composite structures, which maximize the specific load carrying capacity. A micromechanical analysis of several designs, each corresponding to a different manufacturing route, was carried out, in order to find the optimized lattice structure with maximum specific stiffness. An intertwining method was chosen and developed as the best route to make lattice composite materials reinforced by carbon fibers. A sandwich-weaved sample with a three-dimensional intertwined lattice structure core was found to be best. The manufacturing of such a composite lattice material was outlined, In addition to a high shear strength of the core and the integral manufacturing method, the lattice sandwich structure is expected to possess better mechanical capability.