The impulsive response of sandwich beams: Analytical and numerical investigation of regimes of behaviour

An analytical model is developed to classify the impulsive response of sandwich beams based on the relative time-scales of core compression and the bending/stretching response of the sandwich beam. It is shown that an overlap in time scales leads to a coupled response and to the possibility of an enhanced shock resistance. Four regimes of behaviour are defined: decoupled responses with the sandwich core densifying partially or completely, and coupled responses with partial or full core densification. These regimes are marked on maps with axes chosen from the sandwich beam transverse core strength, the sandwich beam aspect ratio and the level of blast impulse. In addition to predicting the time-scales involved in the response of the sandwich beam, the analytical model is used to estimate the back face deflection, the degree of core compression and the magnitude of the support reactions. The predictions of the analytical model are compared with finite element (FE) simulations of impulsively loaded sandwich beams comprising an anisotropic foam core and elastic, ideally plastic face-sheets. The analytical and numerical predictions are in good agreement up to the end of core compression. However, the analytical model under-predicts the peak back face deflection and over-predicts the support reactions, especially for sandwich beams with high strength cores. The FE calculations are employed to construct design charts to select the optimum transverse core strength that either minimises the back face deflections or support reactions for a given sandwich beam aspect ratio or blast impulse. Typically, the value of the transverse core strength that minimises the back face deflection also minimises the support reactions. However, the optimal core strength depends on the level of blast impulse, with higher strength cores required for greater blasts.     

A lattice deformation based model of metallic lattice sandwich plates subjected to impulsive loading

A lattice structure deformation mechanism based theoretical model is developed to predict the dynamic response of square lattice sandwich plates under impulsive loading. The analytical model is established on the basis of the three-stage framework proposed by Fleck and Deshpande (2004). In the first stage, the impulse transmitted from air shock loading to the sandwich plates by fluid-structure interaction is analytically calculated. The lattice core suffers non-uniform compression in the second stage due to the clamped boundary conditions. The structure deformation mechanism is introduced in the lattice core compression and the analytical nominal stress–strain curve of core compression accords well with previous experimental results. In the final stage, the sandwich plate is analyzed as a continuum plate with non-uniform thickness deduced by inconsistent deformation of the front and back sheets.The experiment results of square metallic sandwich plates with tetrahedral lattice core are presented and compared with analytical prediction to validate the theoretical model. Good agreements are found between the predicted and testing results for both the impulse transmitted to the sandwich plates and the maximum deflection of the back face sheet.     

Test method for measuring strength of a curved sandwich beam

A fixture for testing curved sandwich beams in flexure was designed and evaluated. The test specimen is a continuous sandwich beam consisting of a central circular 90° region connected by two straight legs. The fixture was designed according to the four-point flexure principle to produce a pure bending moment in the curved region. The validity of the test fixture in producing the desired loading was examined by fitting a curved aluminum bar of similar bending stiffness as the sandwich beams considered. Strain gage readings were successfully compared to predictions from curved homogeneous beam theory. In addition, the deflection of the beam at the loading points was analyzed using straight and curved beam theory for the various sections of the beam, and predictions were compared to measured load-displacement response. Good agreement was achieved between experimental and analytical results lending confidence to the test principle. Curved sandwich beams consisting of glass/polyester face sheets over a PVC foam core were tested to failure and the loading response of the beams and their failure behavior are discussed. It was found that the beams failed at the upper face/core interface due to radial tension stress.     

爆炸载荷作用下具有可折叠芯层夹芯梁的动态响应

基于目前研究最广泛的刚性折纸(Tachi-origami)样式,通过改变其初始折叠角度构建出4种不同的蜂窝胞元,并且通过排列分布将其组成夹芯梁。采用商用有限元软件Abaqus/explicit对准静态和爆炸载荷作用下可折叠芯层夹芯梁的力学响应进行研究,分析可折叠芯层的泊松比变化规律、夹芯梁背板挠度以及能量吸收机理;并将夹芯梁与等质量的实体梁进行对比。采用后面板最大挠度作为抗爆性能的评价,结果发现:可折叠芯层在准静态载荷下具有一定的负泊松比效应;夹芯梁的抗爆性能优于实体梁,曲边蜂窝的初始折角对其作为芯层夹芯梁的抗爆性能有较大影响,随着初始折角的逐渐增大,其抗爆性能逐渐下降;当初始折角为直角时对应于方孔直边蜂窝,其抗爆性能最差。     

