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.     

复合材料货舱地板立柱压溃响应试验

复合材料已经在民用飞机结构上得到广泛应用,并逐渐应用到主承力结构中,复合材料的脆性特点给飞机的适坠性设计和评估提出了新的挑战。复合材料机身货舱地板支撑立柱作为坠撞过程中的重要吸能元件,对机身结构抗坠撞性能有重要影响。复合材料货舱地板支撑立柱在压溃失效模式下吸收的能量明显多于整体弯曲失效模式。根据民用飞机复合材料货舱地板立柱的设计需求,对不同试件触发模式、高度、截面形式、截面面积等设计参数变化的T700GC碳纤维/环氧树脂复合材料立柱开展准静态和动态压溃试验,得到立柱吸能特性的关键影响参数和设计因子。      

纵向变厚度(LP)矩形钢板弹性屈曲系数的理论分析

纵向变厚度(LP)钢板因适应现代化建筑超高层及大跨度的发展使用需求,将广泛应用于工程结构中。因LP钢板几何形状的特殊性,其局部屈曲变形更容易发生在靠近薄端的位置,并且钢板局部稳定性能与相同受力状态下的等厚度钢板差异较大,需要进行深入研究。基于能量原理,采用Galerkin和Rayleigh-Ritz法(GRM),对单向均匀受压荷载作用下四种不同边界条件下的矩形LP钢板的弹性屈曲系数的计算公式进行了理论推导,并采用ANSYS有限元软件验证了公式的正确性。最后得到了不同厚度放大系数下,四种边界条件下的矩形钢板的弹性屈曲系数与钢板长宽比的关系曲线图,进一步为LP钢板的工程应用提供理论指导和设计依据。     

地震作用下防屈曲支撑减震结构附加有效阻尼比计算及变化规律研究

基于《建筑消能减震技术规程》(JGJ 279-2013)的附加有效阻尼比计算方法,推导防屈曲支撑(Buckling-Restrained Brace, BRB)减震结构等效单自由度体系的附加有效阻尼比计算式,分析主体结构处于不同工作阶段附加有效阻尼比变化规律,并用自由振动衰减法验证其变化规律的正确性。结果表明,主体结构弹性时,附加有效阻尼比随结构变形增加先增大后减小;主体结构塑性时,BRB附加给结构的有效阻尼比与结构屈服后刚度有关。讨论阻尼器型BRB(记为第Ⅲ类)设计原则,并分析结构第一阶段抗震设计时附加有效阻尼比的取值原则。     

成层式铝蜂窝夹芯结构冲击响应试验研究

以牺牲层设计为背景,提出一种成层式铝蜂窝夹芯结构。通过两种能级的落锤冲击试验,得到不同组合试件的局部冲击响应结果。根据能量吸收、荷载峰值、冲头位移和背板挠度的对比分析,得出以下结论:结构在相对较低能级(17~83J)的冲击作用下,除了永久塑性变形,也伴随着一定的弹性变形;同时,在芯层质量相同的前提下,可优先选择胞元较小、高度较低的蜂窝作为单层结构的芯层;全贯穿临界值应当介于83~119J之间,在设计牺牲层时,局部冲击的极限能量设计值应当低于该临界值;芯层的相对密度对抗局部冲击性能的影响较为明显;根据牺牲层的设计标准,在本文的局部冲击试验研究范围内,AB、BA、ABA型结构在综合指标上具有相对优势。研究结果可为成层式铝蜂窝夹芯结构在防护工程中的应用提供参考。     

Progress in braided composite tube crush simulation

The high Specific Energy Absorption (SEA) of composite tubular structures makes them attractive candidates in energy absorbing structural applications such as front rails in vehicles. To incorporate primary composite components in vehicle structures requires numerical simulation tools that can predict the structural performance of the vehicle under various loading conditions including crashworthiness. In previous studies, axial crush simulations of braided composite tubes tended to generate global buckling, which are inconsistent with the steady crush behavior observed in experiments. It was found that the constitutive models based on the continuum damage mechanics (CDM) framework are inadequate to represent the unloading response of damaged composites. In axial crush experiments, braided composite tubes form multiple continuous crush fronds. Local unloading occurs when material moving out of the crush front becomes part of the crush frond. Improper representation of the material unloading response affects the computed total energy absorption of the structure. To address this issue, an analog model was developed to describe the unloading path of compressively damaged composites. This approach was implemented in CODAM, as a user defined composite CDM model for the explicit finite element code LS-DYNA^®. The improved CODAM model results in a significantly improved prediction of the tube crush.     

Lightweight structure design for wind energy by integrating nanostructured materials

Wind power develops very fast nowadays with high expectation. Although at the mean time, the use of taller towers, however, smacks head-on into the issue of transportability. The engineering base and computational tools have to be developed to match machine size and volume. Consequently the research on the light weight structures of tower is carrying out in the main countries which are actively developing wind energy. This paper reports a new design scheme of light weight structure for wind turbine tower. This design scheme is based on the integration of the nanostructured materials produced by the Surface Mechanical Attrition Treatment (SMAT) process. The objective of this study is to accomplish the weight reduction by optimizing the wall thickness of the tapered tubular structure. The basic methods include the identification of the critical zones and the distribution of the high strength materials according to different necessities. The equivalent strength or stiffness design method and the high strength material properties after SMAT process are combined together. Bending and buckling are two main kinds of static loads concerned in consideration. The study results reveal that there is still enough margin for weight reduction in the traditional wind turbine tower design.     

