Crack buckling in soft gels under compression

Recent interest in designing soft gels with high fracture toughness has called for simple and robust methods to test fracture behavior. The conventional method of applying tension to a gel sample suffers from a difficulty of sample gripping. In this paper, we study a possible fracture mechanism of soft gels under uni-axial compression. We show that the surfaces of a pre-existing crack, oriented parallel to the loading axis, can buckle at a critical compressive stress. This buckling instability can open the crack surfaces and create highly concentrated stress fields near the crack tip, which can lead to crack growth. We show that the onset of crack buckling can be deduced by a dimensional argument com- bined with an analysis to determine the critical compression needed to induce surface instabilities of an elastic half space. The critical compression for buckling was verified for a neo-Hookean material model using finite element simulations.     

Asymptotic solutions for buckling delamination induced crack propagation in the thin film-compliant substrate system

In a thin film-substrate system in-plane compressive stress is commonly generated in the film due to thermal mismatch in operation or fabrication process. If the stress exceeds a critical value, part of the film may buckle out of plane along the defective interface. After buckling delamination, the interface crack at the ends may propagate. In the whole process, the compliance of the substrate compared with the film plays an important role. In this work, we study a circular film subject to compressive stress on an infinitely thick substrate. We study the effects of compliance of the substrate by modeling the system as a plate on an elastic foundation. The critical buckling condition is formulated. The asymptotic solutions of post-buckling deformation and the corresponding energy release rate of the interface crack are obtained with perturbation methods. The results show that the more compliant the substrate is, the easier for the film to buckle and easier for the interface crack to propagate after buckling.     

The delamination of a growing elastic sheet with adhesion

We study the onset of delamination blisters in a growing elastic sheet adhered to a flat stiff substrate. When the ends of the sheet are kept fixed, its growth causes residual stresses that lead to delamination. This instability can be viewed as a discontinuous buckling between the complete adhered solution and the buckled solution. We provide an analytic expression for the critical deformation at which the instability occurs. We show that the critical threshold scales with a single dimensionless parameter that comprises information from the geometry of the sheet, the mechanical parameters of material and the adhesive features of the substrate.     

Parametric studies of failure mechanisms in elastic EB-PVD thermal barrier coatings using FEM

Catastrophic failure of thermal barrier coatings (TBCs), usually occurs due to large scale buckling and spallation, primarily originating at the bond coat and TGO interface. Spallation in TBCs is preceded by a competition between buckling and interface delamination that is stimulated by the waviness of the interface. In the presence of thermal loading, the waviness is responsible for growth of interfacial delamination. In this paper, a finite element model of the two and three layer TBC’s is developed in the commercial code ANSYS to investigate the buckle and interface delamination mechanisms and develop a simplified parametric understanding of these mechanisms. The models for simulation are validated with analytical and experimental results. Parametric relations, in terms of geometric and material parameters representing constituents of the TBC, are developed in this paper for critical stresses and energies causing buckling and debonding initiated instabilities. Through these relations, critical parameters that control failure mechanics are identified for a fail-safe design space.     

Long-term non-linear behaviour and buckling of shallow concrete-filled steel tubular arches

This paper presents a theoretical analysis for the long-term non-linear elastic in-plane behaviour and buckling of shallow concrete-filled steel tubular (CFST) arches. It is known that an elastic shallow arch does not buckle under a load that is lower than the critical loads for its bifurcation or limit point buckling because its buckling equilibrium configuration cannot be achieved, and the arch is in a stable equilibrium state although its structural response may be quite non-linear under the load. However, for a CFST arch under a sustained load, the visco-elastic effects of creep and shrinkage of the concrete core produce significant long-term increases in the deformations and bending moments and subsequently lead to a time-dependent change of its equilibrium configuration. Accordingly, the bifurcation point and limit point of the time-dependent equilibrium path and the corresponding buckling loads of CFST arches also change with time. When the changing time-dependent bifurcation or limit point buckling load of a CFST arch becomes equal to the sustained load, the arch may buckle in a bifurcation mode or in a limit point mode in the time domain. A virtual work method is used in the paper to investigate bifurcation and limit point buckling of shallow circular CFST arches that are subjected to a sustained uniform radial load. The algebraically tractable age-adjusted effective modulus method is used to model the time-dependent behaviour of the concrete core, based on which solutions for the prebuckling structural life time corresponding to non-linear bifurcation and limit point buckling are derived.     

