Lattice Core Research Articles

3D-printed SiC lattices integrated with lightweight quartz fiber/silica aerogel sandwich structure for thermal protection system

A lightweight thermal protection/insulation integrated sandwich structure for the aerospace thermal protection system (TPS) was developed with the aim of achieving superior mechanical strength and thermal insulation properties. On the one hand, the lattice frameworks of silicon carbide (SiC) ceramic thermally insulated components with body-centered lattice core (BCLC) were fabricated by selective laser sintering (SLS) 3D printing technology; on the other hand, the sol–gel process was applied to fill quartz fibers reinforced silica (Qf/SiO2) aerogel into the hollow parts of the BCLCs to form a sandwich structure, thus further enhancing the mechanical and thermal insulation properties. To explore the impact of lattice core structure gradient on performance, we designed two types of BCLCs, single-layer one and double-layer one. By comparing the properties of the sandwich structures with the BCLCs, it was found that after the hot surface temperature was kept at 1000℃ for 1500 s, the backside temperature of the single-layer and double-layer sandwich structures decreased by 69.15℃ and 112.73℃, respectively, implying that the thermal insulation efficiency increased by 8.75 % and 13.85 %, respectively. Remarkably, it was precisely due to the filling of the Qf/SiO2 aerogels that the compressive strength of the single-layer and double-layer sandwich structures reached 119.41 MPa and 35.16 MPa, respectively, which were successfully improved by 238.56 % and 256.23 %, respectively, in comparison with the BCLCs structures. Consequently, this study provides an efficient and reliable method for the preparation of thermal protection/insulation integrated components by using 3D printing technology combined with the sol–gel method, which has broader significance among academic and industrial communities.

Liquid metal lattice materials with simultaneously high strength and reusable energy absorption

It is imperative to develop lattice materials with reusable energy absorption for sustainable, economic, and environmental considerations. Unfortunately, existing reusable lattice materials do not usually have both high strength and high energy absorption capacity simultaneously. To overcome this challenge, we developed four types of liquid metal lattice materials and explored their mechanical and recovery behaviors in this work. These beam and shell lattice materials have a liquid metal lattice core coated with two polymer coatings. It is found that the new hybrid coating is stronger and more durable compared to silicone coating alone. The Kelvin beam lattice and Primitive shell lattice are among the best candidates as reusable liquid metal lattice materials. By comparing various reusable lattice materials in the literature, it is found that the liquid metal lattice materials have the highest strength and energy absorption capacity due to the intrinsic metallic features.

Investigation of bird-strike resistance of composite sandwich curved plates with lattice/foam cores

Bird strike is one of the most significant threats to the safe operation of aircraft. Lattice material with high porosity and excellent energy absorption provides more designability for aircraft structures. This paper uses the Finite Element Method and Smoothed Particle Hydrodynamics to investigate the bird impact resistance of composite sandwich curved plates. Lattice material, foam, and lattice-foam hybrid cores are used in this study to enhance the composite against bird impact. The effects of different panel configurations and core structures on the impact response are considered. The results show that the lattice core sandwich structure can enhance the impact resistance of composite materials, mainly reflected in the minor deformation of the structure, which can significantly reduce the bird impact force and reduce the residual kinetic energy of the bird. A thinner front face-sheet assigned to the lattice material sandwich plate would give it better resistance to impact and deformation than the other two sandwich types. Furthermore, a thicker front face-sheet can better resist damage to the composite panel caused by bird impacts.

LatticeOPT: a heuristic topology optimization framework for thin-walled, 2D extruded lattices

This paper introduces a heuristic topology optimization framework for thin-walled, 2D extruded lattice structures subject to complex high-speed loading. The proposed framework optimizes the wall thickness distribution in the lattice cross section through different thickness update schemes, inspired by the idea of equalization of absorbed energy density across all lattice walls. The proposed framework is ubiquitous and can be used in explicit dynamic simulations, which is the primary numerical method used in crashworthiness studies. No information on the material tangent stiffness matrix is required, and complex material behaviors and complex loading conditions can be handled. Three numerical examples are presented to demonstrate framework capabilities: (1) Optimization of a long, slender column under axial compression to maximize specific energy absorption, (2) Optimization of a lattice-filled sandwich panel under off-center blast loading to minimize material damage, (3) Generation of a periodic lattice core design under blast loading. The results show that the framework can effectively increase specific energy absorption or minimize material damage with as few as 25 finite element simulations and optimization iterations.