Computational modelling of irregular open‐cell foam behaviour under impact loading

Cellular structures represent an important class of engineering materials. Typical representative of such structures are metallic foams, which are being increasingly used in many advanced engineering applications due to their low specific weight, appropriate mechanical properties and excellent energy absorption capacity. For optimal design of cellular structures it is necessary to develop proper computational models for use in computational simulations of their behaviour under impact loading. The paper studies the effects of open‐cell metallic foam irregularity on deformation behaviour and impact energy absorption during impact loading by means of parametric computational simulations, using the lattice‐type modelling of open‐cell material structure. The 3D Voronoi technique is used for the reproduction of real, irregular open‐cell structure of metallic foams. The method uses as a reference a regular mesh structure and utilises an irregularity parameter to reproduce the irregularity of real open‐cell structure. A smoothing technique is introduced to assure proper stability and accuracy of explicit dynamic simulations using the produced lattice models. The effects of the smoothing technique were determined by comparative simulations of smoothed and unsmoothed lattices subjected to dynamic loading.     

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.     

Buckling Analysis of Laminated Composite Plates Using Higher Order Semi—Analytical Finite Strip Method

Rectangular plates made of laminated composite material because of the advantageously high strength and stiffness to weight ratio are used frequently as structural component in various branches of engineering, chief of which are aerospace and marine engineering. Design concepts of these plates that lead to the increase in the buckling load can directly lower the structural cost and/or weight. The finite strip method is one of a number of procedures which can be used to solve the buckling problem of plate structures. In the present work the main concern is with the buckling behavior of plates with simply supported ends subjected to uni-axial pure compression loads. The solution is sought by implementing the higher order semi-analytical finite strip method which incorporates additional degrees of freedom for each nodal line by using Reddy’s higher order plate theory. Therefore the current method is more universal in dealing with different plate thicknesses. In addition, in this semi-analytical finite strip method, all the displacements are postulated by the appropriate harmonic shape functions in the longitudinal direction and polynomial interpolation functions in the transverse direction. The solution is based on the concept of principle of minimum potential energy and an eigen-value analysis is subsequently carried out. From the presented results it can be concluded that the higher order semi-analytical finite strip method is very reliable for the preliminary design of composite plates especially in the case of buckling analysis of relatively thick plates.     

“圆板─扁圆锥壳─圆环板”组合结构的弹性突跳分析

本文按非线性大挠度弹性屈曲理论对广泛应用于工程中的“圆板─扁圆锥壳─圆环板”组合结构的弹性突跳现象进行了分析，并对典型算例用积分法与MWR－CM的伽辽金法相结合的方法进行了数值计算，结果表明了几何参数对弹性突跳的影响。本文工作可为工程应用设计提供一定的依据。     

“圆板─扁圆锥壳─圆环板”组合结构的弹性突跳分析

本文按非线性大挠度弹性屈曲理论对广泛应用于工程中的“圆板─扁圆锥壳─圆环板”组合结构的弹性突跳现象进行了分析，并对典型算例用积分法与MWR－CM的伽辽金法相结合的方法进行了数值计算，结果表明了几何参数对弹性突跳的影响。本文工作可为工程应用设计提供一定的依据。     

Advanced composite sandwich structure design for energy absorption applications: Blast protection and crashworthiness

This paper describes an experimental investigation on the response of composite sandwich structures with tubular inserts to quasi-static compression. The performance parameters, namely the peak load, absorbed crash energy, specific energy absorption; average crushing load and crush force efficiency were evaluated. The composite sandwich specimens were fabricated from glass fiber, polystyrene foam and epoxy resin. The primary mode of failure observed was progressive crushing with the composites exhibiting high energy absorption capabilities and high crushes force efficiency. The mechanism of progressive crushing of the sandwich structures and its relation to the energy absorption capabilities was deliberated. Furthermore, a statistical analysis was performed to investigate the effects of the design variables and also to determine if there were interactions between these variables. Such information is vital in the design of polymer composite sandwich structures as energy absorbers.     

A NEW CONCEPT OF OPTIMIZATION FOR POSTBUCKLING BEHAVIOUR

In this paper geometrically nonlinear structures are optimized against instability. The postbuckling analysis performed for structures optimally designed for only buckling constraints shows that in many cases their behaviour after buckling is unstable. That is a weakness of the design and therefore, the alternative design philosophy is proposed, in which the postbuckling analysis is implemented directly into the formulation of optimization problem. As the result the modified optimal structure is created, for which previously unstable behaviour becomes stable. The effect of modification of postbuckling behaviour in most of the known cases has been obtained by changing sizing variables. In this paper a new approach is proposed, namely stabilization of the postbuckling path is obtained by application of additional forces acting on the optimized element. Numerical results are presented for the design of finite-degree-of-freedom systems that model the behaviour of real elastic frame and shell structures.     

