Architected Lattices with High Stiffness and Toughness via Multicore–Shell 3D Printing

The ability to create architected materials that possess both high stiffness and toughness remains an elusive goal, since these properties are often mutually exclusive. Natural materials, such as bone, overcome such limitations by combining different toughening mechanisms across multiple length scales. Here, a new method for creating architected lattices composed of core–shell struts that are both stiff and tough is reported. Specifically, these lattices contain orthotropic struts with flexible epoxy core–brittle epoxy shell motifs in the absence and presence of an elastomeric silicone interfacial layer, which are fabricated by a multicore–shell, 3D printing technique. It is found that architected lattices produced with a flexible core‐elastomeric interface‐brittle shell motif exhibit both high stiffness and toughness.     

Titanium Alloy Lattice Structures with Millimeter Scale Cell Sizes

Titanium sandwich panels with cellular cores of a uniform 1–5 mm diameter open cell size are well suited for impact energy absorption and cross flow heat exchange applications. Periodic cellular structures (lattices) made from high specific strength, high temperature alloys are preferred for these multifunctional uses. A diffusion bonding method has been applied here to make cellular lattice structures from a Ti–6A1–4V alloy. To illustrate the approach, lattice structures with both square and diamond collinear topologies, a 2 mm open cell size, and a relative density of 15% were made from 254 µm diameter titanium alloy wires. These structures were found to have a compressive strength of 40 ± 5 MPa that was controlled by plastic yield followed by buckling of the struts. The cellular structures have been brazed to titanium alloy face sheets to create sandwich panel structures that appear well suited for multifunctional applications up to 420 °C.     

On the buckling of thin tensioned sheets with cracks and slots

The problem of local buckling in tensioned sheets with holes is discussed in relation to its effect on fracture and fatigue characteristics. The results of an experimental investigation designed to determine the tensile buckling stress are presented. The results indicate that for the range of the parameters investigated, the sheet thickness to hole length ratio and a nondimensional hole shape parameter are the dominant geometric variables. It is shown that the results obtained in the investigation described and the results obtained by other investigators can be described by a single formula.

The physical significance of local buckling is discussed and particular emphasis is placed on the importance of accounting for buckling in residual strength analyses of thin cracked sheets. Recommendations are made for the standardization of the buckling stress determination in terms of its relationship to the effect of middle-surface stretching due to the bending. Finally, the influence of the buckling process on plane stress fracture toughness values, K_c, obtained from center cracked sheet specimens is discussed.     

钢梁腹板弹塑性屈曲强度的试验研究

对工字钢梁腹板在弯曲应力作用下的弹塑性屈曲承载能力进行了试验研究,并与理论计算结果进行了对比分析,同时,研究了纵向加劲肋对腹板屈曲系数的影响。提出了腹板高厚比的合理取值,对现行国家标准《钢结构设计规范》(GBJ17)的有关条款进行了讨论。     

Characterization of in‐plane load bearing of a honeycomb paperboard

The in‐plane bearing capacity of the face layer and core layer of a honeycomb paperboard is limited and unstable. However, a combination of the face layer and core layer of the honeycomb paperboard protects cardboard from small‐load buckling instability and provides sufficient stiffness and bearing strength. In the study, the platform theory models of the machine direction and cross direction are established based on plastic deformation, plastic energy dissipation, and the energy conservation theory. Additionally, the marginal pressure strength in the machine direction and cross direction are deduced by combining the practical application of the honeycomb paperboard. A comparison of theoretical and experimental data indicates that the two are in good agreement. Therefore, the theoretical results of the study provide a theoretical basis for the scientific and reasonable selection of important parameters of honeycomb paperboards with different strength requirements.     

Buckling behavior of fiber reinforced plastic–metal hybrid-composite beam

It is known that the buckling is characterized by a sudden failure of a structural member subjected to high compressive load. In this study, the buckling behavior of the aluminum tubular beam (ATB) was analyzed using finite element (FE) method, and the reinforcing arrangements as well as its combinations were decided for the composite beams based on the FE results. Buckling and bending behaviors of thin-walled ATBs with internal cast polyamide (PA6) and external glass and carbon fiber reinforcement polymers (GFRPs and CFRPs) were investigated systematically. Experimental studies showed that the 219% increase in buckling load and 661% in bending load were obtained with reinforcements. The use of plastics and metal together as a reinforced structure yields better mechanical performance properties such as high resistance to buckling and bending loads, dimensional stability and high energy absorption capacity, including weight reduction. While the thin-walled metallic component provides required strength and stiffness, the plastic component provides the support necessary to prevent premature buckling without adding significant weight to the structure. It is thought that the combination of these materials will offer a promising new focus of attention for designers seeking more appropriate composite beams with high buckling loads beside light weight. The developed plastic–metal hybrid-composite structure is promising especially for critical parts serving as a support member of vehicles for which light weight is a critical design consideration.     

