Showing papers on "Flexural rigidity published in 2009"

Subjecting a Graphene Monolayer to Tension and Compression

Abstract: Themechanical behaviorof grapheneflakesunderboth tension and compression is examined using a cantilever-beam arrangement. Twodifferent sets of samples are employed.One consists of flakes just supported on a plastic bar. The other consists of flakesembeddedwithin theplastic substrate.Bymonitoring the shift of the 2DRaman linewith strain, information on the stress transfer efficiency as a function of stress sign and monolayer support are obtained. In tension, the embedded flake seems to sustain strains up to 1.3%, whereas in compression there is an indication of flake buckling at about 0.7% strain. The retainment of such a high critical buckling strain confirms the relative high flexural rigidity of the embedded monolayer. The mechanical strength and stiffness of crystalline materials are normally governed by the strength and stiffness

Cloaking bending waves propagating in thin elastic plates

Abstract: We introduce a cylindrical cloak to control the bending waves propagating in thin plates. This is achieved through radially dependent isotropic mass density and radially dependent and orthotropic flexural rigidity deduced from a coordinate transformation for the biharmonic propagation equation in the spirit of the paper of Pendry et al. [Science 312, 1780 (2006)]. We analyze the response of the cloak surrounding a clamped obstacle in the presence of a cylindrical excitation. We note that whereas the studied bending waves are of different physical and mathematical nature, they are cloaked in many ways as their electromagnetic and acoustic counterparts; e.g., when the source lies inside the coating, it seems to radiate from a shifted location (mirage effect).

Nonlinear bending and stretching of a circular graphene sheet under a central point load

Abstract: Understanding of the bending and stretching properties of graphene is crucial in guiding its growth and applications. In this paper, we investigate the deformation of a single layer, circular, graphene sheet under a central point load by carrying out molecular mechanics (MM) simulations. The bending and stretching of the graphene sheet are characterized by using the von Karman plate theory. Stress concentrations near the loaded region and the boundary due to bending rigidity of the graphene sheet are highlighted. It is shown herein that, with properly selected parameters, the von Karman plate theory can provide a remarkably accurate prediction of the graphene sheet behavior under linear and nonlinear bending and stretching.

Stress distribution of three NiTi rotary files under bending and torsional conditions using a mathematic analysis

Abstract: Aim To compare and evaluate the stress distribution of three NiTi instruments of various cross-sectional configurations under bending or torsional condition using a finite-element analysis model. Methodology Three NiTi files (ProFile, ProTaper and ProTaper Universal) were scanned using Micro-CT to produce a three-dimensional digital model. The behaviour of the instrument under bending or torsional loads was analysed mathematically in software (ABAQUS V6.5-1), taking into consideration the nonlinear mechanical characteristic of NiTi material. Results ProFile showed the greatest flexibility, followed by ProTaper Universal and ProTaper. The highest stress was observed at the surface near the cutting edge and the base of (opposing) flutes during cantilever bending. Concentration of stresses was observed at the bottom of the flutes in ProFile and ProTaper Universal instruments in torsion. The stress was more evenly distributed over the surface of ProTaper initially, which then concentrated at the middle of the convex sides when the amount of angular deflection was increased. Conclusion Incorporating a U-shaped groove in the middle of each side of the convex-triangular design lowers the flexural rigidity of the origin ProTaper design. Bending leads to the highest surface stress at or near the cutting edge of the instrument. Stress concentration occurs at the bottom of the flute when the instrument is subjected to torsion.

Leveraging single protein polymers to measure flexural rigidity.

Abstract: The micrometer-scale length of some protein polymers allows them to be mechanically manipulated in single-molecule experiments This provides a direct way to measure persistence length We have use

Temperature-dependent bending rigidity of graphene

Abstract: Both previous theoretical and experimental work showed that the bending rigidity of a liquid membrane decreases with increasing temperature. We demonstrate that the elastic energy forms for a solid membrane and a liquid membrane are identical under equal-biaxial stretching, implying the bending rigidity of a solid membrane should decrease with increasing temperature. We perform molecular dynamics simulations to study how thermal fluctuation affects the bending rigidity of graphene, and find that the bending rigidity decreases exponentially with increasing temperature. This is in contrast with recent atomistic Monte Carlo simulation result that the bending rigidity of graphene increases with increasing temperature.

