• Title/Summary/Keyword: stress relaxation equation

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The Equilibrium between Dilatant and Thixotropic Flow Units

  • 방정환;김남정;최상원;김응렬;한상준
    • Bulletin of the Korean Chemical Society
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    • v.17 no.3
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    • pp.262-268
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    • 1996
  • Flow properties of all suspensions are controlled by their flow units. The factors effecting on the flow units are the characteristics of the particle itself (surface properties, particle sizes, particle shapes and etc.), the electrostatic interactions among the particles and the influences of the medium in the suspensions. Here, we studied the transition between the flow units with shear rate which can be added to the above factors. For the concentrated starch-water suspensions, by using the Couette type rotational viscometer, we confirmed that at low shear rate, dilatancy is appeared, but it is transformed to thixotropy with increasing shear rate. In order to explain this fact, we derived the following flow equation, representing the transition from dilatancy to thixotropy with shear rate, by assuming the equilibrium between the flow units. f = X1β1s./α1 + 1/(1+Kexp(c0s.2/RT))((1-X1)/α2)sinh-1{(β2)0 s. exp(c2s.2/RT)} + K exp(c0s.2/RT)/(1+K exp(c0s.2/RT))((1-X1)/α3)sinh-1{(β3)0 s. exp(-c3s.2/RT)} By applying this flow equation to the experimental flow curves for the concentrated starch-water suspensions, the flow parameters were obtained. And, by substituting the obtained flow parameters to the flow equation, the theoretical flow curves were reproduced. Also, Ostwald curve was represented by applying the flow equation, and the applicability for stress relaxation was discussed.

Curing Induced Residual Stresses in Laminated Cylindrical Shells

  • Lee, Soo-Yong
    • Journal of Mechanical Science and Technology
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    • v.14 no.1
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    • pp.19-29
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    • 2000
  • A viscoelastic finite element analysis is presented to investigate residual stresses occurred in a laminated cylindrical shell during cure. An incremental viscoelastic constitutive equation that can describe stress relaxation during the cure is derived as a recursive formula which can be used conveniently for a numerical analysis. The finite element analysis program is developed on the basis of a 3-D degenerated shell element and the first order shear deformation theory, and is verified by comparing with an one dimensional exact solution. Viscoelastic effect on the residual stresses in the laminated shell during the cure is investigated by performing both the viscoelastic and linear elastic analyses considering thermal deformation and chemical shrinkage simultaneously. The results show that there is big difference between viscoelastic stresses and linear elastic stresses. The effect of cooling rates and cooling paths on the residual stresses is also examined.

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Modeling of Turbulent Heat Transfer in an Axially Rotating Pipe Flow (축을 중심으로 회전하는 관유동에서 난류열전달의 모형화)

  • Shin, Jong-Keun
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.31 no.9
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    • pp.741-753
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    • 2007
  • The elliptic conceptual second moment model for turbulent heat fluxes, which was proposed on the basis of elliptic-relaxation equation, was applied to calculate the turbulent heat transfer in an axially rotating pipe flow. The model was closely linked to the elliptic blending model which was used for the prediction of Reynolds stress. The effects of rotation on the turbulent characteristics including the mean velocity, the Reynolds stress tensor, the mean temperature and the turbulent heat flux vector were examined by the model. The numerical results by the present model were directly compared to the DNS as well as the experimental results to assess the performance of the model predictions and showed that the behaviors of the turbulent heat transfer in the axially rotating pipe flow were satisfactorily captured by the present models.

Study on the Strain-Rate Dependent Constitutive Equation using Elastoplastic-Viscoplastic Constitutive Model (Bounding Surface 모델을 이용한 변형율속도 의존적인 구성 관계식에 관한 연구)

  • Lee, Ki-Sun;Kim, Dae-Kyu;Lee, Woo-Jin
    • Proceedings of the Korean Geotechical Society Conference
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    • 2001.03a
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    • pp.207-214
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    • 2001
  • 응력-변형률 관계의 모델링에 있어서 creep, stress relaxation, strain rate effect 등의 묘사는 중요한 지반거동중의 하나인 시간 의존적 거동에 대한 simulation은 있어서 대단히 중요한 요소라 할 수 있다. 특히 지반은 변형률 속도에 대하여 때로는 매우 다른 거동 특성을 보이기 때문에 지반의 모델링에 있어서 변형율 속도를 고려한 구성방정식의 제시는 큰 비중을 차지한다 하겠다. 본 연구에서는 변형율에 따라 변화하는 지반의 거동특성을 보다 현실에 가갈게 묘사하기 위한 시간 의존적 구성모델을 제시하는데 있다. Bounding Surface Model의 Stress Invariant 부분을 Perzyna(1966)와 Adachi and Oka(1982)의 변형율 속도 의존적인 구성관계 이론을 이용하여 발전시켰다 제안된 구성모델은 다양한 변형율 속도에 적용에 있어서 기존의 방식보다 간단히 모델 정수들을 결정 할 수 있다. 지반거동의 수치적인 해석을 위하여 기존의 Bounding Surface Model에 사용되었던 Program Code를 발전 시켜 사용하였으며, 엄격히 시행된 실내시험의 결과와 비교/검증하였다.