Bending analysis of sandwich panel composite with a re-entrant lattice core using zig-zag theory

The sandwich panel structures have been widely used in many industrial applications because of their high mechanical properties. The middle layer of these structures is very important factor in controlling and enhancing their mechanical performance under various loading scenarios. The re-entrant lattice configurations, are prominent candidates that can be used as the middle layer in such sandwich structures because of several reasons namely the simplicity in tuning their elastic (e.g., values of Poisson’s ratio and elastic stiffness) and plastic (e.g., high strength-to-weight ratio) properties by only adjusting the geometrical features of the constituting unit cells. Here, we investigated the response of a three-layered sandwich plate with a re-entrant core lattice under flexural bending using analytical (i.e., zig-zag theory), computational (i.e., finite element) and experimental tests. We also analyzed the effects of different geometrical parameters (e.g., angle, thicknesses, and length to the height ratio of unit cells) of re-entrant lattice structures on the overall mechanical behavior of sandwich structures. We found that the core structures with auxetic behavior (i.e., negative Poisson’s ratio) resulted in a higher bending strength and a minimum out-of-plane shear stress as compared to those with conventional lattices. Our results can pave way in designing advanced engineered sandwich structures with architected core lattices for aerospace and biomedical applications.

Heat transfer property of C/SiC composite pyramidal lattice core sandwich structures

An explicit analytical model for predicting the heat transfer in C/SiC composite pyramidal lattice core sandwich structures is proposed with considering the radiation emitted from the struts. Temperature gradient in thickness direction of the lattice core sandwich structuresis considered in the proposed model. The predictions are compared with the published experimental data and analytical results. It indicates the effect of the radiation emitted from the struts on the equivalent thermal conductivity becomes more significant at high temperature and cannot be overlooked. The present model is more accurate in estimating the high-temperature equivalent thermal conductivity of pyramidal lattice core sandwich structures than those models without considering the radiation of struts. The effects of geometry, solid emissivity, and temperature on the equivalent thermal conductivity of pyramidal lattice core sandwich structures are well discussed.

Numerical Investigation of Different Core Topologies in Sandwich-Structured Composites Subjected to Air-Blast Impact

Air-blast loading is a serious threat to military and civil vehicles, buildings, containers, and cargo. Applications of sandwich-structured composites have attracted increasing interest in modern lightweight design and in the construction of dynamic loading regimes due to their high resistance against blast and ballistic impacts. The functional properties of such composites are determined by the interplay of their face sheet material and the employed core topology. The core topology is the most important parameter affecting the structural behavior of sandwich composites. Therefore, this contribution presents a thorough numerical investigation of different core topologies in sandwich-structured composites subjected to blast loading. Special emphasis is put on prismatic and lattice core topologies displaying auxetic and classical non-auxetic deformation characteristics in order to illustrate the beneficial properties of auxetic core topologies. Their dynamic responses, elastic and plastic deformations, failure mechanisms, and energy absorption capabilities are numerically analyzed and compared. The numerical studies are performed by means of the commercial finite element code ABAQUS/Explicit, including a model for structural failure.

Dynamic response of CFRP-lattice sandwich structures subjected to underwater shock wave loading

Carbon fiber reinforced composites (CFRP) and porous lattice structures possess the advantages of high specific strength and outstanding energy absorption efficiency. However, the structures combining their merits for underwater explosion protection receives little attention, and the underlying mechanics are still not clear. In this work, a CFRP-lattice sandwich structure is proposed, and its responses subjected to the underwater shock wave loading is studied via the finite element code ABAQUS/Explicit. The numerical results are first validated by the existing experiments (Huang et al., 2016), and the influences of the geometrical and load factors on the deformation modes and energy absorption performances are further explored. Results shows that with the variation of the load intensity and structural configuration, the failure modes of the plates can be mainly divided into three types. The failure occurs in the middle layer of the metal porous lattice core along the thickness direction. The thickness of the back plate has a greater influence on the overall deformation of the structure than that of the front plate. When the thickness of the back plate increases, the energy absorption of the front plate increases first and then decreases under the condition of a small shock wave load. The impact resistance of composite sandwich structure is the result of the coupling of core layer and plates. The proportion of energy absorption of each layer is affected by the form of structural energy transfer. The work of this paper provides guidance for the design of underwater protective equipment.

