• Journal of the Korean Wood Science and Technology
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• v.43 no.2
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• pp.177-185
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• 2015

The goal of this study is to evaluate the limitation of ASTM D 198 bending and ASTM D 3044 in determination of elastic modulus and shear modulus. Different material properties and span to depth ratios were used to analyze the effects of material property and testing conditions. The ratio of true elastic modulus to apparent elastic modulus evaluated from ASTM D 198 bending sharply decreased with increment of span to depth ratio. Shear modulus evaluated from ASTM D 198 bending decreased with increment of depth, whereas shear modulus evaluated from ASTM D 3044 was hardly influenced by increment of depth. Poisson's ratio influenced shear modulus from ASTM D 198 bending but did not influence shear modulus from ASTM D 3044. Different shearing factor was obtained for different depths of beams to correct shear modulus obtained from ASTM D 198 bending equivalent to shear modulus from theory of elasticity. Equivalent shear modulus of materials could be obtained by applying different shearing factors associated with beam depth for ASTM D 198 bending and correction factor for ASTM D 3044.

• Transactions of Materials Processing
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• v.13 no.5
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• pp.409-414
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• 2004

TRIP steel has got attention in automobile industry because of its high strength and high formability. However, the information on deformation behavior of TRIP steel, including bending and springback, is not enough until now. In this research, the V-die bending experiment and analysis have been done to obtain the information of springback of TRIP steel. And a new numerical method, where elastic modulus is varied with the change of the strain, was suggested. Tensile test for TRIP steel was done to get tensile properties as well as strain dependency of elastic modulus of the material. Strain-dependency of elastic modulus was used the numerical analysis of V-die bending and unbending process to predict springback amount. The results were compared with experiment, showing reasonable agreement. Through the analysis of V-die bending as well as draw bending of TRIP steel, the proposed scheme with variable elastic modulus was proven to well predict the deformation behavior of TRIP steel during bending and springback.

• Current Optics and Photonics
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• v.7 no.4
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• pp.337-344
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• 2023

Three-point bending is the main method for measuring the elastic modulus of a thin plate. Although various displacement transducers may be used to measure the bending, these are single-point measurements, and it is difficult to eliminate the error caused by eccentric load and shear force. Error-correction models for the elastic modulus of quartz glass using digital speckle interferometry are proposed for eccentric load and shear force. First, the positional misalignment between maximum deflection and load is analyzed, and the error caused by eccentric load is corrected. Then, the additional displacement caused by shear force at different positions of the quartz glass plate is explored. The effect of shear deformation is also corrected, by measuring two points. Since digital speckle interferometry has the advantage of full-field measurement, it can simultaneously obtain deflection data for multiple points to realize error correction. Experimental results are presented to demonstrate that the proposed model can effectively correct the measurement error of the elastic modulus.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.24 no.4
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• pp.421-427
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• 2015

In this paper, a description is given of finite element method (FEM) simulations of the elastic bending modulus of multi-layered graphene sheets that were carried out to investigate the mechanical behavior of graphene sheets with different gap thicknesses through molecular mechanics theory. The interaction forces between layers with various gap thicknesses were considered based on the van der Waals interaction. A finite element (FE) model of a multi-layered rectangular graphene sheet was proposed with beam elements representing bonded interactions and spring elements representing non-bonded interactions between layers and between diagonally adjacent atoms. As a result, the average elastic bending modulus was predicted to be 1.13 TPa in the armchair direction and 1.18 TPa in the zigzag direction. The simulation results from this work are comparable to both experimental tests and numerical studies from the literature.

• Computers and Concrete
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• v.30 no.4
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• pp.289-299
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• 2022

Based on the random cracking theory, the cylinder RVE model of reinforced concrete is established and the damage process is divided into three stages as the evolution of the cracks. The stress distribution along longitude direction of the concrete and the steel bar in the cylinder model are derived. The equivalent elastic modulus of the RVE are derived and the user-defined field variable subroutine (USDFLD) for the equivalent elastic modulus is well integrated into the ABAQUS. Regarding the tensile rebars and the concrete surrounding the rebars as the equivalent homogeneous transversely isotropic material, and the FEM analysis for the reinforced concrete beams is conducted with the USDFLD subroutine. Considering the concrete cracking and interfacial debonding, the macroscopic damage process of the reinforced concrete beam under four-point bending loading in the simulation. The volume fraction of rebar and the cracking degree are mainly discussed to reveal their influence on the macro-performance and they are calibrated with experimental results. Comparing with the bending experiment performed with 8 reinforced concrete beams, the bending stiffness of the second stage and the ultimate load simulated are in good agreement with the experimental values, which verifies the effectiveness and the accuracy of the improved finite element method for reinforced concrete beam.