THERMOELASTIC VIBRATION OF FLUID-CONVEYING MICROTUBES EMBEDDED IN ELASTIC MEDIUMS

研究热环境中被弹性介质包围的微米输流管道的横向振动问题. 根据Hamilton 原理及非线性热弹性理论建立管道横向振动控制方程,并利用复模态法对其进行求解,得到了系统的固有频率和屈曲失稳临界流速,讨论了环境温度和一些重要系统参数对管道振动特性的影响. 研究结果表明:环境温度变化、管道和流体的微尺度效应、管道外径及弹性介质刚度对输流微管道固有频率和临界流速都有很大影响.     

The axisymmetric contraction–expansion: the role of extensional rheology on vortex growth dynamics and the enhanced pressure drop

The flow of a polystyrene Boger fluid through axisymmetric contraction–expansions having various contraction ratios (2≤β≤8) and varying degrees of re-entrant corner curvatures are studied experimentally over a large range of Deborah numbers. The ideal elastic fluid is dilute, monodisperse and well characterized in both shear and transient uniaxial extension. A large enhanced pressure drop above that of a Newtonian fluid is observed independent of contraction ratio and re-entrant corner curvature. Streak images, laser Doppler velocimetry (LDV) and digital particle image velocimetry (DPIV) are used to investigate the flow kinematics upstream of the contraction plane. LDV is used to measure velocity fluctuation in the mean flow field and to characterize a global elastic flow instability which occurs at large Deborah numbers. For a contraction ratio of β=2, a steady elastic lip vortex is observed while for contraction ratios of 4≤β≤8, no lip vortex is observed and a corner vortex is seen. Rounding the re-entrant corner leads to shifts in the onset of the flow transitions at larger Deborah numbers, but does not qualitatively change the overall structure of the flow field. We describe a simple rescaling of the deformation rate which incorporates the effects of lip curvature and allows measurements of vortex size, enhanced pressure drop and critical Deborah number for the onset of elastic instability to be collapsed onto master curves. Transient extensional rheology measurements are utilized to explain the significant differences in vortex growth pathways (i.e. elastic corner vortex versus lip vortex growth) observed between the polystyrene Boger fluids used in this research and polyisobutylene and polyacrylamide Boger fluids used in previous contraction flow experiments. We show that the role of contraction ratio on vortex growth dynamics can be rationalized by considering the dimensionless ratio of the elastic normal stress difference in steady shear flow to those in transient uniaxial extension. It appears that the differences in this normal stress ratio for different fluids at a given Deborah number arise from variations in solvent quality or excluded volume effects.     

Axial compression buckling of conical and cylindrical shells

Experiments on the axial compression buckling of high-quality epoxy cylindrical shells with imposed dimpletype defects are described. Additionally, a technique for the manufacture of high-quality epoxy conical shells which buckle at loads approaching the classical critical load is presented. For both types of shells, prebuckling deformations have been monitored optically. The sizes of defects determined from the optical examination when applied in the space-frame approach to shell buckling have led to predicted knock-down factors which are remarkably consistent with measured knock-down factors (i.e., the ratio of actual collapse to classical critical load).     

Effects of layer number and initial pressure on continuum-based buckling analysis of multi-walled carbon nanotubes accounting for van der Waals interaction

The structural instability of multi-walled carbon nanotubes (MWCNTs) has captured extensive attention due to the unique characteristic of extremely thin hollow cylinder structure. The previous studies usually focus on the buckling behavior without considering the effects of the wall number and initial pressure. In this paper, the axial buckling behavior of MWCNTs with the length-to-outermost radius ratio less than 20 is investigated within the framework of the Donnell shell theory. The governing equations for the infinitesimal buckling of MWCNTs are established, accounting for the van der Waals (vdW) interaction between layers. The effects of the wall number, initial pressure prior to buckling, and aspect ratio on the critical buckling mode, buckling load, and buckling strain are discussed, respectively. Specially, the four-walled and twenty-walled CNTs are studied in detail, indicating the fact that the buckling instability may occur in other layers besides the outermost layer. The obtained results extend the buckling analysis of the continuum-based model, and provide theoretical support for the application of CNTs.     

