Bending Buckling Research Articles

Determination of the Critical Buckling Pressure of Blood Vessels Using the Energy Approach

The stability of blood vessels under lumen blood pressure is essential to the maintenance of normal vascular function. Differential buckling equations have been established recently for linear and nonlinear elastic artery models. However, the strain energy in bent buckling and the corresponding energy method have not been investigated for blood vessels under lumen pressure. The purpose of this study was to establish the energy equation for blood vessel buckling under internal pressure. A buckling equation was established to determine the critical pressure based on the potential energy. The critical pressures of blood vessels with small tapering along their axis were estimated using the energy approach. It was demonstrated that the energy approach yields both the same differential equation and critical pressure for cylindrical blood vessel buckling as obtained previously using the adjacent equilibrium approach. Tapering reduced the critical pressure of blood vessels compared to the cylindrical ones. This energy approach provides a useful tool for studying blood vessel buckling and will be useful in dealing with various imperfections of the vessel wall.

Structural Stability of Carbon Nanotube Films: The Role of Bending Buckling

In films, mats, buckypaper, and other materials composed of carbon nanotubes (CNTs), individual CNTs are bound together by van der Waals forces and form entangled networks of bundles. Mesoscopic dynamic simulations reproduce the spontaneous self-assembly of CNTs into continuous networks of bundles and reveal that the bending buckling and the length of CNTs are the two main factors responsible for the stability of the network structures formed by defect-free CNTs. Bending buckling of CNTs reduces the bending energy of interconnections between bundles and stabilizes the interconnections by creating effective barriers for CNT sliding. The length of the nanotubes is affecting the ability of van der Waals forces of intertube interactions to counterbalance the internal straightening forces acting on curved nanotubes present in the continuous networks. The critical length for the formation of stable network structures is found to be ∼120 nm for (10,10) single-walled CNTs. In the simulations where the bending buckling is artificially switched off, the network structures are found to be unstable against disintegration into individual bundles even for micrometer-long CNTs.

Nonlocal shear deformable shell model for bending buckling of microtubules embedded in an elastic medium

A nonlocal shear deformable shell model is developed for buckling of microtubules embedded in an elastic matrix of cytoplasm under bending in thermal environments. The results reveal that the lateral constraint has a significant effect on the buckling moments of a microtubule when the foundation stiffness is sufficiently large.

ＣＦＲＰ積層板の簡便な圧縮試験法の提案

A new test method (NAL-II) for evaluating compressive properties of carbon fiber composites (CFRP) was proposed in this study. The compressive tests based on ASTM D6641 and NAL-II methods were conducted for three kinds of quasi-isotropic composite laminates (T800/3633, T800S/3900-2B, and IM600/133) for direct comparison. The stress-strain curves including compressive modulus obtained by NAL-II method were agreed with those obtained by ASTM D6641. NAL-II methods gave slightly greater compressive strengths (approximately 10%) as compared with ASTM D6641, it would be due to suppression of bending (buckling) before failure. The experimental result suggests the NAL-II method has a potential for domestic and/or international standard test method for non-hole compressive strength of carbon fiber composite laminate.

Chirality independence in critical buckling forces of super carbon nanotubes

The elastic buckling of super carbon nanotubes (STs) under compression and bending were studied by the molecular structure mechanics method. Under compression, the elastic buckling mode of the ST is similar to that of a cantilever column. However, the bending buckling mode of ST could transform from shell wall buckling to beam buckling as the length of ST increases. Therefore, the classical Euler formula could give good prediction both to the critical compression force for ST and to the critical bending force for very long STs. A phenomenological formula for the critical bending force of ST was given in this work, which could well predict the critical bending buckling of STs and bridge over the transformation of the bending buckling mode. Two types of chirality independent phenomena were found: first, the critical compression force carried by the unit carbon nanotube inside STs is independent of the chirality of STs; second, the critical bending force of ST’s is independent of the chirality of STs.

Buckling of microtubules under bending and torsion

Microtubules (MTs) in living cells are frequently bend, e.g., with a mean curvature of about 0.4 rad/μm in fibroblast cells [Odde et al., J. Cell Sci. 112, 3283 (1999)]. This raises a natural question whether bending buckling can occur in a MT. In this paper, an orthotropic model is developed to investigate buckling of MTs upon bending and torsion. A critical buckling curvature for a bent MT is predicted to be about 0.03 rad/μm (to which the corresponding bending moment is 0.85 nN nm), indicating that MTs in living cells are likely buckled. Buckling behavior of torsional MTs is also studied, and a critical buckling torque of 0.077 nN nm is obtained. Comparison to the results from an isotropic model shows that anisotropic properties of the MT wall have severe effect on the mechanical behavior of MTs.