Crack Detection and Quantification in Beams Using Wavelets

Abstract: A new method has been proposed to detect the location and also to quantify the crack using the deflection response of the damaged beams alone. The deflection is measured at a particular point for various locations of a concentrated load on the beam. This static deflection profile is used as the input signal for wavelet (Symlet) analysis. Due to variation in deflection at some points, compared to their adjacent points, peaks are seen in the wavelet coefficient (WC) plot. These peak points are identified as damage points along the length of the beam. The peaks can also be seen at sensor point and supports. These can be eliminated by performing wavelet analysis for the deflection profile measured at another point. In a real damaged structure, it is very difficult to measure deflection at several points, as a large amount of instrumentation needs to be installed to measure the response. This practical difficulty can be avoided by minimizing the number of measuring points in the field as explained in the present work. A parametric study has been carried out by varying the damage, location of damage, intensity of load, flexural rigidity, and length of the beam. It has been observed that the WCs change with variations in damage, location of damage, intensity of load, flexural rigidity, and length of the beam. A generalized curve has been proposed to quantify the damage in a fixed beam by taking envelop of all maximum WCs of the deflection response measured at damage points.

Deflection Hardening and Workability of Hybrid Fiber Composites

Abstract: Using a predetermined performance criterion as a basis, there was development of a deflection-hardening hybrid fiber-reinforced concrete (HyFRC) mixture design. There also was investigation of various hybrid and nonhybrid fiber combinations. There was demonstration, through flexural tests and consistency measurements, that material flowability and cohesiveness can be enhanced while maintaining flexural strength through a concrete-based matrix used with a hybrid fiber combination. Four-point bending was used to cast and test HyFRC beam elements, and there was comparison of results against plain concrete control beam flexural performance with and without conventional steel reinforcement. Post-crack flexural stiffness can be enhanced while lower yield strengths can be maintained in HyFRC with reinforcing bar at 0.3% reinforcing ratios in comparison to a reinforced plain concrete element with a 1.1% reinforcing ratio.

An experimental study on mechanical properties of GFRP braid-pultruded composite rods

Abstract: In this work, a conventional textile braiding machine was modified and added to a pultrusion line in order to pro- duce glass fiber reinforced composite rods by braiding-pultrusion technique. Braid-pultruded (BP) rods were produced with three braid roving linear densities and also with three different braid angles. To study the influence of overbraiding on mechanical properties of pultruded rods, unidirectional (UD) rods, without braided fabric, were produced, as well. All rod types were subjected to tensile, bending and torsion tests. The experimental results showed that BP rods have considerably higher shear modulus, but lower tensile modulus and flexural rigidity than those of UD pultruded rods, when fiber volume fraction is kept constant. Moreover, rods produced with higher braid roving linear densities had better torsional, but lower tensile and flexural properties. The highest shear modulus was observed in BP rods with braid angle of 45°.

Evaluation of Fatigue Models of Hot-Mix Asphalt Through Laboratory Testing

Abstract: Many studies have investigated the fatigue resistance of hot-mix asphalt (HMA) mixtures on the basis of the material properties and structural responses. In this study, a four-point bending-beam fatigue apparatus was used to measure the fatigue life of a typical Michigan HMA mixture under various frequencies (1, 5, and 10 Hz) and temperatures (4°, 13°C, and 21.3°C). The objective of this study was to evaluate laboratory models for predicting fatigue over wide ranges of testing conditions to rank their fatigue performance on the HMA mixtures. In addition, this paper aimed to correlate the flexural stiffness (modulus) with dynamic modulus, because the dynamic moduli of HMA are key input parameters in the Mechanistic-Empirical Pavement Design Guide (MEPDG). The correlation results showed a strong linear correlation between the flexural stiffness and dynamic modulus, with the flexural stiffness being 30% lower than the dynamic modulus. By providing a linkage between dynamic modulus and flexural stiffness, the...