高速颗粒流冲击下负泊松比力学超材料夹芯梁的动态响应及缓冲吸能机理

建立了颗粒流子弹发射有限元模型,利用离散元和有限元的联合模拟方法,研究了高速颗粒流冲击负泊松比内凹蜂窝夹芯梁的动态响应及缓冲吸能机理。分析了加载冲量、冲击角、芯材强度以及颗粒流子弹与面板间的摩擦力等因素对夹芯梁动态响应的影响。研究结果表明:夹芯梁在正向颗粒流子弹冲击载荷作用下表现为局部凹陷和整体弯曲的耦合变形模式,面内设计芯材因胞壁弯曲呈现局部内凹的变形模式,面外设计芯材因胞壁屈曲呈现局部褶皱的变形模式。在等面密度的条件下,采用面外设计的硬芯夹芯梁面板的跨中最大挠度比采用面内设计的软芯夹芯梁小,但初始冲击力峰值和冲击力整体水平较高,冲击力响应时间较短。夹芯梁前后面板的跨中最大挠度与冲击载荷近似呈对数线性递增关系。与正向冲击相比,斜冲击下夹芯梁的变形模式具有非对称性,局部凹陷程度减小;在颗粒流子弹不同冲击角度作用下,夹芯梁前后面板的跨中最大挠度、初始冲击力峰值以及传递到夹芯梁的动能和动量占比随冲击角度的增大而减小,而颗粒流子弹与夹芯梁面板间的摩擦因数对夹芯梁的动态响应无显著影响。     

Impulsive loading of clamped monolithic and sandwich beams over a central patch

An analytical model is developed for the response of clamped monolithic and sandwich beams subjected to impulse loading over a central loading patch. A number of topologies of sandwich core are investigated, including the honeycomb core, pyramidal core, prismatic diamond core and metal foam. The various cores are characterised by their dependencies of through-thickness compressive strength and longitudinal tensile strength upon relative density. Closed-form expressions are derived for the deflection of the beam when the ratio r of length of loading patch to the beam span exceeds 0.5. In contrast, an ordinary differential equation needs to be solved numerically for the choice r<0.5. Explicit finite element calculations show that most practical shock loadings can be treated as impulsive and the accuracy of the impulsive analytical predictions is confirmed. The analytical formulae are employed to determine optimal geometries of the sandwich beams that maximise the shock resistance of the beams for a given mass. The optimisation reveals that sandwich beams have a superior shock resistance relative to monolithic beams of the same mass, with the prismatic diamond core sandwich beam providing the best performance. Further, the optimal sandwich beam designs are only mildly sensitive to the length of the loading patch.     

Blast Performance of Sandwich Composites with In-Plane Compressive Loading

An experimental investigation was conducted to evaluate the dynamic performance of E-glass Vinyl Ester composite face sheet / foam core sandwich panels when subjected to pre-compression and subsequent blast loading. The sandwich panels were subjected to 0 kN, 15 kN and 25 kN of in plane compression respectively, prior to transverse blast wave loading with peak incident pressure of 1 MPa and velocity of 3 Mach. The blast loading was generated using a shock tube facility. During the experiments, a high-speed photographic system utilizing three digital cameras was used to acquire the real-time 3-D deformation of the sandwich panels. The 3D Digital Image Correlation (DIC) technique was used to quantify the back face out-of-plane deflection and in-plane strain. The results showed that in-plane compressive loading facilitated buckling and failure in the front face sheet. This mechanism greatly reduced the blast resistance of sandwich composites.     

