• Title/Summary/Keyword: Constitutive equation

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Cap Model을 이용한 기초식반의 수동해석(I) -범용프로그램의 검증과 수치계산례-

  • 박병기;정진섭
    • Geotechnical Engineering
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    • v.3 no.2
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    • pp.29-40
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    • 1987
  • This paper aims at investigating the characteristics of soil deformation by finite element method (FEM) coupling the cap model with the multi.purpose program developed by authors for the analysis of foundation displacement. The cap model as the constitutive equation has proved to be very useful to a partially saturated roils as well as rocks with high accuracy. As described in the Previous Paper (Park et al 1987) , there exist some difficulties in the determination of soil parameters in order to use the cap model at Present. However the authors have been studying to seek the method for the determination of the soil parameters from the laboratory results of conventional cylindrical triaxial test. Though the computer program advocated by foreign scholars has been kept secret, authors accomplished in performing the FEM analysis by the algorithm and program developed by authors for the cap model. Good results are obtained compared with those published already by Desai(1981) The main conclusions analyzed are as follows: 1. The cap model can be coupled with the multi.purpose computer program of authors bases on the Biot's consolidation theory without loss of generality. 2. Big difference appears in the settlement of center of the embankment between the cap modes and the modified Cam clay model in undrained conditions. The more study on which is more accurate should be performed in this respect.

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Characterization of Dynamic Deformation Behavior of Al 7075-T6 at High Temperature by Using SHPB Technique (SHPB 기법을 사용한 고온에서의 Al 7075-T6 의 동적 변형 거동)

  • Lee, Ouk-Sub;Park, Jin-Su;Choi, Hye-Bin;Kim, Hong-Min
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.34 no.8
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    • pp.981-987
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    • 2010
  • The split Hopkinson pressure bar (SHPB) technique is extensively used to characterize material deformation behavior under high strain rate condition. In this study, the dynamic deformation behavior of aluminum 7075-T6 under a high strain rate and at a high temperature is investigated by using a modified SHPB set-up with the pulse shaper technique. The parameters used in the Johnson-Cook constitutive equation are determined by using the SHPB experimental results including the data on the effects of strain rate, temperature, strain hardening, and thermal softening of the material.

Mechanical analysis of cutout piezoelectric nonlocal nanobeam including surface energy effects

  • Eltaher, Mohamed A.;Omar, Fatema-Alzahraa;Abdalla, Waleed S.;Kabeel, Abdallah M.;Alshorbagy, Amal E.
    • Structural Engineering and Mechanics
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    • v.76 no.1
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    • pp.141-151
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    • 2020
  • This manuscript tends to investigate influences of nanoscale and surface energy on a static bending and free vibration of piezoelectric perforated nanobeam structural element, for the first time. Nonlocal differential elasticity theory of Eringen is manipulated to depict the long-range atoms interactions, by imposing length scale parameter. Surface energy dominated in nanoscale structure, is included in the proposed model by using Gurtin-Murdoch model. The coupling effect between nonlocal elasticity and surface energy is included in the proposed model. Constitutive and governing equations of nonlocal-surface perforated Euler-Bernoulli nanobeam are derived by Hamilton's principle. The distribution of electric potential for the piezoelectric nanobeam model is assumed to vary as a combination of a cosine and linear variation, which satisfies the Maxwell's equation. The proposed model is solved numerically by using the finite-element method (FEM). The present model is validated by comparing the obtained results with previously published works. The detailed parametric study is presented to examine effects of the number of holes, perforation size, nonlocal parameter, surface energy, boundary conditions, and external electric voltage on the electro-mechanical behaviors of piezoelectric perforated nanobeams. It is found that the effect of surface stresses becomes more significant as the thickness decreases in the range of nanometers. The effect of number of holes becomes significant in the region 0.2 ≤ α ≤ 0.8. The current model can be used in design of perforated nano-electro-mechanical systems (PNEMS).

A Comparison Study on the Two Dimensional Consolidation Analysis Methods (2 차원(次元) 압밀해석법(壓密解析法)의 비교연구(比較研究))

  • Park, Byong Kee;Chung, Jin Sup;Park, Hae Kuen
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.5 no.3
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    • pp.39-47
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    • 1985
  • In this paper, a FEM analysis model was developed to solve the consolidation phenomena of embankment on the soft foundation. The developed FEM model was based on the Biot's consolidation equation which was coupled with one of three stress-strain constitutive relationships. In order to check the validity of the newly developed FEM model, the program input data were used by a test embankment which had been already constructed at Cubzac-les-ponts in France by Magnan et al. The FEM results compared to the experimental and analytical results which were obtained by the Magnan's group at Cubzac-les-ponts. The results compared showed that the consolidation phenomena were well explained by the author's FEM model which results were more accurate than the others. As for the pore water pressure, Christian-Boehmer's method used in this paper was considered preferable to Sandhu-Wilson's used by Magnan.