A simplified formulation of adhesion problems with elastic plates

Abstract: The solution of adhesion problems with elastic plates generally involves solving a boundary-value problem with an assumed contact area. The contact region is then found by minimizing the total potential energy with respect to the contact area (i.e. the contact radius for the axisymmetric case). Such a procedure can be extremely long and tedious. Here, we show that the inclusion of adhesion is equivalent to specifying a discontinuous internal bending moment at the contact region boundary. The magnitude of this moment discontinuity is related to the work of adhesion and flexural rigidity of the plate. Such a formulation can greatly reduce the algebraic complexity of solving these problems. It is noted that the related plate contact problems without adhesion can also be solved by minimizing the total potential energy. However, it has long been recognized that it is mathematically more efficient to find the contact area by specifying a continuous internal bending moment at the boundary of the contact region. Thus, our moment discontinuity method can be considered to be a generalization of that procedure which is applicable for problems with adhesion.

Flexural Behavior of RC Beams Strengthened with Carbon Fiber Reinforced Polymer (CFRP) Fabrics

Abstract: This paper explores the flexural behavior of carbon fiber reinforced polymer (CFRP) strengthened reinforced concrete (RC) beams. For flexural strengthening of RC beams, total ten beams were cast and tested over an effective span of 3000 mm up to failure under monotonic and cyclic loads. The beams were designed as under-reinforced concrete beams. Eight beams were strengthened with bonded CFRP fabric in single layer and two layers which are parallel to beam axis at the bottom under virgin condition and tested until failure; the remaining two beams were used as control specimens. Static and cyclic responses of all the beams were evaluated in terms of strength, stiffness, ductility ratio, energy absorption capacity factor, compositeness between CFRP fabric and concrete, and the associated failure modes. The theoretical moment-curvature relationship and the load-displacement response of the strengthened beams and control beams were predicted by using FEA software ANSYS. Comparison has been made between the numerical (ANSYS) and the experimental results. The results show that the strengthened beams exhibit increased flexural strength, enhanced flexural stiffness, and composite action until failure.

Beam to string transition of vibrating carbon nanotubes under axial tension

Abstract: State-of the-art nanoelectromechanical systems have been demonstrated in recent years using carbon nanotube (CNT) based devices, where the vibration of CNTs is tuned by tension induced through external electrical fields. However, the vibration properties of CNTs under axial tension have not been quantitatively determined in experiments. Here, a novel in situ method for precise and simultaneous measurement of the resonance frequency, the axial tension applied to individual CNTs and the tube geometry is demonstrated. A gradual beam-to-string transition from multi-walled CNTs to single-walled CNTs is observed with the crossover from bending rigidity dominant regime to extensional rigidity dominant regime occur much larger than that expected by previous theoretical work. Both the tube resonance frequency under tension and transition of vibration behavior from beam to string are surprisingly well fitted by the continuum beam theory. In the limit of a string, the vibration of a CNT is independent of its own stiffness, and a force sensitivity as large as 0.25 MHz (pN) ―1 is demonstrated using a 2.2 nm diameter single-walled CNT. These results will allow for the designs of CNT resonators with tailored properties.

Strain energy and lateral friction force distributions of carbon nanotubes manipulated into shapes by atomic force microscopy.

Abstract: The interplay between local mechanical strain energy and lateral frictional forces determines the shape of carbon nanotubes on substrates. In turn, because of its nanometer-size diameter, the shape of a carbon nanotube strongly influences its local electronic, chemical, and mechanical properties. Few, if any, methods exist for resolving the strain energy and static frictional forces along the length of a deformed nanotube supported on a substrate. We present a method using nonlinear elastic rod theory in which we compute the flexural strain energy and static frictional forces along the length of single walled carbon nanotubes (SWCNTs) manipulated into various shapes on a clean SiO2 substrate. Using only high resolution atomic force microscopy images of curved single walled nanotubes, we estimate flexural strain energy distributions on the order of attojoules per nanometer and the static frictional forces between a SWCNT and SiO2 surface to be a minimum of 230 pN nm−1.