Novel stacked folded cores for blast-resistant sandwich beams

Recent research has established the effectiveness of sandwich structures with metallic cellular cores for blast mitigation. The choice of core architecture can enhance sandwich performance, dissipating energy through plastic core compression and exploiting fluid–structure interaction effects to reduce the momentum imparted to the structure by the blast. In this paper we describe the first analysis of a novel sandwich core concept for blast mitigation: the stacked folded core. The core consists of an alternating stacked sequence of folded sheets in the Miura (double-corrugated) pattern, with the stack oriented such that the folding kinematics define the out-of plane compressive strength of the core. It offers a number of distinct characteristics compared to existing cellular cores. (i) The kinematics of collapse of the core by a distinctive folding mechanism give it unique mechanical properties, including strong anisotropy. (ii) The fold pattern and stacking arrangement is extremely versatile, offering exceptional freedom to tailor the mechanical properties of the core. This includes freedom to grade the core properties through progressive changes in the fold pattern. (iii) Continuous manufacturing processes have been established for the Miura folded sheets which make up the core. The design is therefore potentially more straightforward and economical to manufacture than other metallic cellular materials. In this first investigation of the stacked folded core, finite element analysis is used to investigate its characteristics under both quasi-static and dynamic loading. A dynamic analysis of an impulsively loaded sandwich beam with a stacked folded core reveals the versatility of the concept for blast mitigation. By altering the fold pattern alone, the durations of key phases of the dynamic sandwich response (core compression, beam bending) can be controlled. By altering both fold pattern and sheet thickness in the core, the same is achieved without altering the density of the core or the mass distribution of the sandwich beam.     

Uniaxial crushing of sandwich plates under air blast: Influence of mass distribution

Motivated by recent efforts to mitigate blast loading using energy-absorbing materials, this paper uses analytical and computational modeling to investigate the influence of mass distribution on the uniaxial crushing of cellular sandwich plates under air blast loading. In the analytical model, the cellular core is represented using a rigid, perfectly-plastic, locking idealization, as in previous studies, and the front and back faces are modeled as rigid, with pressure loading applied to the front face and the back-face unrestrained. This model is also applicable to the crushing of cellular media in “blast pendulum” experiments. Fluid–structure interaction effects are treated using a recent result that accounts for nonlinear compressibility effects for intense air blasts. Predictions of the analytical model show excellent agreement with explicit finite element computations, and the model is used to investigate the response of the system for all possible distributions of mass between the front and back faces and the cellular core. Increasing the mass fraction in the front face is found to increase the impulse required for complete crushing of the cellular core but also to produce undesirable increases in back-face accelerations. Optimal mass distributions for mitigating shock transmission through the sandwich plate are investigated by maximizing the impulse capacity while limiting the back-face accelerations to a specified level.     

撞击载荷下泡沫铝夹芯梁的塑性动力响应

应用泡沫金属子弹撞击加载的方式研究了固支泡沫铝夹芯梁和等质量实体梁的塑性动力响应。 采用激光测速装置和位移传感器测量了泡沫子弹的撞击速度和后面板中心点的位移-时间曲线,研究了加载 冲量、面板厚度和芯层厚度对夹芯梁抗冲击性能的影响。给出了泡沫铝夹芯梁的变形与失效模式,实验结果 表明结构响应对夹芯结构配置比较敏感,后面板中心点的残余变形与加载冲量、面板厚度呈线性关系。与等 质量实体梁的比较表明,泡沫铝夹芯梁具有更好的抗冲击能力。实验结果对多孔金属夹芯结构的优化设计具 有一定的参考价值。     

PVC夹芯板在冲击载荷下的动态响应与失效模式

通过开展对泡沫金属子弹撞击加载聚氯乙烯(polyvinyl chloride, PVC)夹芯板的实验,结合三维数字图像相关性(three dimensional digital image correlation, DIC-3D)技术,研究固支夹芯板在撞击加载条件下的动态响应,获得夹芯板受撞击及响应的变形过程,并结合图像分别分析夹芯板整体及三层结构的变形和失效模式;研究子弹冲量与背板最终变形之间的关系和相似冲量下等面密度不同芯层密度的夹芯结构的抗撞击性能。结果表明:夹芯板的破坏和失效主要集中在泡沫金属子弹直接作用区域,背板挠度由中间向固定端逐渐减小,子弹冲量与背板变形近似成线性关系。在等质量的条件下,降低芯层密度、增加芯层厚度可以有效降低背板的变形,实验结果对聚合物夹芯结构的工程优化设计具有一定的参考意义。     