The Gibson-Ashby model for additively manufactured metal lattice materials: Its theoretical basis,limitations and new insights from remedies

The Gibson-Ashby (G-A) model has been instrumental in the design of additively manufactured (AM-ed) metal lattice materials or mechanical metamaterials. The first part of this work reviews the proposition and formulation of the G-A model and emphasizes that the G-A model is only applicable to low-density lattice materials with strut length-to-diameter ratios greater than 5. The second part evaluates the applicability of the G-A model to AM-ed metal lattice materials and reveals the fundamental disconnections between them. The third part assesses the deformation mechanisms of AM-ed metal lattices in relation to their strut length-to-diameter ratios and identifies that AM-ed metal lattices deform by concurrent bending, stretching, and shear, rather than just stretching or bending considered by the G-A model. Consequently, mechanical property models coupling stretching, bending and shear deformation mechanisms are developed for various lattice materials, which show high congruence with experimental data. The last part discusses new insights obtained from these remedies into the design of strong and stiff metal lattices. In particular, we recommend that the use of inclined struts be avoided.     

Application of Fracture Mechanics Concepts to Hierarchical Biomechanics of Bone and Bone-like Materials

Fracture mechanics concepts are applied to gain some understanding of the hierarchical nanocomposite structures of hard biological tissues such as bone, tooth and shells. At the most elementary level of structural hierarchy, bone and bone-like materials exhibit a generic structure on the nanometer length scale consisting of hard mineral platelets arranged in a parallel staggered pattern in a soft protein matrix. The discussions in this paper are organized around the following questions: (1) The length scale question: why is nanoscale important to biological materials? (2) The stiffness question: how does nature create a stiff composite containing a high volume fraction of a soft material? (3) The toughness question: how does nature build a tough composite containing a high volume fraction of a brittle material? (4) The strength question: how does nature balance the widely different strengths of protein and mineral? (5) The optimization question: Can the generic nanostructure of bone and bone-like materials be understood from a structural optimization point of view? If so, what is being optimized? What is the objective function? (6) The buckling question: how does nature prevent the slender mineral platelets in bone from buckling under compression? (7) The hierarchy question: why does nature always design hierarchical structures? What is the role of structural hierarchy? A complete analysis of these questions taking into account the full biological complexities is far beyond the scope of this paper. The intention here is only to illustrate some of the basic mechanical design principles of bone-like materials using simple analytical and numerical models. With this objective in mind, the length scale question is addressed based on the principle of flaw tolerance which, in analogy with related concepts in fracture mechanics, indicates that the nanometer size makes the normally brittle mineral crystals insensitive to cracks-like flaws. Below a critical size on the nanometer length scale, the mineral crystals fail no longer by propagation of pre-existing cracks, but by uniform rupture near their limiting strength. The robust design of bone-like materials against brittle fracture provides an interesting analogy between Darwinian competition for survivability and engineering design for notch insensitivity. The follow-up analysis with respect to the questions on stiffness, strength, toughness, stability and optimization of the biological nanostructure provides further insights into the basic design principles of bone and bone-like materials. The staggered nanostructure is shown to be an optimized structure with the hard mineral crystals providing structural rigidity and the soft protein matrix dissipating fracture energy. Finally, the question on structural hierarchy is discussed via a model hierarchical material consisting of multiple levels of self-similar composite structures mimicking the nanostructure of bone. We show that the resulting “fractal bone”, a model hierarchical material with different properties at different length scales, can be designed to tolerate crack-like flaws of multiple length scales.     

Circumferential stiffness tailoring of general cross section cylinders for maximum buckling load with strength constraints

Stiffness tailoring of laminated composite structures using steered fibre tows is a design method that maximally uses the directional properties of composite materials. Cylindrical structures usually have circular cross sections while some application, geometric or aerodynamic requirements can necessitate other cross sections, e.g. elliptical. Circumferential tailoring can increase the buckling load of thin cylinders by compensating for non-uniform sectional loading such as bending and/or varying radius of curvature in general cylinders. Here, strength constraints are considered in maximum buckling load design, to ensure that the failure load is greater than the buckling load. A two-step optimisation framework is used to separate the theoretical and manufacturing issues in design. A computationally cheap semi-analytical finite difference method is used to solve the linear static and buckling problems. Conservative failure envelopes based on Tsai-Wu failure criterion are used for strength evaluation. To avoid repetitive analyses, successive convex approximation method is used. For demonstration, circumferential tailoring framework is applied to a circular cylinder under bending and an elliptical cylinder under axial compression. The improvements in buckling capacity of variable over constant stiffness designs are shown and verified using nonlinear buckling analysis in the commercial FEM software Abaqus^TM, and the mechanisms of improvements are investigated.     