Energy absorption of an axially crushed square tube with a buckling initiator

Axially crushed thin-walled square tubes have been widely used as energy absorbers because of their high specific energy absorption capacity and long stroke. However, they render extremely high initial peak forces which may cause serious injury or damage to the people or structures being protected. This paper proposes a novel idea that by installing a buckling initiator near the impact end which is composed of a pre-hit column and pulling strips, the initial peak force of the square tube could be greatly reduced while its deformation mode and excellent energy absorption are retained. Both experimental and numerical investigations are conducted on aluminum alloy square tubes. The peak force, mean force and half-length of a fold of the tested specimens are examined. The results show that the mean crushing force and deformation mode are not affected by the buckling initiator, while the reduction of the peak force strongly depends on the pre-hit height. It is also found that the buckling initiator can ensure the deformation more stable and uniform. Finally, a simplified analytical model is developed to study the relationship between the reduction of the peak force and the geometric imperfections; and the model can successfully predict the effectiveness of the buckling initiator.     

不同截面梁构件的刚度和稳定性优化设计

本文运用有限元分析与优化设计软件JIFEX，对五种常用截面梁结构的尺寸和形状进行了抗剪、抗弯、抗扭的刚度优化设计和在轴力、剪力作用下的结构稳定性优化设计。通过对优化设计的计算结果分析，得到了对工程设计有意义的若干结论。然后通过飞机结构中一种波形梁构件的优化，进一步讨论了波形梁的波数对结构稳定性和刚度的影响。     

Teaching energy methods in a final year course on mechanics of materials

Now that computer power is so readily available, engineers may contemplate design models of far greater sophistication than previously. When a design analysis task involves stress and deformation analysis, the energy (or variational) principles of mechanics provide such a powerful methodology for the formulation of complex models that it is important for such topics to be introduced to undergraduates. In this paper, the structure and underlying philosophy of a one term package suitable for final year mechanical engineering students is discussed.     

Crushing of axially compressed steel tubes filled with aluminium foam

Summary This study, with the emphasis on experiments, investigates the applicability of aluminium foam as filler material in tubes made of mild steel having square or circular cross sections, which are crushed axially at low loading velocities. In addition to the experiments finite element studies are performed to simulate the crushing behaviour of the tested square tubes, were a crushable foam material model is shown to be suitable for describing the inelastic response of aluminium foam with respect to the considered problems. The experimental results for the square tubes reveal efficiency improvements with respect to energy absorption of up to 60%, resulting from changed buckling modes of the tubes and energy dissipation during the compression of the foam material itself. The principal features as well as the changes of the crushing process due to filling can also be studied by the numerical simulations. A global failure mechanism due to a high foam density can be observed for filled circular tubes. Aluminium foam is shown to be a suitable material for filling thin-walled tubular steel structures, holding the potential of enhancing the energy absorption capacity considerably, provided the plastic buckling remains characterized by local modes.Dedicated to Prof. Dr. Dr. h. c. Franz Ziegler on the occasion of his 60th birthday     

泡沫铝填充薄壁铝合金多胞构件与单胞构件吸能性能研究

为研究泡沫铝填充薄壁铝合金多胞结构与单胞结构的吸能能力,该文基于有限元软件LS-DYNA建立了泡沫铝填充薄壁铝合金多胞结构与单胞结构的数值仿真。对经典薄壁圆管试验及泡沫铝填充薄壁圆管试验进行了数值模拟,分析表明该数值模型能够较好的模拟泡沫铝填充薄壁圆管在轴向冲击过程中的撞击力和变形发展。基于该模型对比研究了不同因素下泡沫铝填充薄壁铝合金多胞结构与单胞结构的轴向吸能特性,分析了其破坏模式、吸能机理和两者吸能效率。结果表明:在轴向冲击荷载作用下,泡沫铝填充薄壁铝合金的破坏模式为轴对称渐进折叠破坏模式,冲击力-位移曲线和变形模态图显示其变形过程分为3个阶段:弹性阶段、平台阶段和强化阶段。当冲击压缩距离为构件高度的80%时,7种不同参数下的泡沫铝填充薄壁铝合金多胞结构的吸能效率明显高于7种单胞结构,吸收的能量E和比吸能SEA都提高了50%以上,是一种优秀的吸能构件,可广泛应用于防护工程中。     

受径向约束细长水平管柱的正弦屈曲

本文首先利用能量变分原理得到了受径向约束水平受压管柱的屈曲微分方程及其应满足的端部边界条件。通过能量方法得到了管柱处于正弦屈曲状态时变形与载荷的关系,并证明了正弦屈曲中管柱的平衡状态是稳定的;求出了初始正弦屈曲的临界载荷和能保持正弦屈曲状态的最大载荷。屈曲微分方程的数值结果与理论解有良好的一致性。