Nonlinear vibration responses of lattice sandwich beams with FGM facesheets based on an improved thermo-mechanical equivalent model

An investigation on the nonlinear vibration behaviors of a lattice sandwich beam with pyramidal truss core and functionally graded material (FGM) facesheets under thermo-mechanical loads is performed with consideration of the temperature-dependency of material properties. In present work, an improved equivalent methodology is proposed to determine the transverse shear modulus of pyramidal core subjected to a non-uniform thermal field across thickness direction and makes lattice truss core transformed to a continuous layer. Finally, the lattice sandwich beam is modeled as a three-layered sandwich structure. The facesheets are made of FGMs with mixture of ceramics and metals in a pow-law form. The outer surfaces of facesheets are ceramic-rich, while the inner surfaces are metal-rich. The nonlinear strain–displacement relations are established based on the von Kármán large deflection and classical beam theory. The Lagrange method are implemented to yield equations governing the free and forced vibration behaviors. With the help of Newton-Raphson iteration technique as well as the Newmark-β method, the nonlinear time-independent responses of the sandwich beam under thermal environment are solved. A comprehensive parameter study is directed to address the effects of non-uniform thermal environment, FMG facesheets, external load, and lattice core on the nonlinear vibrations of the beams.

Blast shock wave attenuation in square cross-sectional truss based meso-scale lattice architectures

With the rapid growth in defense and civilian industry interests, high-performance materials like lattice materials capable of resisting high strain-rate loads are urgently required. Researchers mainly focus on the irreversible plastic deformation of lattice core sandwich structures under out-of-plane loads, whereas the potential application of cellular core without sandwiched face sheets has not been explored. In fact, when shock waves directly act on a cellular core without sandwiched face sheet, the energy would be consumed in the voids during the wave propagation. This article gives an insight into the shock wave attenuation characteristics and the attenuation mechanisms of square cross-sectional truss based meso-scale lattice architectures. Two types of lattice configurations with the same porosity but different truss sectional arrangements are employed. It is reported that both types of the lattice architectures can considerably dissipate the shock wave. The variation trends of overpressure-time history for the meso-scale lattice architectures are significantly different from those obtained in the free air field. As the truss-sectional size decreases the detected first peak overpressure decreases and becomes gradually lower than the second peak overpressure due to the increasing truss layers. When the edge length of truss section, d, decreases from 0.4 mm to 0.1 mm at a constant scaled distance of 0.896, the attenuation efficiency of the peak overpressure is increased by 30 % to 70 %, and the efficiency of the impulse is increased by 60 %, together with a highly-improved increasing rate for the delaying efficiency of the arrival time. Considering distinct scaled distances, the type II architecture and type I architecture behave superiorly with respect to the attenuation efficiencies of peak overpressure and impulse, respectively. Compared to the free field scenario, a shorter wave propagation distance could be observed for the meso-scale lattice architectures to achieve the same peak overpressure and impulse. The considerable shock wave attenuation of the meso-scale lattice architecture is attributed to the complex interactions of the shock wave reflection, diffraction, and superposition around the truss sections and in the voids. This investigation provides a novel method for the shock wave attenuation and energy consumption to protect vital targets and precise equipment.

Free vibration analysis of curved lattice sandwich beams

In this paper, the effects of initial curvature and lattice core shape on the bending vibration of sandwich beams are investigated. The three-dimensional (3D) sandwich beam is simulated by combining a two-dimensional (2D) cross-sectional analysis with a one-dimensional (1D) nonlinear beam analysis. The sandwich beam is composed of two identical isotropic faces covering a lattice core. Four different lattice core structures are used to take into account the effect of core unit cell shape on the dynamic properties of the sandwich beam. The nonlinear governing equations of the sandwich beam are Discretized using a time-space scheme. Numerical results show that the lattice unit cell shape affects both in-plane and out of plane stiffness values and hence changes the dynamic behavior of the beam. Furthermore, it is observed that by changing the density ratio of the beam, modes veer away from each other at a specific value of density ratio for specific unit cell types. Moreover, the initial curvature of the beam is shown to affect the dynamics of the beam especially lower modes. Finally, it is obtained that the dynamics of the beam is different when it is initially curved or curved due to an applied end follower moment.

