Investigation on the Static Response and Failure Process of Metallic Open Lattice Cellular Structures

Abstract: The response of three different cellular core types, suitable for manufacturing crashworthiness sandwich cellular structures, is investigated in this paper. A methodology is developed, comprising linear static and eigenvalue buckling analysis, as well as nonlinear material elastoplastic analysis. The methodology is used to study the structural response and failure process of open lattice metallic cellular cores and derive the most important structural properties of the cellular core, i.e. elasticity modulus, plateau stress and compaction strain. The critical elastoplastic buckling stress of the metallic struts is approximated by analytical solutions, while a simple engineering approach is applied for the estimation of the compaction strain. The influence of core basic design parameters, i.e. strut aspect ratio (radius/length), unit‐cell spatial configuration and unit‐cell size on the structural behaviour is assessed.     

In-plane effective elastic properties of a novel cellular core for sandwich structures

Within this paper an analytical model is presented for the calculation of the in-plane effective elastic properties E_x and E_y of a novel cellular structure which is proposed to be used as a core in sandwich structures. The proposed cellular core may represent a less expensive and easily to produce alternative to the already known cellular structures used for the construction of sandwich structures. The developed analytical model is validated through experimental tests. The results obtained by analyzing the theoretical model show a good agreement with the tests. The structure topology is studied using a parameterized unit cell and it is shown the way in which the in-plane stiffness depends on the geometric parameters and relative density of the core.     

Corrugated all-composite sandwich structures. Part 1: Modeling

An analytical model for the compressive and shear response of monolithic and hierarchical corrugated composite cores has been developed. The stiffness model considers the contribution in stiffness from the bending- and the shear deformations of the core members in addition to the stretching deformation. The strength model is based on the normal stress and shear stress distribution over each core member when subjected to a shear or compressive load condition. The strength model also accounts for initial imperfections. In part 1 of this series, the analytical model is described and the results are compared to finite element predictions. In part 2, the analytical model is compared to experimental results and the behaviour of the corrugated structures is investigated more thoroughly using failure mechanism maps.     

多层钢板剪力墙水平荷载作用下结构性能的有限元分析

利用有限元数值模型分别计算了四边简支和四边固支均匀受剪矩形板弹性屈曲剪应力及屈曲后极限强度。考虑内填板的屈曲后强度,通过相关文献的单层和4层钢板剪力墙试验数据验证了多层钢板剪力墙有限元数值模拟方法的正确性。利用试验验证的有限元分析方法分别研究了单层和4层钢板剪力墙在水平荷载作用下内填板高厚比的变化对结构性能的影响,并与相应的单层和4层纯框架结构进行了比较,这为钢板剪力墙在不同阶段的结构性能分析提供了依据。     

Research on the Shear Behaviour of Plain Weave Prepreg at Lateral Compaction Stage

Abstract:  An investigation of the shear behaviour of plain weave prepreg at lateral compaction stage was undertaken by the picture-frame test. A unit cell of weave prepreg was modelled and three moments were assumed in the unit cell: (i) the moment of shear force that picture frame applies on the unit cell; (ii) the friction moment at crossover of yarns; and (iii) the compaction moment between the yarns. Through moment balance, a relationship between the load and the shear rate was deduced. A plain sheet shearing film resin model was established to obtain the friction moment at crossover. To get the compaction moment, a constitutive equation of a single prepreged yarn was deduced and a transverse viscosity coefficient equation was given. Moreover, through an equivalent cross-sectional area model, the lateral contact thickness between the yarns was obtained. The comparison between the experimental and theoretical results shows that the presented model can describe the shear behaviour of weave prepreg at lateral compaction stage well.     

