Shear stability of metallic glasses

The effect of sample size on the shear deformation and compressive plasticity of different metallic glasses were investigated. The experimental results showed that the deformation and fracture behaviors of samples prepared from chemically identical Zr-, Ti-, Fe-, or Mg-based metallic glass ingots were strongly dependent on the sample size and machine stiffness, and a super-high compressive plasticity was achieved in the Zr-based metallic glasses with sample size of 1.0 mm in width. It is also found that the sample size can significantly influence the density of elastic energy dissipated in the shear band: with sample size decreasing and machine stiffness increasing, the density of the elastic energy dissipated in the shear band of metallic glasses is prominently decreased, thus the shear deformation turns to be more stable, resulting in the improvement of plasticity in ductile metallic glasses and the transition from fragmentation fracture to shear fracture in brittle metallic glasses. This finding is important for the potential applications of the present metallic glasses and for designing new metallic glasses with better mechanical properties.     

On the experimental investigation of the stiffness of clamped machined surfaces

Experiments were conducted to determine the effects of surface texture and normal load on the stiffness of joints formed by two machined surfaces. The experiments involved deformation measurements and examination of the contact surfaces of joints subjected to normal loads. It was shown that surface-displacement results can be affected by assuming that the compressive strain in the joint specimen is the same as in an equivalent solid piece. The elastic stiffness of joints were found to increase with an increase in the maximum nominal surface pressure. Results were also shown to illustrate that the elastic stiffness of a joint is affected by the loading history. Surface-profile measurements indicated that the topography of a joint surface changed with normal load, and that the deformation of a surface profile was related to the permanent change measured by extensometers placed across the joint interface.

     

Reprint of “Size dependence and orientation dependence of elastic properties of ZnO nanofilms” [In. J. Solids Struct. 45 (2008) 1730–1753]

The elastic properties of ZnO nanofilms with different film thickness, surface orientations and loading directions are investigated by using molecular mechanics (MM) method. The size dependence of elastic properties is relevant to both the film surface crystallographic orientation and loading direction. Both atomic structure analysis and energy calculation are employed to identify the mechanisms of the size-dependent elastic properties, under different loading directions and surface orientations. Upon small axial deformation, the relationship between intralayer and interlayer bond length variation and film elastic stiffness is established; it is found that the atomic layers with larger bond length variation have higher elastic stiffness. The strain energies of atomic layers of ZnO nanofilm and bulk are decoupled, from which the stiffness of film surface, intralayers, and interlayers are derived and compared with their bulk counterparts. The surface stiffness is found to be much lower than that of the interior layers and bulk counterpart, and with the decrease of film thickness, the residual tension-stiffened interior atomic layers are the main contributions of the increased elastic modulus of ZnO nanofilms.     

Size dependence and orientation dependence of elastic properties of ZnO nanofilms

The elastic properties of ZnO nanofilms with different film thickness, surface orientations and loading directions are investigated by using molecular mechanics (MM) method. The size dependence of elastic properties is relevant to both the film surface crystallographic orientation and loading direction. Both atomic structure analysis and energy calculation are employed to identify the mechanisms of the size-dependent elastic properties, under different loading directions and surface orientations. Upon small axial deformation, the relationship between intralayer and interlayer bond length variation and film elastic stiffness is established; it is found that the atomic layers with larger bond length variation have higher elastic stiffness. The strain energies of atomic layers of ZnO nanofilm and bulk are decoupled, from which the stiffness of film surface, intralayers, and interlayers are derived and compared with their bulk counterparts. The surface stiffness is found to be much lower than that of the interior layers and bulk counterpart, and with the decrease of film thickness, the residual tension-stiffened interior atomic layers are the main contributions of the increased elastic modulus of ZnO nanofilms.     