Static statement of the stability problem under creep

In technological processes of rod bending, the critical time is determined [1] by the criterion of unbounded increase A → ∞ in the bent axis amplitude, which is equivalent to the requirement A ≫ A 0, where A 0 is value of the amplitude at the initial time t = 0. In this case, the mathematical models of the process of buckling of rods and plates [2] are constructed in the framework of the theory of small displacements. This contradiction can be removed by the assumption that the critical state is realized for deflections A of the order of several A 0, i.e., at the time instant corresponding to a sharp increase in displacements. Naturally, this assumption is of local character, because the instant of the transition to the accelerated increase in deflections depends on specific conditions such as, for example, the support conditions, the creep coefficient, the type of the system imperfectness, the value of A 0, and the eccentricity of the load application. In what follows, we show that, in the case of longitudinal bending (buckling), the time instant directly preceding the beginning of the catastrophic increase in deflections can be determined by the variation in the phase volume of the system.

매개 가진되는 얇은 외팔보의 비선형 진동 안정성

This paper presents the study on the stability of nonlinear oscillations of a thin cantilever beam subject to harmonic base excitation in vertical direction. Two partial differential governing equations under combined parametric and external excitations were derived and converted into two-degree-of-freedom ordinary differential Mathieu equations by using the Galerkin method. We used the method of multiple scales in order to analyze one-to-one combination resonance. From these, we could obtain the eigenvalue problem and analyze the stability of the system. From the thin cantilever experiment using foamax, we could observe the nonlinear modes of bending, twisting, sway, and snap-through buckling. In addition to qualitative information, the experiment using aluminum gave also the quantitative information for the stability of combination resonance of a thin cantilever beam under parametric excitation.

The buckling of single-walled carbon nanotubes upon bending: The higher order gradient continuum and mesh-free method

The bending buckling of single-walled carbon nanotubes (SWCNTs) is studied in the theoretical scheme of the higher order gradient continuum. The deformation of the underlying lattice vectors is approximated with an extended Cauchy–Born rule in which the effect of the second order deformation gradient is considered, and the continuum constitutive responses are determined by minimizing the energy of the representative cell. A mesh-free method is developed to implement the numerical modeling of SWCNTs, and their bending buckling behavior is numerically simulated with the developed method. The results are compared with those obtained with a full atomistic simulation, and it is revealed that the developed mesh-free method can accurately exhibit the bending deformation of SWCNTs. Different types of carbon nanotubes (CNTs) are studied, and the buckling mechanism is investigated.

Application of the higher‐order Cauchy–Born rule in mesh‐free continuum and multiscale simulation of carbon nanotubes

AbstractThis paper investigates the application of a recently proposed higher‐order Cauchy–Born rule in the continuum simulation and multiscale analysis of carbon nanotubes (CNTs). A mesh‐free computational framework is developed to implement the numerical computation of the hyper‐elastic constitutive model that is derived from the higher‐order Cauchy–Born rule. The numerical computation reveals that the buckling pattern of a single‐walled carbon nanotube (SWCNT) can be accurately displayed by taking into consideration the second‐order deformation gradient, and fewer mesh‐free nodes can provide a good simulation of homogeneous deformation. The bridging domain method is employed to couple the developed mesh‐free method and the atomistic simulation. The coupling method is used to simulate the bending buckling of an SWCNT and the tensile failure of an SWCNT with a single‐atom vacancy defect, and good computational results are obtained. Copyright © 2008 John Wiley & Sons, Ltd.

Mechanical response of metallic honeycomb sandwich panel structures to high-intensity dynamic loading

Explosive tests were performed in air to study the dynamic mechanical response of square honeycomb core sandwich panels made from a super-austenitic stainless steel alloy. Tests were conducted at three levels of impulse load on the sandwich panels and solid plates with the same areal density. Impulse was varied by changing the charge weight of the explosive at a constant standoff distance. At the lowest intensity load, significant front face bending and progressive cell wall buckling were observed at the center of the panel closest to the explosion source. Cell wall buckling and core densification increased as the impulse increased. An air blast simulation code was used to determine the blast loads at the front surfaces of the test panels, and these were used as inputs to finite element calculations of the dynamic response of the sandwich structure. Very good agreement was observed between the finite element model predictions of the sandwich panel front and back face displacements and the experimental observations. The model also captured many of the phenomenological details of the core deformation behavior. The honeycomb sandwich panels suffered significantly smaller back face deflections than solid plates of identical mass even though their design was far from optimal for such an application.

