• Title/Summary/Keyword: strain energy theory

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Distortion and Dilatatioin in the Tensie Failure of Paper

  • Park, Jong-Moon;James L. Thorpe
    • Journal of Korea Technical Association of The Pulp and Paper Industry
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    • v.31 no.5
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    • pp.73-85
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    • 1999
  • Yield and fracture are separated in the tensile failure of paper. Failure in the machine direction of photocopy paper is contrasted with failure in the cross-machine direction . The ratios of distortion (shape change) to dilatation (volume change) for individual elements at yield and fracture are described. The ratios of distortion to dilatation are measured and compared to predicted values of the strain energy density theory. To evaluate the effect of the angle from the principal material direction on the strain energy density theory. To evaluate the effect of the angle from the principal material direction on the strain energy density factor, samples are prepared from machine direction to cross-machine direction in 15 degree intervals. the strain energy density of individual elements are obtained by the integration of stress from finite element analysis with elastic plus plastic strain energy density theory. Poison's ratio and the angle from the principal material direction have a great effect ion the ratio fo distortion to dilatation in paper. During the yield condition, distortion prevails over dilatation . At fracture, dilatation is at a maximum.

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Analysis of cavity expansion based on general strength criterion and energy theory

  • Chao Li;Meng-meng Lu;Bin Zhu;Chao Liu;Guo-Yao Li;Pin-Qiang Mo
    • Geomechanics and Engineering
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    • v.37 no.1
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    • pp.9-19
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    • 2024
  • This study presents an energy analysis for large-strain cavity expansion problem based on the general strength criterion and energy theory. This study focuses on the energy dissipation problem during the cavity expansion process, dividing the soil mass around the cavity into an elastic region and a plastic region. Assuming compliance with the small deformation theory in the elastic region and the large deformation theory in the plastic region, combined with the general strength criterion of soil mass and energy theory, the energy dissipation solution for cavity expansion problem is derived. Firstly, from an energy perspective, the process of cavity expansion in soil mass is described as an energy conversion process. The energy dissipation mechanism is introduced into the traditional analysis of cavity expansion, and a general analytical solution for cavity expansion related to energy is derived. Subsequently, based on this general analytical solution of cavity expansion, the influence of different strength criterion, large-strain, expansion radius, cavity shape and characteristics of soil mass on the stress distribution, displacement field and energy evolution around the cavity is studied. Finally, the effectiveness and reliability of theoretical solution is verified by comparing the results of typical pressure-expansion curves with existing literature algorithms. The results indicate that different strength criterion have a relatively small impact on the displacement and strain field around the cavity, but a significant impact on the stress distribution and energy evolution around the cavity.

A study on strain specification and safety degree of connection joints of steel structural member (강구조부재 연결부의 변형특성 및 안전도에 관한 연구)

  • 김경진;김두환
    • Journal of the Korean Professional Engineers Association
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    • v.19 no.4
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    • pp.5-10
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    • 1986
  • On SWS 41 Plates jointed by the F11T M 20 high strength bolts the study on stress behavior and safety degree until rupture in static tensile tests were performed. By these results, in case of no clamping force stress concentration was extremed for strain of about 10% higher ratio. Elastic strain occurred to change of test specimens depth by the load and plastic strain occurred to local minute sleep after elastic strain. compared shear stress with tension stress from the fracture load it was showned lower values than the maximum shear stress theory and stress strain energy theory.

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Size dependent effect on deflection and buckling analyses of porous nanocomposite plate based on nonlocal strain gradient theory

  • Khazaei, Pegah;Mohammadimehr, Mehdi
    • Structural Engineering and Mechanics
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    • v.76 no.1
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    • pp.27-56
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    • 2020
  • In this paper, the deflection and buckling analyses of porous nano-composite piezoelectric plate reinforced by carbon nanotube (CNT) are studied. The equations of equilibrium using energy method are derived from principle of minimum total potential energy. In the research, the non-local strain gradient theory is employed to consider size dependent effect for porous nanocomposite piezoelectric plate. The effects of material length scale parameter, Eringen's nonlocal parameter, porosity coefficient and aspect ratio on the deflection and critical buckling load are investigated. The results indicate that the effect of porosity coefficient on the increase of the deflection and critical buckling load is greatly higher than the other parameters effect, and size effect including nonlocal parameter and the material length scale parameter have a lower effect on the deflection increase with respect to the porosity coefficient, respectively and vice versa for critical buckling load. Porous nanocomposites are used in various engineering fields such as aerospace, medical industries and water refinery.

Strain Dependence of Adsorption Energy of Single Layer MoS2: Possibility of Catalytic Usage

  • Jeon, Bu-Gyeong;Lee, Chang-Hui
    • Proceeding of EDISON Challenge
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    • 2016.03a
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    • pp.355-356
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    • 2016
  • It is shown that the maximum value of exchange current is obtained where hydrogen adsorption energy is near 0. This enables to estimate catalytic efficiency of a material with hydrogen adsorption energy, which is relatively easier to calculate with density fuctional theory (DFT) method. Strain dependence of the adsorption energy was studied with DFT method and adsorption energy of 0.04 eV per hydrogen atom is obtained at 30% strain.