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Lossless Snubber with Minimum Voltage Stress for Continuous Current Mode Tapped-Inductor Boost Converters for High Step-up Applications

  • Kang, Jeong-Il;Han, Sang-Kyoo;Han, Jonghee
    • Journal of Power Electronics
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    • v.14 no.4
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    • pp.621-631
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    • 2014
  • To invigorate the tapped-inductor boost (TIB) topology in emerging high step-up applications for off-grid products, a lossless snubber consisting of two capacitors and three diodes is proposed. Since the switch voltage stress is minimized in the proposed circuit, it is allowed to use a device with a lower cost, higher efficiency, and higher availability. Moreover, since the leakage inductance is fully utilized, no effort to minimize it is required. This allows for a highly productive and cost-effective design of the tapped-inductor. The proposed circuit also shows a high step-up ratio and provides relaxation of the switching loss and diode reverse-recovery. In this paper, the operation is analyzed in detail, the steady-state equation is derived, and the design considerations are discussed. Some experimental results are provided to confirm the validity of the proposed circuit.

Stress Constraint Topology Optimization using Backpropagation Method in Design Sensitivity Analysis (설계민감도 해석에서 역전파 방법을 사용한 응력제한조건 위상최적설계)

  • Min-Geun, Kim;Seok-Chan, Kim;Jaeseung, Kim;Jai-Kyung, Lee;Geun-Ho, Lee
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.35 no.6
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    • pp.367-374
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    • 2022
  • This papter presents the use of the automatic differential method based on the backpropagation method to obtain the design sensitivity and its application to topology optimization considering the stress constraints. Solving topology optimization problems with stress constraints is difficult owing to singularities, the local nature of stress constraints, and nonlinearity with respect to design variables. To solve the singularity problem, the stress relaxation technique is used, and p-norm for stress constraints is applied instead of local stresses for global stress measures. To overcome the nonlinearity of the design variables in stress constraint problems, it is important to analytically obtain the exact design sensitivity. In conventional topology optimization, design sensitivity is obtained efficiently and accurately using the adjoint variable method; however, obtaining the design sensitivity analytically and additionally solving the adjoint equation is difficult. To address this problem, the design sensitivity is obtained using a backpropagation technique that is used to determine optimal weights and biases in the artificial neural network, and it is applied to the topology optimization with the stress constraints. The backpropagation technique is used in automatic differentiation and can simplify the calculation of the design sensitivity for the objectives or constraint functions without complicated analytical derivations. In addition, the backpropagation process is more computationally efficient than solving adjoint equations in sensitivity calculations.

Rheological Properties of Rehydrated Freeze Dried Instant Rice (동결건조 즉석미반의 리올로지적 성질)

  • Kim, Kwan-Yu;Lee, Shin-Young;Joo, Hyun-Kyu
    • Applied Biological Chemistry
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    • v.32 no.4
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    • pp.332-337
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    • 1989
  • Rheological properties of rehydrated freeze dried instant rice were investigated in comparison with that of cooked rice. The time changes in reciprocal hardness of instant rice grains at various rehydration temperatures$(60{\sim}90^{\circ}C)$ could be expressed by the first order reaction rate equation regardless of rehydration temperature and reaction rate constant increased as the rehydration temperature increased. Activation energy for rehydrating instant rice was 6.1 kcal/g-mol. Analysis of compressive stress relaxation test showed that the viscoelastic properties of both rehydrated instant rice and cooked rice grains could be expressed by 6-elements generalized Maxwell model. Rehydrated instant rice revealed higher relaxation decay than that of cooked rice and showed the elastic property increased by increasing the rehydration temperature.

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CAVITY FORMATION IN INTERFACE BETWEEN POWER LAW CREEP PARTICLE AND ELASTIC MATRIX SUBJECTED TO A UNIAXIAL STRESS