Effect of Facesheet Thickness on Dynamic Response of Composite Sandwich Plates to Underwater Impulsive Loading

The response of sandwich structures to underwater blast loading is analyzed. The analysis focuses on the effect of varying structural attributes on energy dissipation and deformation. The structures analyzed are planar sandwich plates with polymer foam cores and fiber-reinforced polymer composite facesheets. The thickness of the facesheets is varied under the conditions of constant material properties and core dimensions. The fully three-dimensional finite-element simulations carried out account for underwater blast loading through the use of the Mie-Gruneisen equation-of-state of a linear Hugoniot form and a modified Drucker-Prager core crushing model. The impulse imparted to the panels is varied from 4 to 42 kPa·s. The results show that there exists an optimal thickness of the facesheets which maximizes energy absorption in the core and minimizes the overall deflection of the structure.     

撞击载荷下泡沫铝夹层板的动力响应

应用泡沫金属子弹撞击加载的方式研究了固支方形夹层板和等质量实体板的动力响应,分别应用激光测速装置和位移传感器测量了泡沫子弹的撞击速度和后面板中心点的位移历史,给出了夹层板的变形与失效模式,研究了子弹冲量、面板厚度、泡沫芯层厚度及芯层密度对夹层板抗撞击性能的影响。结果表明,后面板中心点挠度最大,周边最小,整体变形为穹形,且伴有花瓣形的变形。参数研究表明,通过增加面板厚度或芯层厚度均能有效控制后面板的挠度,改善夹层板的能量吸收能力,结构响应对子弹冲量和芯层密度比较敏感。实验结果对多孔金属夹层结构的优化设计具有一定的参考价值。 更多还原     

冲击波载荷作用下拉－弯耦合梁的瞬态响应分析

采用大挠度弹性理论和中心差分法分析了拉压变形和弯曲变形之间存在弹性耦合的非线性薄梁结构对冲击波载荷作用的大挠度瞬态响应。为了充分描述冲击波载荷的强度大小，文中应用了冲击波载荷的冲量概念。通过进一步研究模态数、时间步长、拉－弯耦合、拉／弯刚度比、冲击波冲量对挠度响应的影响，得到了一些有用的结论。     

孔结构金属复合夹芯板抗爆炸冲击响应及吸能特性研究

采用有限元方法研究爆炸载荷下四边固支孔结构金属复合夹芯板的动力响应及吸能特性,给出了孔结构金属复合夹芯板的动力响应过程,得到夹芯板的变形模式,比较了孔结构金属复合夹芯板与非孔结构金属复合夹芯板的抗爆炸冲击性能,同时讨论了孔大小、间距、排布方式和面板质量分布等因素对孔结构金属复合夹芯板抗爆炸冲击性能的影响。研究结果表明,迎爆面外面板的孔设计使爆炸冲击波穿过孔洞直接作用在芯材上,增强了芯材的压缩,从而提高了夹芯板的能量吸收能力。同等面密度情况下,内外面板厚度比大于1的孔结构金属复合夹芯板变形挠度小于内外面板厚度比小于1的孔结构金属复合夹芯板。进一步研究发现,通过合理设计内外面板的质量分布,可以使孔结构金属复合夹芯板的抗爆炸冲击性能最优。     