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The effect of strain on the electronic properties of MoS2 monolayers

  • Park, Soon-Dong;Kim, Sung Youb
    • Coupled systems mechanics
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    • v.5 no.4
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    • pp.305-314
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    • 2016
  • We utilize first-principles calculations within density-functional theory to investigate the possibility of strain engineering in the tuning of the band structure of two-dimensional $MoS_2$. We find that the band structure of $MoS_2$ monolayers transits from direct to indirect when mechanical strain is applied. In addition, we discuss the change in the band gap energy and the critical stains for the direct-to-indirect transition under various strains such as uniaxial, biaxial, and pure shear. Biaxial strain causes a larger change, and the pure shear stain causes a small change in the electronic band structure of the $MoS_2$ monolayer. We observe that the change in the interaction between molecular orbitals due to the mechanical strain alters the band gap type and energy.

A study on the modified energy theory for the bellows problem (벨로우즈 문제 해석을 위한 수정 에너지 이론)

  • 이완익;김태완
    • Journal of the korean Society of Automotive Engineers
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    • v.11 no.2
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    • pp.55-65
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    • 1989
  • In this paper, the bellows problem under axial load were investigated. A modified energy theory, which has the improved strain energy and stress description taken from governing equation of general shells of revolution, were proposed. From the analysis, the results obtained from the modified theory were more accurate and in stable state with varing geometric parameter of bellows than those of other theory.

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Computational modelling for description of rubber-like materials with permanent deformation under cyclic loading

  • Guo, Z.Q.;Sluys, L.J.
    • Interaction and multiscale mechanics
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    • v.1 no.3
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    • pp.317-328
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    • 2008
  • When carbon-filled rubber specimens are subjected to cyclic loading, they do not return to their initial state after loading and subsequent unloading, but exhibit a residual strain or permanent deformation. We propose a specific form of the pseudo-elastic energy function to represent cyclic loading for incompressible, isotropic materials with stress softening and residual strain. The essence of the pseudo-elasticity theory is that material behaviour in the primary loading path is described by a common elastic strain energy function, and in unloading, reloading or secondary unloading paths by a different strain energy function. The switch between strain energy functions is controlled by the incorporation of a damage variable into the strain energy function. An extra term is added to describe the permanent deformation. The finite element implementation of the proposed model is presented in this paper. All parameters in the proposed model and elastic law can be easily estimated based on experimental data. The numerical analyses show that the results are in good agreement with experimental data.

Optimal Approximated Development of General Curved Plates Based on Deformation Theory (변형 이론을 기반으로한 곡면의 최적 근사 전개)

  • 유철호;신종계
    • Korean Journal of Computational Design and Engineering
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    • v.7 no.3
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    • pp.190-201
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    • 2002
  • Surfaces of many engineering structures, specially, those of ships and airplanes are commonly fabricated as doubly curved shapes as well as singly curved surfaces to fulfill functional requirements. Given a three dimensional design surface, the first step in the fabrication process is unfolding or planar development of this surfaces into a planar shape so that the manufacturer can determine the initial shape of the flat plate. Also a good planar development enables the manufacturer to estimate the strain distribution required to form the design shape. In this paper, an algorithm for optimal approximated development of a general curved surface, including both singly and doubly curved surface is developed in the sense that the strain energy from its planar development to the design surface is minimized, subjected to some constraints. The development process is formulated into a constrained nonlinear programming problem, which is on basis of deformation theory and finite element. Constraints are subjected to characteristics of the fabrication method. Some examples on typical surfaces and the practical ship surfaces show the effectiveness of this algorithm.

Nonlinear bending and post-buckling behaviors of FG small-scaled plates based on modified strain gradient theory using Ritz technique

  • Ghannadpour, S. Amir M.;Khajeh, Selma
    • Advances in nano research
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    • v.13 no.4
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    • pp.393-406
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    • 2022
  • In the present article, functionally graded small-scaled plates based on modified strain gradient theory (MSGT) are studied for analyzing the nonlinear bending and post-buckling responses. Von-Karman's assumptions are applied to incorporate geometric nonlinearity and the first-order shear deformation theory is used to model the plates. Modified strain gradient theory includes three length scale parameters and is reduced to the modified couple stress theory (MCST) and the classical theory (CT) if two or all three length scale parameters become zero, respectively. The Ritz method with Legendre polynomials are used to approximate the unknown displacement fields. The solution is found by the minimization of the total potential energy and the well-known Newton-Raphson technique is used to solve the nonlinear system of equations. In addition, numerical results for the functionally graded small-scaled plates are obtained and the effects of different boundary conditions, material gradient index, thickness to length scale parameter and length to thickness ratio of the plates on nonlinear bending and post-buckling responses are investigated and discussed.