Needle Penetration Through Polymeric Cellular Foam Materials

This article presents an analytical model for predicting the needle penetration force through relatively hard polymeric cellular foam. Prediction of needle penetration force is of importance to a number of applications, including textile and composites manufacture as well as robotic surgery. With the aid of this analytical model, a complete nonlinear force-displacement relation can be predicted for any needle size, material hardness, thickness, or inclination. The model assumes the needle to be a cylinder with a conical tip and ignores features, such as needle eye. The primary mechanism for needle penetration force is cell crushing while the friction between the needle and the foam plays a secondary role. There is a good agreement between the experimental and analytical force-displacement curves. In comparison to numerical methods that require nonlinear finite element analysis, this analytical model can be implemented with the knowledge on only two material properties: compression strength and frictional resistance.     

Elastic buckling of hexagonal chiral cell honeycombs

The paper describes a combined analytical, numerical and experimental analysis on the compressive strength of hexagonal chiral honeycombs due to elastic buckling of the unit cells under flatwise compressive loading. Hexagonal chiral honeycombs are cellular structures composed noncentresymmetric unit cells, with an in-plane negative Poisson’s ratio (NPR) with a value of −1. Cylinders connected by tangent ligaments at 60° degrees compose the unit cells. Approximated analytical models are proposed for the purpose of initial design assuming the main contribution to the elastic collapse stress being given by the nodes, and considering also the superposition of the critical elastic loads of each component of the unit cell. The models are expressed in terms of nondimensional geometric unit cell parameters (ligament to cylinder radius aspect ratio and relative density), and core material properties. Finite element calculations using shell and brick elements are also performed on unit cell models with periodic boundary conditions using linear bifurcation buckling analysis. The analytical and numerical results are compared with the outcome of a series of experimental flatwise compressive tests carried out on chiral honeycomb samples manufactured using rapid prototyping technique in PA sintered powder and ABS plastics. The comparison shows good convergence between the sets of results, and highlights the specific deformation mechanisms of the hexagonal chiral honeycomb cell.     

基于多尺度模型的复合材料厚板G_(13)剪切失效分析

针对复合材料厚板强度分析问题,通过对子层压板的刚度等效和应力/应变分解建立了一种多尺度分析模型,并引入了剪切非线性本构关系。实现了复合材料厚板结构在子层压板水平的有限元计算和铺层水平的失效判断。采用FORTRAN语言编写了适用于Abaqus/Explicit求解器的VUMAT子程序,用于模拟复合材料厚板剪切非线性响应以及面内失效,子层压板之间采用内聚力模型来模拟分层损伤。分别采用多尺度线性模型和非线性模型对厚层压板G_(13)剪切试验进行了数值预测,并与试验结果进行了对比。分析结果表明:线性计算模型在预测结构承载能力方面有较高的精度,但在预测整体载荷-位移响应时与试验值偏差较大;由多尺度非线性计算模型得到的破坏模式以及载荷-位移曲线均与试验结果吻合较好。     

CFRP圆形胞元蜂窝芯层面外剪切模量

为了减少卫星的热变形,将碳纤维增强树脂基复合材料（CFRP）材料圆管周期排布获得新型圆形胞元蜂窝芯层。考虑无论是Ressiner理论还是商业有限元软件ABAQUS,层合板计算热变形时,芯层的面外剪切模量均很重要,因此对CFRP圆形胞元蜂窝芯层的面外剪切进行了研究。分别从应力与应变的角度基于能量等效原理求出圆形胞元蜂窝芯层的面外剪切模量公式。以T300/环氧材料的工程常见铺层为例,比较基于ABAQUS软件计算所得剪切模量仿真解与公式计算所得理论解,其最大误差仅为10.4%,证实公式对于CFRP材料的适用性。同时用（±45°）₂铺层的T300/环氧芯层完成双剪试验,试验结果与理论结果误差为24.1%,与前人研究的铝蜂窝面外剪切模量理论解与试验解的误差相近。最后通过仿真手段证实,24.1%的误差对整体夹层结构影响较小,说明公式具有良好的工程应用价值。为以后CFRP圆形胞元蜂窝芯层的设计提供重要基础。     

剪切流场对塑料发泡成核行为的影响

本文着重讨论了剪切流场对成核行为的影响,对宏观规律进行微观分析。通过剪切流场对高聚物熔体中分子取向排列的影响,在熔体中形成大量均匀分布的成核点,这不仅为开发优质泡体提供了理论依据,也是为国外正在加紧开发的微孔发泡技术提供参考。     