Performance-Based Approach for the Design of a Deflection Hardened Hybrid Fiber-Reinforced Concrete

Abstract: A numerical model that uses a nonlinear cracked hinge was developed to characterize the flexural behavior of a beam element composed of hybrid fiber-reinforced concrete (HyFRC). Deflection hardening performance criteria were established based on an average tensile strain capacity of 0.002 and a deterministic sensitivity analysis of the model. A HyFRC mix design is proposed that exceeds these performance criteria. The HyFRC flexural behavior and its flexural stiffness are compared against conventional reinforced concrete. Implications of the material flexural performance on performance-based structural design methods are discussed.

Scale-Dependent Electrostatic Stiffening in Biopolymers

Abstract: Using a combination of the molecular dynamics simulations and theoretical calculations, we have demonstrated that bending rigidity of biological polyelectrolytes (semiflexible charged polymers) is scale-dependent. A bond−bond correlation function describing a chain’s orientational memory can be approximated by a sum of two exponential functions manifesting the existence of the two characteristic length scales. One describes the chain’s bending rigidity at the distances along the polymer backbone shorter than the Debye screening length, whereas another controls the long-scale chain’s orientational correlations. The short-length scale bending rigidity is proportional to the Debye screening length at high salt concentrations and shows a weak logarithmic dependence on salt concentration when the Debye screening length exceeds a crossover value of κcr−1 ∝ (lBα2/lp)−1/2 (where lB is the Bjerrum length, α is the fraction of ionized groups, and lp is a bare persistence length). The long-scale chain’s bending rigi...

On the spectrum of fluctuations of a liquid surface: from the molecular scale to the macroscopic scale.

Abstract: We show that to account for the full spectrum of surface fluctuations from low scattering vector qd 1 (bulklike fluctuations), one must take account of the interface's bending rigidity at intermediate scattering vector qd approximately < 1, where d is the molecular diameter. A molecular model is presented to describe the bending correction to the capillary wave model for short-ranged and long-ranged interactions between molecules. We find that the bending rigidity is negative when the Gibbs equimolar surface is used to define the location of the fluctuating interface and that on approach to the critical point it vanishes proportionally to the interfacial tension. Both features are in agreement with Monte Carlo simulations of a phase-separated colloid-polymer system.

The flexural stiffness characteristics of viscoelastically prestressed polymeric matrix composites

Abstract: A novel composite material is described, where tension, applied to polymeric fibres, is released prior to moulding them into a matrix. On matrix solidification, compressive stresses imparted by the viscoelastically strained fibres improve mechanical properties. Previous studies showed that these viscoelastically prestressed composites had improved impact and tensile properties compared with control (unstressed) counterparts. In the current study, three-point bend tests on composites using nylon 6,6 fibre reinforcement in epoxy and polyester resins have demonstrated that the viscoelastic prestressing effect increases flexural stiffness. From deflections at 5 s and 900 s, using a freely suspended load on large span/thickness ratio ( L / h ) samples, the flexural modulus was increased by ∼50% relative to control counterparts. Stiffness-increasing mechanisms relating to pre-tensioned fibre and matrix prestress effects are discussed. For small L / h samples (using controlled rate deflection up to ∼5 s), the flexural modulus and resulting increase from viscoelastic prestressing were lower. This is attributed to shear effects and possibly fibre–matrix load transfer mechanisms. By exploiting time–temperature superposition, all samples were aged to the equivalent of 100 years at 20 °C and subsequent bend tests revealed no significant change in the modulus increase resulting from viscoelastic prestressing.

Effects of gold patterning on the bending profile and frequency response of a microcantilever

Abstract: We have systematically investigated the effect of various gold patterns on the bending profile and frequency response of a microcantilever. The gold patterns were deposited on the cantilever arrays using four types of shadow mask. The local bending profile, slope, and curvature varied depending on the area and position of the gold pattern. Also, the variations in the first three modes of the flexural resonance frequencies of the gold patterned cantilevers were measured to understand the opposing effects of mass loading and flexural rigidity; both of these parameters are dependent on the position and area of the gold pattern. The experimental results validated the theoretical one-dimensional model introduced by Tamayo et al. [Appl. Phys. Lett. 89, 224104 (2006)] and our calculations using the finite element method. The gold patterns giving the maximum response of the mass loading and flexural rigidity change were determined by examining how the relative resonance frequency shifts as a function of the dista...