Propagating buckles in long confined cylindrical shells

In many practical engineering applications, relatively stiff, long, circular cavities are lined with more compliant liner shells. Pressure applied through the porous walls of the confining medium can cause buckling of the shells. Such buckling is usually local in nature and occurs at a section with the biggest geometric imperfection. The paper presents experimental evidence which demonstrates that, once such a shell has been locally dented, a buckle which propagates within the confines of the cavity can be initiated. Such a buckle has the potential of completely collapsing the liner. The lowest pressure at which this buckle will propagate is established experimentally through a parametric study of the problem. The phenomenon is found to be physically similar to the propagating buckle problem which can develop in offshore pipelines. A difference is that in the case of the confined shell, the instability is shown to have a strong geometric dependence and, as a result, it can be developed in the case of thin elastic as well as elasto-plastic shells.     

Small-scale effect on torsional buckling of multi-walled carbon nanotubes

The small-scale effect on the torsional buckling of multi-walled carbon nanotubes coupled with temperature change is investigated in this paper. A nonlocal multiple-shell model for the multi-walled carbon nanotubes surrounded an elastic medium under torsional and thermal loads is established, and then general solutions are obtained from the governing equations. The influence of the nonlocal effect on critical shear force and change in temperature is investigated. It is demonstrated that the critical shear force could be overestimated by the classical continuum theory and the nonlocal effect on critical buckling force decreases as the change in temperature increases at room or low temperature but increases as the change in temperature increases at higher temperature. Meanwhile, the effect of small size-scale is dependent on the buckling mode under different thermal environments. It is also shown that the innermost radius and the number of layer can affect the small-scale effect on critical change in temperature and buckling shear force. When the ratio of tube length and outmost radius are given, the critical shear force in each layer decreases and the nonlocal effect on the critical shear force becomes weaker as the innermost radius and the layer number increase.     

INVESTIGATION OF THE DYNAMIC BUCKLING OF DOUBLEWALLED CARBON NANOTUBE SUBJECTED TO AXIAL PERIODIC DISTURBING FORCES

IntroductionThediscoveryofthefirstcarbonnanotubes[1]hasattractedwideattentionandstimulatedextensivestudies[2 - 5 ].Thestudiesshowedthatthecarbonnanotubesexhibitsuperiormechanical,electronicandchemicalproperties.Onthemechanicalbehavior,thecarbonnanotubespossessexceptionallyhighstrength ,stiffnessandelasticmodulus.Theestimatemodulusofthecarbonnanotubemayreachashighas 1TPa.Itisthelargestofallknownmaterials.Thestrengthorstiffnessishigherthananyknownfiber[3].Thecarbonnanotubeareusedascompositemat…     

Buckling of yeast modeled as viscoelastic shells with transverse shearing

Yeast cells can be regarded as micron-sized and liquid-filled cylindrical shells. Owing to the rigid cell walls, yeast cells can bear compressive forces produced during the biotechnological process chain. However, when the compressive forces applied on the yeast go beyond a critical value, mechanical buckling will occur. Since the buckling of the yeast can change the networks in its cellular control, the experimental research of the buckling of the yeast has received considerable attention recently. In this paper, we apply a viscoelastic shell model to study the buckling of the yeast. Meanwhile, the turgor pressure in the yeast due to the internal liquid is taken into account as well. The governing equations are based on the first-order shear deformation theory. The critical axial compressive force in the phase space is obtained by the Laplace transformation, and the Bellman numerical inversion method is then applied to the analytical result to obtain the corresponding numerical results in the physical phase. The concepts of instantaneous critical buckling force, durable critical buckling force, and delay buckling are set up in this paper. And the effects of the transverse shear deformation and the turgor pressure on the buckling phenomena are also given. The numerical results show that the transverse shearing effect will decrease the instantaneous critical buckling force and the durable critical buckling force, while the turgor pressure will increase both of them.     