The dynamic response of composite sandwich beams to transverse impact

The dynamic response of glass fibre–vinylester composite beams is measured by impacting the beams at mid-span with metal foam projectiles. The beams exist in composite monolithic form, and in sandwich configuration with composite face-sheets and a core made from PVC foam or end-grain balsa wood. High-speed photography is used to measure the transient transverse deflection of the beams and to record the dynamic modes of deformation and failure. For both monolithic and sandwich configurations, a flexural wave travels from the impact site towards the supports. Ultimate failure of the monolithic and sandwich beams is by tensile tearing of the faces. The sandwich beams also exhibit cracking of the core, and face-sheet delamination. The dynamic strength of the beams is quantified by the maximum transient transverse deflection at mid-span of the beams as a function of projectile momentum. It is demonstrated that sandwich beams can outperform monolithic beams of equal mass. The trade-off between core strength and core thickness is such that a low density PVC foam core outperforms a higher density PVC foam core. End-grain balsa wood has a superior stiffness and strength to that of PVC foam in compression and in shear. Consequently, sandwich beams with a balsa core outperform beams with a PVC foam core for projectiles of low momentum. The order reverses at high values of projectile momentum: the sandwich beams with a balsa wood core fail prematurely in longitudinal shear by splitting along the grain.     

Finite element analysis of the dynamic response of clamped sandwich beams subject to shock loading

The finite element (FE) method is employed to analyse the response of clamped sandwich beams subject to shock loadings. Pressure versus time histories representative of shock loadings are applied uniformly to the outer face of the sandwich beam; an impulse applied uniformly to the outer face of the sandwich beam is shown to model adequately shock loadings. Material elasticity and strain hardening representative of structural steels have only a minor effect upon the beam response. Further, the magnitude of the compressive strength of the core has only a limited influence upon the dynamic response of the sandwich beam for the representative range of core strengths considered. The FE results for the deflections and structural response time agree well with the rigid ideally-plastic analytical predictions of Fleck and Deshpande (J. Appl. Mech. (2003), in press).     

Influence of imperfections on the performance of metal foam core sandwich panels

Sandwich panels and beams are used in bending and compression dominated components. The retention of their load capacity in the presence of imperfections is a central consideration. To address this issue, sandwich beams with metallic foam cores have been tested in four-point bending following the introduction of imperfections, created by impressing the face sheets. Limit load expressions for face yielding, core shear, and indentation failure have been developed and used to construct failure mechanism maps. From these maps, specimen designs were determined. Imperfections were introduced by indenting to varying penetrations. The indents were located on both the compressive and tensile side of bending configurations. Experimental measurements of the load/deflection response are obtained and compared with finite element results.     

铝面板PMI泡沫芯夹层梁弹性弯曲的二维模型

将面板PMI泡沫芯夹层梁的弯曲问题按平面应力问题研究,采用弹性理论建立了铝面板PMI泡沫芯夹层梁弯曲变形的微分方程,利用奇异函数把作用在梁上的外载荷表示为分布载荷,推导出了铝面板PMI泡沫芯夹层梁弯曲变形时的挠曲线表达式．采用该方法对面板PMI泡沫芯夹层梁弯曲挠度进行计算,将求得的计算结果与有限元法结果及实验数据进行对比,发现该方法求得的梁中点挠度更接近实验值,这说明该方法可靠的．该方法给出了铝面板PMI泡沫芯夹层梁弯曲时的挠度计算通式,而且梁中点挠度计算公式的表达形式也较为简便,可方便工程设计人员在工程实际中推广应用．     

高速冲击载荷下梯度金属泡沫夹芯梁的动态响应与失效

采用泡沫弹冲击加载实验对梯度金属泡沫夹芯梁结构开展了不同冲击强度下的动态响应和失效研究,分析了由三种不同密度泡沫铝组成的等面密度的五种不同梯度的夹芯结构在夹支边界条件下的抗高速冲击性能,结合三点弯曲实验,研究梯度效应对夹芯结构抗冲击性能的影响。研究表明：密度梯度对结构的失效过程和失效模式有着明显的影响,且夹芯梁结构的初始失效模式对结构整体响应和主要的能量吸收机制起着主导作用;当冲击条件不足以使得均质芯材发生压缩时,均质及负梯度夹芯结构初始失效模式为整体弯曲变形,低强度芯层位于前两层的梯度结构随着冲击强度的变化出现不同程度的局部芯层压缩;当冲击强度较低时,梯度结构通过丰富的局部失效表现出明显优于均质结构的抗冲击变形能力;当冲击强度大于临界值时,均质结构具有更好的抗冲击变形能力。通过合理地设计密度梯度实现逐层压缩吸能,能够有效的提升防护结构的抗冲击性能。