双功能带缝剪力墙的弹塑性地震动力反应分析

本文根据双功能带缝剪力墙的试验研究，利用所建立的弹塑性受力分析模型对其进行了受力全过程非线性分析，理论分析结果与试验结果吻合较好。根据双重抗震结构模型，由双功能带缝剪力墙反复荷载试验得到滞回曲线，选择了Takeda滑移型滞回模型，对其进行了弹塑性地震反应分析。分析结果表明，双功能带缝剪力墙具有较好的抗震性能。     

Predicting the longitudinal elastic modulus of braided tubular composites using a curved unit-cell geometry

Predicting the elastic constants of braided composites has gained increasing importance over the years. This is mostly due to the broad use of the braided composites and the need to accurately predict their response during stiffness critical applications. This paper outlines an analytical study to predict longitudinal elastic modulus of two-dimensionally braided composites. The developed model analyzes a small repeating representative block, a unit cell, of the braided structure. Unlike most of the previous studies in the field, the model recognizes the effects of curvature of the unit cell on tubular braided composites as a function of braided tube diameter. This paper outlines the development of the proposed analytical model, as well as validation of the model for stiffness critical applications by comparison of the results with available literature data and experimental findings.     

Bewertung von Spannungszuständen bei der experimentellen Bestimmung des Schubmoduls an zellularen Materialien

Evaluation of stress states for the experimental determination of the shear modulus of cellular materials The experimental determination of the shear modulus of materials proves to be problematic in practice. The different methods do not only preduce the desired pure shear stress state. In this paper, starting from several experimental implementations of the shear test, possible sources of errors in determination of the shear modulus are discussed. An estimation of the possible error is calculated by numerical simulations. Two examples from the field of cellular metals are given to illustrate the effect of just an approximate realization of the pure shear stress state.     

Estimating mechanical properties of 2D triaxially braided textile composites based on microstructure properties

Textile composites manufactured using Resin Transfer Modeling (RTM) can offer advantages in some automotive applications including reduction in weight, while being relatively simpler to fabricate than standard laminated composites used for aerospace applications. However, one of the challenges that arise with these textile composite materials is that the mechanical properties are inherently dependent on the local and final (in-situ) architecture of the textile itself as a result of the molding and curing processes. While this provides additional latitude in the composite design process it also necessitates the development of analytical models that can estimate the mechanical properties of a textile composite based on the textile architecture and the properties of the manufactured component.In this paper, an analytical model is developed and its estimations are compared against experimental in-plane engineering properties for composites with various textile architectures. Results from the model are also compared against finite element (FE) based computational results. The microstructures of the 2D triaxially braided composite (2DTBC) studied were extensively characterized. The microstructure properties thus measured were used in the analytical model to estimate the mechanical properties. Uniaxial tension and V-notched rail shear tests were conducted on 2DTBC with different textile architectures. Good agreement between the analytical, computational, and experimental results were observed and are reported here. Furthermore, computational estimations of matrix mechanical properties are limited to the linear elastic range of a representative material volume (unit cell) and coupon data. Full mechanical response of larger 2DTBC structures, albeit of prime interest, is beyond the scope of this work and could be the focus of follow up studies.     

Polymeric foams and sandwich composites: Material properties,environmental effects,and shear-lag modeling

Marine composite sandwich structural materials, comprising of low density PVC foam core and carbon fiber reinforced vinyl ester based resin composite facings, are studied for associated degradation in mechanical behavior caused by sea water. This paper presents experimental and analytical results concerning the properties and response of closed cell polymeric foams (PVC H100) and their sandwich composites. Data regarding the elastic properties of foam (shear and Young’s modulus) are collected by means of novel custom made devices and interpreted by means of displacement based analytical models. Emphasis is placed on environmental effects and a novel approach of using expansional strain analogy to study the effects of both sea water and temperature are proposed.     