A study on the bending stiffness of single-walled carbon nanotubes and related issues

Single-walled carbon nanotubes (SWCNTs) are usually modeled as elastic tubes and their bending stiffness D is often related to their axial stretching modulus E (Young's modulus) as in mechanics of materials (i.e. D=EI where I is the moment of inertia of the tube). However, recent studies show that large discrepancies may exist when this relationship is used to predict Young's modulus of carbon nanotubes (CNTs) through bending dominated deformations. In the present paper, the bending stiffness of SWCNTs and some related issues are investigated by the combined use of the molecular-mechanics (M-M) model and the deformation mapping technique. Based on the analysis results, the contradictions mentioned above can be explained well. Furthermore, an analytical expression for the bending stiffness of SWCNTs is also presented. It shows that the bending stiffness of a SWCNT is approximately proportional to the cube of its radius which agrees well with the existing molecular dynamics simulation and continuum theory based results.     

Nonlinear low-velocity impact on damped and matrix-cracked hybrid laminated beams containing carbon nanotube reinforced composite layers

This paper investigates the low-velocity impact response of a shear deformable laminated beam which contains both carbon nanotube reinforced composite (CNTRC) layers and carbon fiber reinforced composite (CFRC) layers. The effect of matrix cracks is considered, and a refined self-consistent model is selected to describe the degraded stiffness caused by the damage. The beam including damping effects rests on a two-parameter elastic foundation in thermal environments. Based on a higher-order shear deformation theory and von Kármán nonlinear strain–displacement relationships, the motion equations of the beam and impactor are established and solved by means of a two-step perturbation approach. The material properties of both CFRC layers and CNTRC layers are assumed to be temperature-dependent. To assess engineering application of this hybrid structure, two conditions for outer CNTRC layers and outer CFRC layers are compared. Besides, the effects of the crack density, volume fraction of carbon nanotube, temperature variation, the foundation stiffness and damping on the nonlinear low-velocity impact behavior of hybrid laminated beams are also discussed in detail.

     

蜂窝芯层的等效弹性参数

反映蜂窝材料等效弹性参数的Gibson公式结果简单，便于应用然而由于对应于蜂窝壁板伸缩变形的刚度被忽略，导致蜂窝夹层结构数值分析时，芯层材料的弹性矩阵表现出不确定性本文重新考虑了蜂窝壁板的伸缩变形对面内刚度的影响，对Gibson公式进行了修正本本文结果不但克服了Gibson公式的缺陷，同时提出了考虑蜂窝芯层面内刚度的一种简化方案,该方案可以方便地应用于蜂窝夹层结构的计算。     

Some basic questions on mechanosensing in cell–substrate interaction

Cells constantly probe their surrounding microenvironment by pushing and pulling on the extracellular matrix (ECM). While it is widely accepted that cell induced traction forces at the cell–matrix interface play essential roles in cell signaling, cell migration and tissue morphogenesis, a number of puzzling questions remain with respect to mechanosensing in cell–substrate interactions. Here we show that these open questions can be addressed by modeling the cell–substrate system as a pre-strained elastic disk attached to an elastic substrate via molecular bonds at the interface. Based on this model, we establish analytical and numerical solutions for the displacement and stress fields in both cell and substrate, as well as traction forces at the cell–substrate interface. We show that the cell traction generally increases with distance away from the cell center and that the traction-distance relationship changes from linear on soft substrates to exponential on stiff substrates. These results indicate that cell adhesion and migration behaviors can be regulated by cell shape and substrate stiffness. Our analysis also reveals that the cell traction increases linearly with substrate stiffness on soft substrates but then levels off to a constant value on stiff substrates. This biphasic behavior in the dependence of cell traction on substrate stiffness immediately sheds light on an existing debate on whether cells sense mechanical force or deformation when interacting with their surroundings. Finally, it is shown that the cell induced deformation field decays exponentially with distance away from the cell. The characteristic length of this decay is comparable to the cell size and provides a quantitative measure of how far cells feel into the ECM.     