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A Study of Extensional Viscosity of Fluid M1 in Converging Channel Rheometer Using K-BKZ Intergral Constitutive Equation (수렴관 유변측정기에서 K-BKZ 적분형 구성식을 사용한 M1유체의 신장점도에 관한 연구)

  • 김동회
    • The Korean Journal of Rheology
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    • v.6 no.1
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    • pp.30-40
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    • 1994
  • 고분자 물질의 신장점도를 측정하기 위하여 설계된 수렴관을 지나는 시험 유체 M1 에대하여 유한요소방법으로 수치모사를 수행하였다. 구성방정식은 세 개의 이완시간을 가진 적분형 K-BKZ모형을 사용하였다. 신장변형이 지배적이고 변형속도가 매우 큰 흐름에 대하 여 실험적 방법으로 측정이 가능한 범위까지 수치모사를 수행하였다. 두 개의 압력 측정꼬 지 사이의 벽면 압력차에 대하여 압력 신호로 측정한 실험값을 수치모사결과와 비교하였다. 걷보기 전단속도가 매우 큰 1300s-1에 이르는 높은 유속의 전 실험범위에 대하여 안정된 수 치해를 얻을수 있었다. 3$0^{\circ}C$에서는 모든 실험범위의 유속에서 압력차에 대한 수치모사 결과 가 실험값과 잘일치했다. 21$^{\circ}C$에서는 0.1$\times$10-3m3/s보다 낮은 유속범위에서 실험값과 일치하 는 결과를 얻었으나 그보다 높은 유속에서 실험값과 일치하는 결과를 얻었으나 그보다 높은 유속에서 실험값과 다른 경향의 결과를 얻었다. 이것은 낮은 온도 높은 유속 조건에서 M1 유체의 성질이 불안정하고 또한 그러한 조건의 실험에서 발생한 압력 측정꼭지 부근의 기포 들이 정확한 압력측정에 영향을 끼쳤기 때문이다. 수치모사 결과로부터 얻은 압력과 응력분 포로부터 수렴관 유변측정기의 유동특성을 밝힐수 있었다. 이는 실험적 방법을 통해서는 얻 기 어려운 결과들로서 중요한의미를 가진다. 특별한 모양을 갖도록 설계된 수렴관을 통과하 는 M1 유체가 중심부근에서 일정한 신장변형속도로 변형됨을 확인할 수 있었으며 수직응력 은 지수적으로 증가하다가 축소부분을 지난 후 매우 장점도를 얻기 위하여 신장변형속도가 일정한 구역이 두 배로 확장된 수렴관이 수치적으로 다루어졌고 이를 통하여 기존의 수렴관 에서 구한 값보다 큰 신장점도를 얻을 수 있었다.

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Numerical Analysis Method of Overlay Model for Material Nonlinearity Considering Strain Hardening (변형률 경화를 고려한 오버레이 모델의 재료비선형 수치해석기법)

  • Baek, Ki Youl
    • Journal of Korean Society of Steel Construction
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    • v.19 no.3
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    • pp.291-301
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    • 2007
  • The overlay model is a certain kinds of numerical analysis method to present the material non-lineariy which is represented the baushinger effect and the strain hardening. This model simulates the complex behavior of material by controlling the properties of the layers which like the hardening ratio, the section area and the yield stress. In this paper, the constitutive equation and plastic flow rule of each layer which are laid in the plane stress field are obtained by using the thermodynamics. Two numerical examples were tested for the validity of proposed method in uniaxial stress and plane stress field with comparable experimental results. The only parameter for the test is the yield stress distribution of each layers.

Influences of Geometric Configurations of Bypass Grafts on Hemodynamics in End-to-Side Anastomosis

  • Choi, Jae-Sung;Hong, Sung-Chul;Kwon, Hyuck-Moon;Suh, Sang-Ho;Lee, Jeong-Sang
    • Journal of Chest Surgery
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    • v.44 no.2
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    • pp.89-98
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    • 2011
  • Background: Although considerable efforts have been made to improve the graft patency in coronary artery bypass surgery, the role of biomechanical factors remains underrecognized. The aim of this study is to investigate the influences of geometric configurations of the bypass graft on hemodynamic characteristics in relation to anastomosis. Materials and Methods: The Numerical analysis focuses on understanding the flow patterns for different values of inlet and distal diameters and graft angles. The Blood flow field is treated as a two-dimensional incompressible laminar flow. A finite volume method is adopted for discretization of the governing equations. The Carreau model is employed as a constitutive equation for blood. In an attempt to obtain the optimal aorto-coronary bypass conditions, the blood flow characteristics are analyzed using in vitro models of the end-to-side anastomotic angles of $45^{\circ}$, $60^{\circ}$ and $90^{\circ}$. To find the optimal graft configurations, the mass flow rates at the outlets of the four models are compared quantitatively. Results: This study finds that Model 3, whose bypass diameter is the same as the inlet diameter of the stenosed coronary artery, delivers the largest amount of blood and the least pressure drop along the arteries. Conclusion: Biomechanical factors are speculated to contribute to the graft patency in coronary artery bypass grafting.