  • Lee, Yong-Sun;Ha, Young-Min;Hwang, Su-Chul
    • Journal of Theoretical and Applied Mechanics
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    • v.1 no.1
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    • pp.69-88
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    • 1995
  • The paper attempts to estimate the incubation time of a cavity in the interface between a power law creep particle and an elastic matrix subjected to a uniaxial stress. Since the power law creep particle is time dependent, the stresses in the interface relax. Through previous stress analysis related to the present physical model, the relaxation time is defined by ${\alpha}$2 which satisfies the equation $\Gamma$0 |1+${\alpha}$2k|m=1-${\alpha}$2 [19]. $\Gamma$0=2(1/√3)1+m($\sigma$$\infty$/2${\mu}$)m($\sigma$0/$\sigma$$\infty$tm) where $\sigma$$\infty$ is an applied stress, ${\mu}$ is a shear modulus of a matrix, $\sigma$$\infty$ is a material constant of a power law particle, $\sigma$=$\sigma$0 $\varepsilon$ and t elapsed time. the volume free energy associated with Helmholtz free energy includes strain energies associated with Helmholtz free energy includes strain energies caused by applied stress anddislocations piled up in interface (DPI). The energy due to DPI is found by modifying the results of Dundurs and Mura[20]. The volume free energies caused by both applied stress and DPI are a function of the cavity size(${\gamma}$) and elapsed time(t) and arise from stress relaxation in the interface. Critical radius ${\gamma}$ and incubation time t to maximize Helmholtz free energy is found in present analysis. Also, kinetics of cavity fourmation are investigated using the results obtained by Riede[16]. The incubation time is defied in the analysis as the time required to satisfy both the thermodynamic and kinetic conditions. Through the analysis it is found that [1] strain energy caused by the applied stress does not contribute significantly to the thermodynamic and kinetic conditions of a cavity formation, 2) in order to satisfy both thermodynamic and kinetic conditions, critical radius ${\gamma}$ decreases or holds constant with increase of time until the kinetic condition(eq.40) is satisfied. Therefore the cavity may not grow right after it is formed, as postulated by Harris[11], and Ishida and Mclean[12], 3) the effects of strain rate exponent (m), material constant $\sigma$0, volume fraction of the particle to matrix(f) and particle size on the incubation time are estimated using material constants of the copper as matrix.

Explicit Stress-Erection and Ultimate Load Analysis of Unit STRARCH Frame Considering Geometrically and Materially Nonlinear Characteristics (기하학적 재료적 비선형 특성을 고려한 스트라치 단위부재의 명시적 긴장설치 및 극한하중 해석)

  • Lee, Kyoung-Soo;Han, Sang-Eul
    • Journal of Korean Society of Steel Construction
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    • v.23 no.4
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    • pp.429-438
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    • 2011
  • In this study, the explicit numerical algorithm was proposed to simulate the stress erection process and ultimate-load analysis of the strarch (stressed arch) system. The strarch system is a unique and innovative structural system and member prestress comprising prefabricated plane truss frames erected through a post-tensioning stress erection procedure. The flexible bottom chord, which has sleeve and gap details, is closed by the reaction force of the prestressing tendon. The prestress imposed on the tendon will enable the strarch system to be erected. This post-tensioning process is called "stress erection process." During this process, plastic rigid-body rotation occurs to the flexible top chord due to the excessive amount of plastic strain, and the structural characteristic is unstable. In this study, the dynamic relaxation method (DRM) was adopted to calculate the nonlinear equilibrium equation of the system, and a displacement-based finite-element-formulated filament beam element was used to simulate the nonlinear behavior of the top chord sections of the strarch system. The section of the filament beam element was composed by the amount of filaments, which can be modeled by various material models. The Ramberg-Osgood and bilinear kinematic elastic plastic material models were formulated for the nonlinear material behaviors of the filaments. The numerical results that were obtained in the present study were compared with the experiment results of the stress erection and with the results of the ultimate-load analysis of the strarch unit frame. The results of the present studies are in good agreement with the previous experiment results, and the explicit DRM enabled the analysis of the post-buckling behaviors of the strarch unit frame.

Non-Newtonian Intrinsic Viscosities of Biopolymeric and Non-biopolymeric Solutions (II)

  • Jang, Chun-Hag;Kim, Chang-Hong;Ree, Taik-Yue
    • Bulletin of the Korean Chemical Society
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    • v.8 no.4
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    • pp.332-335
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    • 1987
  • This paper is a continuation of our previous $paper,^1$ and deals with Eq.(1) (see the text), which was theoretically derived in the $paper,^1$$ [{\eta}]^f\; and\; [{\eta}]^0$ is the intrinsic viscosity at stress f and f = O, respectively. Equation (1) predicts how $[{{\eta}}]^f / [{\eta}]^0$ changes with stress f, relaxation time ${\beta}_2$ of flow unit 2 and a constant $c_2$ related with the elasticity of molecular spring of flow unit 2. In this paper, Eq.(1) is applied to a biopolymer, e.g., poly (${\gamma}$-benzyl L-glutamate), and nonbiopolymers, e.g., polyisobutylene, polystyrene, polydimethylsiloxane and cellulose triacetate. It was found that the $c_2$ factor is zero for non-biopolymers while $c_2{\neq}0$ for biopolymers as found $previously.^1$ Because of the non-Newtonian nature of the solutions, the ratio $[{{\eta}}]^f / [{\eta}]^0$ drops from its unity with increasing f. We found that the smaller the ${\beta}_2,$ the larger the $f_c$ at which the viscosity ratio drops from the unity, vice versa.