Effect of Compressive Straining on Nanoindentation Elastic Modulus of Trabecular Bone

Trabecular bone with its porous structure is an important compressive load bearing member. Different structural factors such as porosity, non-homogeneous deformation, varying trabeculae thickness, connectivity, and nanoscale (10 nm to 1 μm) to macroscale (~0.1 mm to 10 mm) composition hierarchy determine the failure properties of trabecular bone. While the above factors have important bearing on bone properties, an understanding of how the local nanoscale properties change at different macroscale compressive strain levels can be important to develop an understanding of how bone fails. In the present work, such analyses are performed on bovine femoral trabecular bone samples derived from a single animal. Analyses focus on measuring nanoindentation elastic moduli at three distinct levels of compressive strains in the bone samples: (1) when the samples are not loaded; (2) after the samples have been loaded to a strain level just before apparent yielding and the macroscale compression test is stopped; and (3) after the samples have been compressed to a strain level after apparent yielding and the macroscale compression test is stopped. Nanoindentation elastic modulus values are two orders of magnitude higher than the macroscale compressive elastic modulus values of all samples. A high variability in macroscale compressive elastic modulus values is observed because of porous architecture and small sample size. Nanoindentation elastic modulus values show a progressive reduction with increase in the extent of macroscale compressive deformation. Apparent yielding has a significant effect on this trend. The decrease in nanoindentation modulus value for all samples accelerates from approximately 20% before yielding to approximately 60% after yielding in comparison to the nanoindentation modulus values at 0% strain level. The level of variation in the predicted nanoindentation modulus values is the lowest for uncompressed samples (~16–18%). However, with increase in the extent of compression, the level of variation increases. It varied between 50% and 90% for the samples tested after yielding showing a widespread heterogeneity in local nanoscale structural order after apparent yielding. Scanning electron microscope (SEM) observations suggest that apparent yielding significantly destroys local nanoscale structural order. However, quantitative results suggest that a significant residual nanoscale stiffness varying from 5 GPa to 8 GPa among different samples still remains for possible repair facilitation.     

Compressive response and failure of braided textile composites: Part 2—computations

In this, the second part of a two part paper, results obtained by using the finite element (FE) method in conjunction with micromechanics to predict the effective elastic stiffness and strength of a carbon 2D triaxially braided composite (2DTBC), are presented. The 3D FE based micromechanics study was carried out on one representative unit cell (RUC) of the carbon 2DTBC (the “micromodel”). The FE models were first used to determine the macroscopic elastic orthotropic stiffnesses of the 2DTBC. The micromodel was deemed acceptable (in terms of the number of elements used in the mesh of the micromodel) if the elastic stiffnesses it displayed were within 5% of the elastic properties found experimentally. Subsequently, buckling eigenmodes were determined for the FE RUC under uniaxial and biaxial loading states, corresponding to the experimental investigation reported in part I of this two part paper. The lowest symmetric modes were identified and these mode shapes were used as imperfections to the FE model for a subsequent nonlinear response analysis using an arc-length method in conjunction with the ABAQUS commercial FE code. The magnitude of the imperfections was left as a parameter and its effect on the predicted response was quantified. The present micromechanics computational model provides a means to assess the compressive and compressive/tensile biaxial strength of the braided composites and its dependence on various microstructural parameters. It also serves as a tool to assess the most significant parameter that affects compressive strength.     

On the compressive strength of open-cell metal foams with Kelvin and random cell structures

Two families of finite element models of anisotropic, aluminum alloy, open-cell foams are developed and their predictions of elastic properties and compressive strength are evaluated by direct comparison to experimental results. In the first family of models, the foams are idealized as anisotropic Kelvin cells loaded in the <100> direction and in the second family more realistic models, based on Surface Evolver simulations of random soap froth with N³ cells are constructed. In both cases the ligaments are straight but have nonuniform cross sectional area distributions that resemble those of the foams tested. The ligaments are modeled as shear deformable beams with elasto-plastic material behavior. The calculated compressive response starts with a linearly elastic regime. At higher stress levels, inelastic action causes a gradual reduction of the stiffness that eventually leads to a stress maximum, which represents the strength of the material. The periodicity of the Kelvin cell enables calculation of the compressive response up to the limit stress with just a single fully periodic characteristic cell. Beyond the limit stress, deformation localizes along the principal diagonals of the microstructure. Consequently beyond the limit stress the response is evaluated using finite size 3-D domains that allow the localization to develop. The random models consist of 3-D domains of 216, 512 or 1000 cells with periodicity conditions on the compressed ends but free on the sides. The compressive response is also characterized by a limit load instability but now the localization is disorganized resembling that observed in experiments. The foam elastic moduli and strengths obtained from both families of models are generally in very good agreement with the corresponding measurements. The random foam models yield 5–10% stiffer elastic moduli and slightly higher strengths than the Kelvin cell models. Necessary requirements for this high performance of the models are accurate representation of the material distribution in the ligaments and correct modeling of the nonlinear stress–strain response of the aluminum base material.     