Closed-cell Al alloy composite foams: Production and characterization

Foamy Al alloy SiCp composites of different densities ranging from 0.4 to 0.7 g/cm³ were manufactured by melt-foaming process, which consisted of direct CaCO₃ addition into the molten A356 aluminum bath. Mechanical properties and morphological observations indicated that the three-stage deformation mechanism of typical cellular foams is dominant in the produced A356 aluminum foams. Middle-stage stress plateau shrinkage plus compressive strength and bending stress enhancements were observed in denser foams. With the same Al/SiCp ratio, energy absorption ability and plastic collapse strength of the closed-cell foams were increased with the foam density. Doubling cell-face bending effects resulted in larger compressive than bending strengths in the closed-cell foams; while stiffness lowering was due to the cell-face stretching conditions.     

Glulam beams reinforced with FRP externally-bonded: theoretical and experimental evaluation

The glued- laminated lumber (glulam) technique is an efficient process for the rational use of wood. Fiber-reinforced polymer (FRPs) associated with glulam beams provide significant improvements in strength and stiffness and alter the failure mode of these structural elements. In this context, this paper presents guidance for glulam beam production, an experimental analysis of glulam beams made of Pinus caribea var. hondurensis species without and with externally-bonded FRP and theoretical models to evaluate reinforced glulam beams (bending strength and stiffness). Concerning the bending strength of the beams, this paper aims only to analyze the limit state of ultimate strength in compression and tension. A specific disposal was used in order to avoid lateral buckling, once the tested beams have a higher ratio height-to-width. The results indicate the need of production control so as to guarantee a higher efficiency of the glulam beams. The FRP introduced in the tensile section of glulam beams resulted in improvements on their bending strength and stiffness due to the reinforcement thickness increase. During the beams testing, two failure stages were observed. The first was a tensile failure on the sheet positioned under the reinforcement layer, while the second occurred as a result of a preliminary compression yielding on the upper side of the lumber, followed by both a shear failure on the fiber-lumber interface and a tensile failure in wood. The model shows a good correlation between the experimental and estimated results.     

Strengthening RC beams with composite fiber cement plate reinforced by prestressed FRP rods: Experimental and numerical analysis

This paper deals with the development of a new strengthening system for reinforced concrete beams with externally-bonded plate made of composite fiber cement reinforced by rebars made of fiber-reinforced plastic (FRP) [1]. The proposed strengthening material involves the preloading of FRP rod before mortar casting. The paper presents experimental and numerical analysis carried out on many large-scale beams strengthened by well-known reinforcement techniques, such as externally bonded Carbon Fiber-Reinforced Plastic (CFRP) plate and the Near Surface Mounted (NSM) technique, which are compared to the proposed new strengthening material through four-point bending tests. Results are analyzed with regard to the load-displacement curve, bending stiffness, cracking load, yield strength and failure load. The developed numerical model is in agreement with the experimental results. It clearly shows the effects of prestressed FRP rod on cracking mechanisms and internal strength distribution in the analyzed beams.     

Mechanical property of lattice truss material in sandwich panel including strut flexural deformation

Lattice truss materials are usually assumed to be stretching dominated neglecting the bending resistance of struts. In this paper, bending resistance of struts is considered for lattice truss sandwich panels. The mechanical behaviors are not only decided by the relative density of the lattice and the strut inclination, but also the slenderness ratio of the strut. For stout and hierarchical struts, the slenderness ratio turns to smaller, and the shear force and the bending moment are comparable to the strut axial force. Compared with the stretching dominated theory, the stiffness of the lattice material should be improved while the strength reduced, which has been proved to be more consistent with experimental results.     

Shear buckling in the core of a corrugated board structure

In some situations, a corrugated board package can experience loading of such a kind so that the corrugated core, or as it is most often referred to, the fluting, is loaded in transverse shear. This might cause the fluting to collapse and through this, cause a decrease in the bending stiffness. In this paper, an exact solution for the elastic instability of an infinite linear elastic strip with an initial curvature and loaded in pure in-plane shear is given. The solution is a modification of an existing solution for an isotropic strip. To experimentally investigate the accuracy of the model, a special device has been developed in which paper strips are loaded in pure in-plane shear to observe the buckling behavior. According to the experiments performed, the model seems to quantitatively well capture the main buckling behavior and lends some confidence to the theory. With use of the model it is easy to judge which deformation process most likely will occur, shear buckling or plastic deformation, and thereby allows one to structurally optimize the geometric ratio, i.e. the ratio between thickness and height of the fluting, when designing the corrugated core structure. Finally, it is illustrated that going below a certain critical thickness of the fluting may cause the structural strength of the board panel to decrease drastically.     