• Journal of Mechanical Science and Technology
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• v.15 no.7
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• pp.1022-1031
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• 2001

The elastic modulus and fatigue properties of canine and human trabecular bone tissues (single trabecular) were experimentally determined on a microstructural level using four-point bending cyclic test, and they were compared based on microstructural characteristics and mineral density. The results showed that canine trabecular bone tissue had significantly lower modulus and lower fatigue strength than human tissue. The observed microstructural differences between the two tissues may be more responsible for the differences, although the lower mineral density in canine tissue might also have contributed to the lower modulus and fatigue strength.

• Structural Engineering and Mechanics
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• v.80 no.6
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• pp.657-668
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• 2021

In this study, a relationship between the resonance frequency ratio and Poisson's ratio was proposed that can be used to directly determine the elastic constants. Using this relationship, the frequency ratio between the 1st bending mode and 2nd bending mode for any rectangular Timoshenko beam can be directly estimated and used to determine the elastic constants efficiently. The exact solution of the Timoshenko beam vibration frequency equation under free-free boundary conditions was determined with an accurate shear shape factor. The highest percent difference for the frequency ratio between the theoretical values and the estimated values for all the beam dimensions studied was less than 0.02%. The proposed equations were used to obtain the elastic constants of beams with different material properties and dimensions using the first two measured transverse bending frequencies. Results show that using the equations proposed in this study, the Young's modulus and Poisson's ratio of rectangular Timoshenko beams can be determined more efficiently and accurately than those obtained from industry standards such as ASTM E1876-15 without the need to test the torsional vibration.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.04a
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• pp.45-52
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• 1997

The elastic deflection of thin ice sheets due In bending and shear deformation is considered. The in-plane Young's modulus and the transverse shear modulus are calculated by least squres fit of transverse plate deflection data. Results show that thin ice plates behave predominantly in shear. Previously, the Young's moduli were calaulated based on bending theory alone. The Young's moduli of thin model ice sheets, estimated using the bending and shear theory, are more than an order of magnitude greater than calculated previously, and hence are more realistic. Further, the previous ambiguity in the Young's modulus, arising from fitting the data at various distances from the point of loading, is removed by considering shear and bending deformation.

• Journal of Korean Society of Steel Construction
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• v.13 no.5
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• pp.443-455
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• 2001

An energy method has been used for an elastic formulation of bending vibration and buckling analysis of laminated composite plates on two-parameter elastic foundations. A quasi-elastic method is used for the solution of viscoelastic analysis of the laminated composite plates. The third-order shear deformation theory is applied by using the double-fourier series. To validate the derived equations the obtained displacements for simply supported orthotropic plates on elastic foundations are compared with those of LUSAS program Numerical results of the viscoelastic bending vibration and buckling analysis are presented to show the effects of layup sequence number of layers material anisotropy and shear modulus of foundations.

• Structural Engineering and Mechanics
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• v.20 no.4
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• pp.477-493
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• 2005

In case of Mindlin plate, not only the bending deformation but also the shear behavior is allowed. While the bending and shear stiffness are given in the same order in terms of elastic modulus, they are in different order in case of plate thickness. Accordingly, bending and shear contributions have to be dealt with independently if the stochastic finite element analysis is performed on the Mindlin plate taking into account of the uncertain plate thickness. In this study, a formulation is suggested to give the response variability of Mindlin plate taking into account of the uncertainties in elastic modulus as well as in the thickness of plate, a geometrical parameter, and their correlation. The cubic function of thickness and the correlation between elastic modulus and thickness are incorporated into the formulation by means of the modified auto- and cross-correlation functions, which are constructed based on the general formula for n-th joint moment of random variables. To demonstrate the adequacy of the proposed formulation, a plate with various boundary conditions is taken as an example and the results are compared with those obtained by means of classical Monte Carlo simulation.