考虑损伤的节理本构模型

本文在弹塑性损伤的理论框架内，讨论了节理等地质间断面的本构模型。这个模型能够反映节理面的损伤弱化，扩容和弹性刚度劣化等复杂特性。这个模型的另一优点是，塑性变形增量与屈服面是非正交的，但本构矩阵具有对称性。这种对称性在岩石力学的理论研究和数值分析中是至关紧要的。     

Thermal buckling and post-buckling of pinned–fixed Euler–Bernoulli beams on an elastic foundation

In this article, both thermal buckling and post-buckling of pinned–fixed beams resting on an elastic foundation are investigated. Based on the accurate geometrically non-linear theory for Euler–Bernoulli beams, considering both linear and non-linear elastic foundation effects, governing equations for large static deformations of the beam subjected to uniform temperature rise are derived. Due to the large deformation of the beam, the constraint forces of elastic foundation in both longitudinal and transverse directions are taken into account. The boundary value problem for the non-linear ordinary differential equations is solved effectively by using the shooting method. Characteristic curves of critical buckling temperature versus elastic foundation stiffness parameter corresponding to the first, the second, and the third buckling mode shapes are plotted. From the numerical results it can be found that the buckling load-elastic foundation stiffness curves have no intersection when the value of linear foundation stiffness parameter is less than 3000, which is different from the behaviors of symmetrically supported (pinned–pinned and fixed–fixed) beams. As we expect that the non-linear foundation stiffness parameter has no sharp influence on the critical buckling temperature and it has a slight effect on the post-buckling temperature compared with the linear one.     

Micromechanics and macromechanics of carbon nanotube-enhanced elastomers

The effects of carbon nanotubes on the mechanical behavior of elastomeric materials is investigated. The large deformation uniaxial tension and uniaxial compression stress-strain behaviors of a representative elastomer are first presented. This elastomer is then reinforced with multi-wall carbon nanotubes (MWNTs) and the influence of weight fraction of MWNTs on the large deformation behavior of the resulting composite is quantified. The initial stiffness and subsequent strain-induced stiffening at large strains are both found to increase with MWNT content. The MWNTs are also found to increase both the tensile strength and the tensile stretch at break. A systematic approach for reducing the experimental data to isolate the MWNT contribution to the strain energy of the composite is presented. A constitutive model for the large strain deformation behavior of MWNT-elastomer composites is then developed. The effects of carbon nanotubes are modeled via a constitutive element which tracks the stretching and rotation of a distribution of wavy carbon nanotubes. The MWNT strain energy contribution is due to the bending/unbending of the initial waviness and provides the increase in initial stiffness as well as the retention and further enhancement of the increase in stiffness with large strains. The model is shown to track the stretching and rotation of the CNTs with macroscopic strain as well as predict the dependence of the macroscopic stress-strain behavior on the MWNT content for both uniaxial tension and uniaxial compression.     

绳牵引并联机器人弹性变形对动平台位姿精度的影响Influence of elastic deformation on pose precision of moving platform for wire-driven parallel robot

针对六自由度绳牵引并联机器人在风洞试验中的应用,分析了牵引绳弹性变形对动平台位姿精度的影响,其实质是运动学正解问题。鉴于牵引绳只能受拉力的特点,以及风洞试验的目的,须考虑系统的刚度和绳拉力的优化。基于系统运动学和动力学方程,推导了系统刚度矩阵;以提高系统主方向刚度为目标函数,对绳拉力进行了动态优化分布,以求解弹性变形;采用L‐M数值方法进行运动学正解,量化分析了两种不同弹性模量的牵引绳对系统刚度的影响,以及弹性变形引起的动平台位姿误差。研究结果表明,以刚度增强为优化目标,有利于提高系统稳定性;采用弹性模量较大的牵引绳,可以有效提高系统的刚度,减小绳长变形引起的飞行器模型位姿误差,满足风洞试验的精度要求。上述结果可为后续机构的改善和系统高精度的力位混合控制提供依据和指导。     