Calculation of the collapse load of an axially compressed laminated composite stringer-stiffened curved panel–An engineering approach

Abstract The effective width method that is widely applied for the analysis of isotropic planar stringer-stiffened panels has been extended to laminated composite stringer-stiffened circular cylindrical panels. The approach was modified and adapted to handle curved composite structures. Panels stiffened by blade type stiffeners, J-form stiffeners and T-form stiffeners were considered in the present study. Bending buckling of the stiffeners, their torsional buckling, combined bending and torsion buckling and local buckling of the stringers were accounted for in the investigation. Using the proposed extended effective width method, a MATLAB based software code TEW 1 was developed and implemented. To validate this code, predictions obtained by it were compared with experimental results and with finite element calculations. Good agreement between the present proposed method, experiments and finite element simulations was found, thus yielding an efficient, simple to apply and fast engineering code to be used in design and optimization stages.

Bending buckling of single-walled carbon nanotubes by atomic-scale finite element

This paper employs the atomic-scale finite element method to study bending buckling of single-walled carbon nanotubes (SWNTs). As the bending angle increases, kinks will appear and the morphology of the SWNT will change abruptly. The (15, 0) SWNT changes into a one-kinked structure, and finally contains two kinks; while the (10, 0) SWNT changes into a one-kinked structure, then into a two-kinked one, and finally contains three kinks. Strain energy grows initially as a quadratic function of bending angle, then increases gradually slowly, and finally changes approximately linearly. The energy releases suddenly at morphology bifurcations and the amount depends on degree of morphology change. The simulation shows that the appearance of kinks associated with the large deformation nearby reduces the slope of the strain energy curve in the post-buckling stages and hence increases the flexibility of the SWNTs.

Compression testing of periodic cellular sandwich cores

Periodic cellular metal (PCM) hybrid sandwich cores with 95 pet open porosity have been constructed from perforated 3003 aluminum alloy (AA3003) sheets using perforation-stretching methods. Two compressive collapse mechanisms (i.e., plastic hinging and plastic buckling) were studied using two limiting test conditions: first, where the PCM nodes were restricted only by interfacial friction (i.e., free compression) and compressive forces were resisted primarily through strut bending and plastic hinging mechanisms; and, second, where the PCM nodes were laterally confined (i.e., confined compression) and compressive forces were resisted primarily through strutbuckling mechanisms. The contribution of each collapse mechanism to the overall truss core performance was studied. The strut bending during free compression was tracked by a nodal displacement mapping (NDM) technique, while the progression of confined compression strut buckling was correlated to the truss core stress-strain profile. The present data can be used to illustrate the different strengths between strut bending (free-PCM) and strut buckling (confined-PCM) collapse mechanisms.

Buttressing angle of the double-plating fixation of a distal radius fracture: a finite element study

Treatment of a distal radius fracture should consider principles including stable fixation and early motion. The aim of this study was to investigate the biomechanical interactions of plate-fixation angles in the internal double-plating method coupled with various load conditions using non-linear finite element analysis (FEA). A 3D finite element distal radius fracture model with three separation angles (50, 70, and 90 degrees ) between the buttressed L- and straight plates was generated based on computed tomography data. After model verification and validation, frictional (contact) elements were used to simulate the interface condition between the fixation plates and the bony surface. The stress/strain distributions and displacements at the radius end were observed under axial, bending, and torsion load conditions. The simulated results indicated that the bending and torsion increased the stress values more than the axial load. The radius and straight plate stress values decreased significantly with increasing fixation angles for all load conditions. However, the L-plate stress values increased slightly under the bending buckling effect. The displacements at the radius end and strains at the fracture healing interface decreased with increasing fixation angles for axial and torsion conditions but displayed a slight difference for the bending condition. The findings using FEA provide quantitative evidence to identify that much larger plate fixation angles could provide better mechanical strength to establish favorable stress-transmission and prevent distal fragment dislocation.