Formulation of Mass Conservation and Linear Momentum Conservation for Saturated Porous Media in Arbitrary Lagrangian Eulerian(ALE) Description (포화된 다공질 매체의 질량 보존과 운동량 보존에 대한 Arbitrary Lagrangian Eulerian(ALE) 정식화)

  • Park, Tae-Hyo;Jung, So-Chan;Kim, Won-Cheul
    • Journal of the Korean GEO-environmental Society
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    • v.4 no.1
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    • pp.5-10
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    • 2003
  • The solids and the fluids in porous media have a relative velocity to each other. Due to physically and chemically different material properties and their relative velocity, the behavior of saturated porous media is extremely complicated. Thus, in order to describe and clarify the deformation behavior of saturated porous media, constitutive models for deformation of porous media coupling several effects need to be developed in frame of Arbitrary Lagrangian Eulerian(ALE) description. The aim of ALE formulations is to maximize the advantages of Lagrangian and Eulerian elements, and to minimize the disadvantages. Therefore, this method is appropriate for the analysis of porous media which are considered for the behavior of the solids and the fluids. For this reason, mass balance equations for saturated porous media are derived here in ALE description frames. ALE formulations of mass conservation for the solid phase and the fluid phase are expressed. Then, linear momentum balance equation for porous media as multiphase media is expressed.

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Study on the Time Dependent Stress-Strain Behavior of Clay (점성토의 시간의존적 응력 - 변형 특성에 관한 연구)

  • 지인택;강우묵
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.30 no.4
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    • pp.134-153
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    • 1988
  • This paper was carried out to investigate the existence of a unique stress- strain behavior by obtaining some factors influencing the time dependent stress- strain behavior of clay. The results obtained from this study were summarized as follows ; 1. The relationship between stress ratro and strain in normally consolidated clay was in- dependent on pre-shear consolidation pressure. Therefore, shear strain could be expressed as a function with stress ratio. 2. The constitutive equation of shear strain on Modified Carn Clay Model coincided better with the observed value than Cam Clay Model. 3. The relationships between deviator stress and shear strain, between pore water pressure and shear strain were unified by the mean equivalent pressure. 4. The shear strain contour in norrnally consolidated clay was increased linearly through origin, but that in overconsolidated clay was not in accordance with the result of the former. 5. Because the effective stress path of normally consolidated clay was unified by the mean equivalent pressure, state boundary surface in (e,p,q) space was transformed into two dimensional surface. But it was considered to be suitable that the unified stress- strain in overconsolidated clay be expressed by a function with overconsolidation ratio. 6. The deviator for constant strain was increased linearly with increment of strain rate ($\varepsilon$) on semi-log scale, but pore water pressure was decreased. 7. The behavior of stress relaxation was transformed from linear to curvilinear with inc - rement of strain rate before stress relaxation test, and pore water pressure was increased in total range. 8. The strain of creep was increased linearly with increment of time on semi-log scale. The greater the strain rate before creep test became, the greater the increment of strain of creep became. And the pore water pressure during creep test was increased generally with increment of time on semi-log scale.

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Flow Stress Properties of Electric Resistance Welded Small-Sized Subsea Pipeline Subjected to Temperature and Strain Rate Variations (심해저용 전기 저항 용접 소구경 송유관 소재의 온도 및 변형률 속도 에 따른 유동 응력 특성)

  • Kim, Younghun;Park, Sung-Ju;Yoon, Sung-Won;Choung, Joonmo
    • Journal of Ocean Engineering and Technology
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    • v.29 no.3
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    • pp.241-248
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    • 2015
  • A subsea pipeline for oil/gas transportation or gas injection is subjected to extreme variations in internal pressure and temperature, which can involve a strain rate effect on the pipeline material. This paper describes the flow stress characteristics of a pipeline material called API 5L X52N PSL2, using and experimental approach. High-speed tensile tests were carried out for two metal samples taken from the base and weld parts. The target temperature was 100℃, but two other temperature levels of –20℃and 0℃ were taken into account. Three strain rates were also considered for each temperature level: quasi static, 1/s, and 10/s. Flow stress data were proposed for each temperature level according to these strain rates. The dynamic hardening behaviors of the base and weld metals appeared to be nonlinear on the log-scale strain rate axis. A very high material constant value was required for the Cowper-Symonds constitutive equation to support the experimental results.