T形短肢剪力墙静力性能有限元仿真分析

利用有限元分析软件ANSYS,首先采用其中三维实体单元SOLID65建立了T形短肢剪力墙有限元分析模型,从弹性到混凝土开裂直至破坏的全过程进行了仿真试验分析。分析了影响短肢剪力墙受力的几种因素:混凝土强度等级、配筋率、轴压比、墙肢截面高厚比对短肢剪力墙承载能力、变形能力及延性的影响,剖析了短肢剪力墙破坏过程及其原因。比较真实的反映了短肢剪力墙在轴压力和逐步加载侧向力共同作用下的响应。试验结果表明:增加混凝土等级和轴压比能提高试件的开裂、屈服和极限荷载,但应综合考虑其与变形能力、延性的关系。截面配筋率具有其特殊性,配筋率在1.4%¹.6%之间时试件的承载能力、变形能力及延性较好。墙肢截面高厚比是不稳定因素但在高厚比为6.5⁷.1时,延性及变形能力较强。     

DYNAMIC ANALYSIS OF FLEXIBLE BODY WITH DEFINITE MOVING ATTITUTE

The nonlinear dynamic control equation of a flexible multi-body system with definite moving attitude is discussed.The motion of the aircraft in space is regarded as known and the influence of the flexible structural members in the aircraft on the motion and attitude of the aircraft is analyzed.By means of a hypothetical mode,the defor- mation of flexible members is regarded as composed of the line element vibration in the axial direction of rectangular coordinates in space.According to Kane’s method in dy- namics,a dynamic equation is established,which contains the structural stiffness matrix that represents the elastic deformation and the geometric stiffness matrix that represents the nonlinear deformation of the deformed body.Through simplification the dynamic equation of the influence of the planar flexible body with a windsurfboard structure on the spacecraft motion is obtained.The numerical solution for this kind of equation can be realized by a computer.     

Effects of shear deformation on vibration of doublewalled carbon nanotubes embedded in an elastic medium

In this study, free vibration of simply supported multi-walled carbon nanotubes (CNTs) embedded in an elastic medium was investigated by using the generalized shear deformation-beam theory (GSDBT). The effects of surrounding elastic medium, which is considered as a spring, defined by the Winkler model, and van der Waals forces from adjacent nanotubes are taken into account. Third-order shear deformation (TOSD) theory is used to study free vibration of a multi-walled carbon nanotube embedded in an elastic medium. Unlike Timoshenko beam theory, TOSD theory satisfies zero traction boundary conditions on the upper and lower surface of the structures, so there is no need to use a shear correction factor. Free vibration frequencies and amplitude ratios were obtained for various sides to thickness ratios and elastic medium effects and results are compared with previous studies. The results showed that significant difference exist between TOSD and Euler beam theory. It is also interesting to note that, although frequency parameter is increasing by increasing stiffness of embedded medium, amplitude ratios are insensitive to stiffness of embedded elastic medium. Dedicated to the honorable memory of my beloved mother Fatma Aydogdu (Romania,1933-Tekirdag, August 7, 2007)     

PVC-FRP管混凝土柱组合抗压刚度理论分析

为研究PVC-FRP管混凝土柱的组合抗压刚度,应用弹性力学中的位移变分原理,对PVC-FRP管混凝土柱进行小变形下的弹性理论分析。考虑PVC-FRP管和核心混凝土径向位移和纵向应变协调,分别推导出PVCFRP管和核心混凝土的抗压刚度以及PVC-FRP管对核心混凝土套箍系数的理论计算公式。在此基础上,建立PVC-FRP管混凝土柱组合抗压刚度计算理论。分析CFRP条带体积含纤维率,混凝土泊松比以及混凝土强度等级等因素对PVC-FRP管混凝土柱组合抗压刚度的影响规律。理论计算结果与试验值吻合较好。