基于拟力法的钢支撑非线性滞回行为模拟

钢支撑在轴力作用下会同时发生材料非线性和几何非线性,复杂的力与变形关系是数值模拟过程中的重点与难点。该文基于拟力法的基本理论,提出了支撑非线性滞回行为的计算模型,通过塑性转动铰来模拟由屈曲行为引起的塑性弯曲变形;通过滑动铰来模拟由拉伸屈服和增长效应产生的轴向塑性伸长行为,模型中计及了弹性弯曲变形本身的几何非线性行为。该模型物理意义简单、力学行为明确,在模拟支撑非线性滞回行为的过程中保持初始刚度不变,塑性铰的变形可直观地衡量支撑的屈曲程度。数值模拟与试验结果对比验证了该方法的精确性与适用性。将该模型应用于某钢框架-支撑结构地震反应分析中,计算结果表明:该方法可以模拟支撑在复杂荷载作用下的非线性行为,具备拟力法所特有的精确、高效及稳定等优点。     

Delamination and kink-band failure of pultruded GFRP laminates under elevated temperatures and compression

Compression experiments were conducted on slender glass fiber-reinforced polymer (GFRP) laminates at different temperatures in the elevated range. Experimental buckling loads, lateral second-order deformations, and shear strength decreased with increasing temperature until stable values were reached at a much lower level in the leathery material state. The resin-dominated bending stiffness decreased at a higher rate than the fiber-dominated compressive stiffness. Global buckling followed by a delamination failure during the post-buckling process was observed for temperatures below 180 °C, while pre-buckling kink-band failure occurred when the temperature increased to 220 °C. Recently proposed thermomechanical models were further validated and enabled the changing failure mode and associated Tresca and kink-band shear stress and strength conditions to be modeled.     

Influence of the prebuckling stress-field on the critical loads of inhomogeneous composite laminates

The paper studies the uniaxial buckling behavior of composite laminates in which preselected variations of fiber spacing in the constituent laminae are adopted. Such laminates are referred to as inhomogeneous laminates because of the variable elastic stiffness along the coordinate axes. A non-uniform prebuckling stress state observed even under constant uniaxial compression has a pronounced influence on the buckling behaviour of an inhomogeneous laminate. A procedure is summarized for computing the critical load of a laminate using the Ritz method which exploits an analogy between the bending and stretching formulations and utilizes Gram-Schmidt orthogonal polynomials. The paper illustrates that the variation in fiber spacing is an innovative way of increasing the critical load for a prescribed amount of fiber and highlights its remarkable sensitivity to the nature of fiber spacing, in-plane and out-of-plane boundary conditions, fiber type and the aspect ratio of the laminate.     

考虑柱纵向钢筋屈曲特征的修正材料本构模型

纵筋屈曲会加速钢筋混凝土（RC）柱峰值后承载力退化，在钢筋的材料本构关系中合理地考虑屈曲效应是RC柱的有限元模型可信的基础之一。Gomes等提出的屈曲钢筋材料本构模型（G-A模型）力学概念清楚，但两个基本假定存在明显误差。在OpenSees平台上，采用基于纤维截面的集中塑性铰非线性梁柱单元对24个钢筋试件的屈曲受力性能循环加载试验进行模拟。基于有限元计算结果，对G-A模型采用的全截面塑性弯矩M_p、忽略杆件轴向变形的几何关系进行了误差分析。通过回归分析，建立了修正G-A模型。研究结果表明，屈曲钢筋试件关键截面的应力分布与G-A模型的全截面塑性基本假定差别较大，忽略轴向变形影响会导致屈曲钢筋跨中侧向位移计算结果存在误差。原始G-A模型的模拟效果较差，修正G-A模型对全截面塑性弯矩、几何关系均进行改进，其计算精度明显提高。     

Fabrication and Mechanical Testing of Ultralight Folded Lattice-Core Sandwich Cylinders

In this research, two novel folded lattice-core sandwich cylinders were designed, manufactured, and tested. The lattice core has periodic zigzag corrugations, whose ridges and valleys are directed axially or circumferentially. Free vibration and axial compression experiments were performed to reveal the fundamental frequency, free vibration modes, bearing capacity, and failure mode of the cylinder. A folded lattice core effectively restricts local buckling by reducing the dimension of the local skin periodic cell, and improves the global buckling resistance by enhancing the shear stiffness of the sandwich core. The cylinders fail at the mode of material failure and possess excellent load-carrying capacity. An axially directed folded sandwich cylinder has greater load-carrying capacity, while a circumferentially directed folded sandwich cylinder has higher fundamental frequencies. These two types of folded lattices provide a selection for engineers when designing a sandwich cylinder requiring strength or vibration. This research also presents a feasible way to fabricate a large-dimensional folded structure and promote its engineering application.