On low-velocity impact behavior of sandwich composites with negative Poisson’s ratio lattice cores

In order to investigate the low-velocity impact performance of a new type of sandwich composite structure with negative Poisson’s ratio lattice cores, low-velocity impact tests were carried out using the sandwich composite specimens, which were prepared by 3D printing lattice cores and glass/epoxy composite sheets. A finite element dynamic analysis strategy was also employed to investigate the mechanical response, the total energy absorption, and energy absorptivity of the sandwich panel at impact energies of 5 J, 10 J, 15 J, 20 J, 30 J and 40 J, respectively. Results show that the new sandwich structure can better disperse the concentrated impact load received by the upper sheet and dissipate most of the impact energy in the process of transferring the loads during cushioning. The negative Poisson’s ratio lattice structure can guide damages, and it is found that the position of the impact point will affect the impact mechanical response and energy absorption ability of the sandwich panel.

2D Elasticity solution for sandwich panels with functionally graded lattice cores

The quest for weight-reduced components while maintaining strength requires new structures and lightweight concepts that promise more advantages than existing structures. In sandwich panels, improving the mechanical performance of the face sheets is almost exhausted due to using ultra-high-strength materials. By contrast, the sandwich core offers a high light-weight potential when it constitutes the largest part of the total weight of the sandwich. Novel structures such as lattices can significantly enhance the core’s mechanical performance. Lattice structures fabricated by additive manufacturing (AM) provide comparable mechanical properties to honeycombs and allow multifunctional use of the core. Another benefit of using AM is the ability to customize the core mechanical properties. Such a design could be achieved by using a functionally graded lattice core. In this work, an analytical model is derived to determine stresses and deformations in graded lattice cores of sandwich panels. Compared to the classical sandwich theory, the presented model enables the determination of the out-of-plane stresses near the load application areas. Furthermore, evaluating the stresses in the lattice struts of the graded core highlights the benefits of using graded cores in sandwich panels since the stress in graded cores exhibits a more homogeneous distribution, enabling better material exploitation.

Erratum to ‘Experimental and numerical investigation on the buckling of 3D printed sandwich structure with lattice core”

Erratum to ‘Experimental and numerical investigation on the buckling of 3D printed sandwich structure with lattice core”

Equivalent in-plane dynamic elastic moduli of lattice structures with Plateau borders

Lattice structures with Plateau borders (LSPB) have attracted increasing interests recently due to the improved stiffness, strength, energy absorption properties. Undoubtedly, vertexes with Plateau borders (VPB) play a significant role on the dynamic elastic moduli. This paper proposes an analytical framework of the frequency-dependent equivalent in-plane dynamic elastic moduli (Young’s moduli E1(ω), E2(ω), Poisson’s ratio ν12(ω), ν21(ω) and shear modulus G12(ω)) of LSPB. First, dynamic stiffness (DS) matrix of a lattice cell edge (based on rod and Timoshenko theories) connected to VPBs (modelled as rigid bodies) at both ends is formulated. Then, based on the above DS matrix and the unit cell method, closed-form expressions of equivalent in-plane dynamic elastic moduli are proposed, which are sufficient general to be applied to four types of lattices. The effects of mass, inertia moment and size of VPB on the equivalent dynamic elastic moduli are studied, with both physical and mathematical interpretations. Furthermore, the proposed expressions are applied to honeycomb, rectangular, auxetic and rhombus LSPB and some interesting and important observations are made. This research provides analytical expressions for broadband dynamic elastic moduli of LSPB, which can be directly used in the design and optimization of composite structures with lattice cores.