Torsional buckling of an elastic thick-walled tube made of rubber-like material

The elastic stability of a rubber-like, thick-walled tube which is subjected to finite torsional deformation is investigated both theoretically and experimentally. The analysis is based on the theory of finite elastic deformations, in cojunction with the method of small displacements superposed on large elastic deformations. The governing field equations are solved by a numerical scheme which determines the critical buckling torque and the associated buckling mode of the tube. The predicted results compare closely with the experimental measurements of the buckling of thick-walled silicone rubber tubes tested under finite twist.     

考虑范德华力曲率效应的双壁碳纳米管外压屈曲

针对双壁碳纳米管外压屈曲问题,研究了层间范德华力的曲率效应对临界外压的影响。应用弹性双层圆柱壳模型,考虑层间范德华力不仅与层间距有关而且与挠度曲率的变化有关,导出了外压屈曲临界压力解析公式。计算得出在不同半径、不同长细比下,外压屈曲临界压力的数值结果,并与经典壳的结果和忽略范德华力曲率效应的结果做了比较。结果显示,对于小半径的双壁碳纳米管曲率效应对外压屈曲有效明显的影响。     

冲击载荷作用下矩形薄板的弹性动力屈曲

为了研究冲击载荷作用下考虑应力波效应弹性矩形薄板的动力屈曲,根据动力屈曲发生瞬间的能量转换和守恒准则,导出板的屈曲控制方程和波阵面上的补充约束条件,真实的屈曲位移应同时满足控制方程和波阵面上的附加约束条件。满足上述条件,建立了该问题的完整数值解法,对屈曲过程中冲击载荷、屈曲模态和临界屈曲长度之间的关系进行研究,定量计算了横向惯性效应对提高薄板动力屈曲临界应力的贡献。研究表明:板的厚宽比一定时,临界屈曲长度随冲击载荷的增大而减小;由于屈曲时的横向惯性效应,应力波作用下薄板一阶临界力参数是相应边界板的静力失稳临界力参数的1.5倍;随着边界约束逐渐减弱,板临界力参数逐渐减小,动力特征参数逐渐增大。     

Mechanical properties of single-walled carbon nanotube bundles as bulk materials

Single-walled carbon nanotubes (SWNTs) in crystalline bundles may exhibit a transition in which the cross-sections of tubes turn from perfectly circular to hexagonal, depending upon the tube diameter and externally applied pressure, and this structural instability leads to an abrupt change in the bulk elastic properties of SWNT bundles. This paper presents a hybrid atom/continuum model to study the bulk elastic properties of SWNT bundles, and the predicted characteristics of this structural instability agree well with the experimental observations available in the literature. Linearized bulk elastic properties of SWNT bundles with respect to a stable configuration are transversely isotropic and hence can be characterized by five independent elastic moduli. A complete set of these five moduli is predicted for the first time. It is found that the deformability of tube cross-sections play a dominant role in characterizing the transverse moduli.     

DIVERGENCE INSTABILITY OF VARIABLE-ARC-LENGTH ELASTICA PIPES TRANSPORTING FLUID

A flexible elastic pipe transporting fluid is held by an elastic rotational spring at one end, while at the other end, a portion of the pipe may slide on a frictional support. Regardless of the gravity loads, when the internal flow velocity is higher than the critical velocity, large displacements of static equilibrium and divergence instability can be induced. This problem is highly nonlinear. Based on the inextensible elastica theory, it is solved herein via the use of elliptic integrals and the shooting method. Unlike buckling with stable branching of a simply supported elastica pipe with constant length, the variable arc-length elastica pipe buckles with unstable branching. The friction at the support has an influence in shifting the critical locus over the branching point. Alteration of the flow history causes jumping between equilibrium paths due to abrupt changes of direction of the support friction. The elastic rotational restraint brings about unsymmetrical bending configurations; consequently, snap-throughs and snap-backs can occur on odd and even buckling modes, respectively. From the theoretical point of view, the equilibrium configurations could be formed like soliton loops due to snapping instability.