Influence of the curvature of thin-walled elements with cracks on the parameters of fracture (Theoretical and experimental investigation)

The influence of curvature of a cylindrical panel containing a crack on the value of the J-integral in the process of axial loading is investigated. We study the entire range of curvatures of the panel, namely, from a plate to a closed cylindrical shell. The critical values of the J-integral are determined numerically according to the experimentally obtained values of critical loads corresponding to the onset of crack propagation. The contributions of membrane and bending strains to the total value of the J-integral are evaluated. In the case of an almost plane panel, we analyze the influence of nonlinear bending (buckling) in the vicinity of the crack on the increase in the J-integral. The influence of crack length on the critical value of the J-integral is studied.

Buckling of single-walled carbon nanotubes upon bending: Molecular dynamics simulations and finite element method

The bending buckling behaviors of single-walled carbon nanotubes (SWCNTs) are systematically investigated by using both molecular dynamics (MD) simulation and finite element method (FEM), to analyze the relationships between critical bending buckling curvature, critical buckling strain and nanotube geometry parameters (e.g., tube diameter, length and chirality). The postbuckling shape of SWCNT and the effect of loading boundary conditions are also discussed. The comparison between MD and FEM simulations shows that the continuum shell model provides some useful insights into the bending buckling mechanisms, yet it cannot quantitatively reproduce the bending buckling behavior of SWCNTs, since the continuum model does not account for the geometrical imperfections in the atomic system that are critical to the onset of buckling. Improvements of continuum models are suggested based on the findings.

Compressive Deformation Behaviour of a Closed-Cell Aluminum

The mechanical properties of a closed-cell aluminium foam were investigated by compressive tests, and the deformation behaviours of the aluminium foams were studied using Xray microtomography. The results indicate that the deformation of the aluminium foams under compressive loading was localized in narrow continuous deformation bands having widths of order of a cell diameter. The cells in the deformation bands collapsed by a mixed deformation mechanism, which includes mainly bending and minor buckling and yielding. Different fractions of the three deformation modes led to variations in the peak stress and energy absorption for different foam samples with the same density. It was also found that the cell morphology affects the deformation mechanism significantly, whilst the cell size shows little influence.

Bending stability of multiwalled carbon nanotubes

This paper reports the results of an investigation on bending stability of an individual multiwalled carbon nanotube. Based on the point of view of continuum modeling, a multilayer shell model is presented for the pure bending buckling of an individual multiwalled carbon nanotube, in which the effect of van der Waals forces between adjacent two tubes is taken into account. Here, the critical bending moment and the bending buckling mode for three types of multiwalled carbon nanotubes with different layer numbers and ratios of radius to thickness are calculated. Results carried out show that the bending buckling mode corresponding the critical bending moment is unique, which is obviously different from the purely axial compression buckling of an individual multiwalled carbon nanotube. It is also seen from numerical examples that the distribution of the critical bending strain for each tube of multiwalled carbon nanotubes under bending is dependent on the radius-to-thickness ratio and the layer number of the multiwalled carbon nanotubes. The new features and interesting numerical results in the present work are helpful for the application and the design of nanostructures in which multiwalled carbon nanotubes act as basic elements.

Strain-energy based homogenisation of two- and three-dimensional hyperelastic solid foams

A possible classification of cellular solids can be made based on the dimension into honeycombs and foams. In numerical simulations 2D models that are employed primarily to study honeycombs can also be used to model open-cell foams. Thereby, a loss of information regarding the 3D connectivity of the microstructure is involved. To answer the question how the missing third dimension in 2D models affects the overall properties, spatially periodic 2D and 3D model foams are adopted. From the point of homogenisation, a strain-energy based scheme is used for adequately determining the effective mechanical properties at large strains. The key idea behind this method is to use directly the equivalence condition between the meso-strain energy and the macro-strain energy. In a first step a representative volume element with the given microstructure and a corresponding volume element containing the effective medium are subjected to equivalent states of deformation. Subsequently, the macroscopic stress-strain relationships are determined by volume-averaging of the stored strain energy. The results of some fundamental loading cases indicate that both model foams represent the deformation characteristics of hyperelastic solid foams like localized bending and elastic buckling. In addition, the development of anisotropy due to microstructural changes at large strains can be traced with both model foams. Nevertheless, the different cell morphology affects the stress-strain curves in a quantitative manner.