Experimental investigation of the compressive strength of hybrid composite sandwich beams with double-corrugated sinusoidal core reinforced by graphene and polyurethane foam

In this paper, the effects of some system parameters such as nanographene, core geometry, and polyurethane foam on the compressive strength of composite sandwich beams with double corrugated lattice core subjected to flatwise-compression load are investigated experimentally. The face sheets and core of the sandwich beams are made of 10-layers bidirectional carbon fibers using the vacuum infusion process. According to the results of the flatwise-compression test, it was revealed that some factors, including height and angle of the core, the weight percentage of nanographene, and polyurethane foam, can be considered as effective parameters to enhance the compressive strength of the composite sandwich beams. Scanning electron microscopy images were utilized to observe the composition and distribution of the nanoparticles. It was observed that adding nanographene particles to the composite laminates significantly affects the mechanical properties and flexural strength of the sandwich beams. In addition, experimental results showed that the shape of the core can be an effective parameter to control the elasticity and strength of the sandwich beams, and also polyurethane foam dramatically increases the compressive strength and can postpone core failure.

Optimal Density of the Lattice Cores for Impact-Resistant Structural Elements Produced by FDM Technology

Optimal Density of the Lattice Cores for Impact-Resistant Structural Elements Produced by FDM Technology

Compression behaviour of TPMS-filled stainless steel tubes

One of the most promising options for future crashworthiness applications is thin-walled tubes filled with various cellular materials (e.g. metal foam). Of higher interest are the shell-based lattices, which have lately gained popularity due to their superior qualities over strut-based lattices. In this work, we investigate the mechanical response of foam-filled tubes where the tube's core was represented by Triply Periodic Minimal Surface (TPMS) diamond lattices. Samples made of stainless steel 316L comprising the diamond lattice core, empty tubes, and in-situ TPMS-filled tubes were additively manufactured and mechanically tested under compressive loading. As-fabricated welded tubes and ex-situ TPMS-filled tubes were also analysed and compared. Under the axial loading, the ex-situ and in-situ TPMS-filled tubes showed very similar behaviour. Enhanced energy absorption up to 21% and 44% compared to the sum of empty tubes and the core responses was noted. The energy absorption enhancement of 12% in the case of transversal loading is limited to in-situ TPMS-filled tubes, where the connection between the tube and core prevents the tube's walls from buckling. Computational models with homogenised core were developed and validated based on the experimental data. These straightforward, fast, and accurate computational models can be efficiently used for large-scale real-life applications, e.g. crash and impact.

High-speed impact analysis of reinforced GFRP sandwich structure with lattice core using experimental and finite element methods

ABSTRACT High-speed impact behaviour of composite sandwich panels reinforced by nano-SiO2 has been studied in the present article. The sandwich panels were manufactured by glass/fibre epoxy composite face sheets and an M-shaped core using the vacuum-assisted resin transfer moulding (VARTM) method. To enhance the mechanical strength of the matrix, especially impact resistance, the nanoparticles were added to the resin epoxy matrix as filler. A scanning electron microscope (SEM) was utilised to observe the microscopic structure of the composites. The experimental results indicated that adding 1–3 wt-% of nano-SiO2 into the matrix remarkably increased the impact resistance of the composite. In order to validate the results, the experimental data were compared to the finite element models, and good agreement was observed.

Correlation Decay and Partition Function Zeros: Algorithms and Phase Transitions

We explore connections between the phenomenon of correlation decay and the location of Lee-Yang and Fisher zeros for various spin systems. In particular we show that, in many instances, proofs showing that weak spatial mixing on the Bethe lattice (infinite $\Delta$-regular tree) implies strong spatial mixing on all graphs of maximum degree $\Delta$ can be lifted to the complex plane, establishing the absence of zeros of the associated partition function in a complex neighborhood of the region in parameter space corresponding to strong spatial mixing. This allows us to give unified proofs of several recent results of this kind, including the resolution by Peters and Regts of the Sokal conjecture for the partition function of the hard core lattice gas. It also allows us to prove new results on the location of Lee-Yang zeros of the anti-ferromagnetic Ising model. We show further that our methods extend to the case when weak spatial mixing on the Bethe lattice is not known to be equivalent to strong spatial mixing on all graphs. In particular, we show that results on strong spatial mixing in the anti-ferromagnetic Potts model can be lifted to the complex plane to give new zero-freeness results for the associated partition function. This extension allows us to give the first deterministic FPTAS for counting the number of $q$-colorings of a graph of maximum degree $\Delta$ provided only that $q\ge 2\Delta$. This matches the natural bound for randomized algorithms obtained by a straightforward application of Markov chain Monte Carlo. We also give an improved version of this result for triangle-free graphs.