Flexural Stiffness Control of Multilayered Beams

Abstract: This paper focuses on the ability to introduce change in the flexural bending stiffness of a niultilayered beam. The multilayered beam comprises a base layer with polymer layers on the upper and lower surfaces and stiff cover layers. The flexural stiffness can be reduced by effecting a reduction in the shear modulus of the polymer layers by heating through glass transition. Stiffer polymer layers strongly couple the cover layers to the base beam and the entire multilayered beam bends more as an integral unit On heating, a reduction in the shear modulus of the polymer layer results in its undergoing shear deformation as the base beam undergoes flexural bending and results in the cover layers decoupling from the base beam. This reduces the overall flexural bending stiffness. A finite element analysis is developed for the multilayered beam, and after experimentally verifying its ability to predict change in flexural bending deflection under load with a change in the polymer-layer shear modulus, it is used to conduct parametric studies. The results of the parametric studies provide broad insights into how the achievable change in flexural bending stiffness with a change in the polymer-layer modulus varies with design parameters such as the modulus and thickness of both the cover layers and the polymer layers. Changes in flexural bending stiffness by a factor of over 70 for a clamped-free beam and by a factor of over 130 for a pinned-pinned beam were observed for certain configuration designs.

Determination of Critical Buckling Loads for Euler Columns of Variable Flexural Stiffness with a Continuous Elastic Restraint Using Homotopy Perturbation Method

Abstract: In this paper, stability analysis of continuously restrained Euler columns of variable flexural stiffness is conducted by using homotopy perturbation method (HPM). The restraint considered in this study is an elastic foundation model in engineering practice and it is of great interest to foundation engineers. Critical buckling loads are investigated considering different end conditions. Obtaining analytical solutions for these types of problems was very difficult, now the condition is changed. The study proves that HPM is a very efficient and promising approach to the elastic stability analysis of specified problems.

Theoretical analysis and experimental investigation on flexural performance of steel reinforced ultrahigh toughness cementitious composite (RUHTCC) beams

Abstract: UHTCC (ultrahigh toughness cementitious composite), which is a kind of ultrahigh toughness cementitious composites material, exhibits pseudo strain hardening feature when subjected to tension load, and has enormous ductility and prominent crack dispersal ability. Accordingly, UHTCC can improve mechanical behavior of ordinary concrete structure especially its durability, and has been regarded as historical breakthrough to traditional cementitious materials. In this paper, the study focuses on flexure behavior of steel reinforced beam made of UHTCC. Based on the plane section assumption, along with two equilibrium equations of force and moment, the formulae to calculate the flexural load capability for the reinforced ultrahigh toughness cementitious composite (RUHTCC) beam were developed under the assumption that the compression stress-strain relationship in the UHTCC material is a bilinear model. Following this, the simplified formulae were further evolved by effective rectangle stress distribution approach in order to facilitate design of practical engineering. Two effective parameters introduced in effective rectangle approach were determined. The mathematical expressions to evaluate limited reinforcement ratio, flexural stiffness as well as ductility index were proposed, too. Last, two series of different reinforcement ratios of the RUHTCC beams were tested in four-point flexure loading. For comparison purposes, ordinary RC (reinforced concrete) beams also were prepared. Both moment curvature curves and load mid-span displacement curves were recorded and compared with the theoretical calculations. A good agreement between them was found, which validates the proposed theoretical formulae. For ductility index, a slightly big difference between the experimental values and the calculated ones exists. The experimental results show that, compared to control RC beams, the RUHTCC beam can improve both flexural capacity and ductility index, and the degree of improvement will decrease with the increase in the reinforcement ratio. Particularly, the results also reveal that lager crack width in control beams can be greatly reduced by formation of tightly-spaced fine cracks in UHTCC, which offers more durable structures.