预期损伤部位采用FRC梁柱组合件层间剪力-变形计算模型研究

通过分析梁柱组合件层间变形与梁端变形、柱端变形和节点核心区剪切变形之间的关系,梁端、柱端弯矩与曲率之间的三折线关系及节点核心区剪力与柱顶剪力之间的关系,提出预期损伤部位采用纤维增强混凝土（FRC）梁柱组合件层间剪力-变形计算模型;以节点核心区剪切破坏为主要破坏模式,分析FRC梁柱组合件在开裂点、屈服点和峰值点处的层间剪力、梁端变形、柱端变形和节点核心区剪切变形及各部分变形引起的层间变形占层间总变形中的比例及变化规律。将模型计算结果与试验结果进行比较,结果表明:提出的层间剪力-变形理论计算模型可较好地反映FRC梁柱组合件在地震作用下的层间剪力-变形关系。     

Experimental Characterisation and Numerical Modelling of Hexagonal Honeycomb Cellular Solids under Multi‐axial Loading

Abstract: Cellular solids are becoming increasingly popular for sandwich core and energy‐absorbing applications in many automotive and other transportation structures. This paper investigates experimentally and numerically the strength and post‐failure energy absorption of a popular hexagonal aluminium honeycomb material under multi‐axial loading conditions. For the experimental work, an improved Arcan test apparatus is used so that interaction of multi‐axial compression and shear loading on failure and crushing may be studied; optical measuring methods are used to extract deformation data. In addition, experimental work to characterise the material with pre‐deformation in the in‐plane directions has also been conducted. This experimental work provides input for computational modelling of the material and two alternative modelling approaches have been investigated. First, a three‐dimensional anisotropic, elastic–plastic model, with coupling of loading components is used to represent the material at the macro‐level and, second, a meso‐modelling approach using a fine shell representation of the thin‐walled honeycomb cellular structure is applied. For practical analysis of large‐scale structures, the former approach is computationally efficient and can reasonably treat the most important failure and crush characteristics of the material. However, for more accurate analysis, particularly in the case of complex non‐proportional loading, the meso‐shell model may provide a more realistic solution.     

Dynamic models for low-velocity impact damage of composite sandwich panels – Part B: Damage initiation

Equivalent single and multi degree-of-freedom systems are used to predict low-velocity impact damage of composite sandwich panels by rigid projectiles. The composite sandwich panels are symmetric and consist of orthotropic laminate facesheets and a core with constant crushing resistance. The transient deformation response of the sandwich panels subjected to impact were predicted in a previous paper, and analytical solutions for the impact force and velocity at damage initiation in sandwich panels are presented in this second paper. Several damage initiation modes are considered, including tensile and shear fracture of the top facesheet, core shear failure, and tensile failure of back facesheet. The impact failure modes are similar to static indentation failure modes, but inertial resistance and high strain rate material properties of the facesheets and core influence impact damage loads. Predicted damage initiation loads and impact velocities compare well with experimental results.     

A new contact detection method for arbitrary dilated polyhedra with potential function in discrete element method

Contact detection significantly affects the computational efficiency of discrete element simulations, especially for irregularly shaped elements. The dilated polyhedron is constructed by the Minkowski sum of a dilated sphere and a core convex polyhedron. One of the greatest advantages of using the dilated polyhedron in contact detection lies in its ability to be solved by calculating the nearest distance between corresponding core polyhedra. The approximate envelope function (AEF) of a dilated polyhedron is formed by the weighted summation of the second-order dilated function of the polyhedral and spherical functions. The AEF can be used to represent the element in the optimization model for the contact center. Geometric calculations are then employed for the contact points on the core polyhedron, whereupon the contact detection is solved. The accuracy and stability of the proposed method by a 3-D Voronoi tessellation are validated using analytical solutions and previously published simulation results. The efficiency tests show that the speedup of the CPU-based multithread algorithm can reach 14 on a desktop. The direct shear test of the Voronoi shaped ballast is analyzed by this method. The shear stress under different vertical pressure is compared with previously published experimental and simulated results.