• Korea-Australia Rheology Journal
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• 제21권4호
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• pp.203-211
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• 2009

In flows with deformation rates larger than the inverse Rouse time of the polymer chain, chains are stretched and their confining tubes become increasingly anisotropic. The pressures exerted by a polymer chain on the walls of an anisotropic confinement are anisotropic and limit chain stretch. In the Molecular Stress Function (MSF) model, chain stretch is balanced by an interchain pressure term, which is inverse proportional to the $3^{rd}$ power of the tube diameter and is characterized by a tube diameter relaxation time. We show that the tube diameter relaxation time is equal to 3 times the Rouse time in the limit of small chain stretch. At larger deformations, we argue that chain stretch is balanced by two restoring tensions with weights of 1/3 in the longitudinal direction of the tube (due to a linear spring force) and 2/3 in the lateral direction (due to the nonlinear interchain pressure), both of which are characterized by the Rouse time. This approach is shown to be in quantitative agreement with transient and steady-state elongational viscosity data of two monodisperse polystyrene melts without using any nonlinear parameter, i.e. solely based on the linear-viscoelastic characterization of the melts. The same approach is extended to model experimental data of four styrene-butadiene random copolymer melts in shear flow. Thus for monodisperse linear polymer melts, for the first time a constitutive equation is presented which allows quantitative modeling of nonlinear extension and shear rheology on the basis of linear-viscoelastic data alone.

• Steel and Composite Structures
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• 제26권6호
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• pp.673-691
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• 2018

The main goal of this research is to examine the in-plane and out-of-plane forced vibration of a curved nanocomposite microbeam. The in-plane and out-of-plane displacements of the structure are considered based on the first order shear deformation theory (FSDT). The curved microbeam is reinforced by functionally graded carbon nanotubes (FG-CNTs) and thus the extended rule of mixture is employed to estimate the effective material properties of the structure. Also, the small scale effect is captured using the strain gradient theory. The structure is rested on a nonlinear orthotropic viscoelastic foundation and is subjected to concentrated transverse harmonic external force, thermal and magnetic loads. The derivation of the governing equations is performed using energy method and Hamilton's principle. Differential quadrature (DQ) method along with integral quadrature (IQ) and Newmark methods are employed to solve the problem. The effect of various parameters such as volume fraction and distribution type of CNTs, boundary conditions, elastic foundation, temperature changes, material length scale parameters, magnetic field, central angle and width to thickness ratio are studied on the frequency and force responses of the structure. The results indicate that the highest frequency and lowest vibration amplitude belongs to FGX distribution type while the inverse condition is observed for FGO distribution type. In addition, the hardening-type response of the structure with FGX distribution type is more intense with respect to the other distribution types.

• Elastomers and Composites
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• 제43권1호
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• pp.25-30
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• 2008

자동차 부싱은 차체로 전달되는 하중을 줄여주는 역할을 하는 자동차 현가장치의 주요 부품으로 바깥쪽 슬리브와 안쪽의 축 사이에서 가운데가 비어 있는 실린더의 형상을 가진다. 차축에 작용되는 힘과 모멘트에 대한 부싱의 상대변위 및 변형각도는 점탄성 성질을 나타내며, 부싱에서 힘과 모멘트와 이에 대한 변위와 변형각도의 관계는 다물체 동역학 시뮬레이션에 매우 중요하다. 본 연구는 자동차 부싱의 회전방향 모드에 대한 모멘트와 변형각도의 점탄성 관계를 변형각도에 의존하는 모멘트 완화함수를 통하여 부싱모델을 완성하였으며, 완성된 점탄성 부싱 모델은 회전방향 모드에 대한 실험값과 비교하여 검증하였다.

• Korea-Australia Rheology Journal
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• 제17권3호
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• pp.131-140
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• 2005

In this work we show the results of our most recent Direct Numerical Simulations (DNS) of turbulent viscoelastic channel flow using spectral spatial approximations and a stabilizing artificial diffusion in the viscoelastic constitutive model. The Finite-Elasticity Non-Linear Elastic Dumbbell model with the Peterlin approximation (FENE-P) is used to represent the effect of polymer molecules in solution, The corresponding rheological parameters are chosen so that to get closer to the conditions corresponding to maximum drag reduction: A high extensibility parameter (60) and a moderate solvent viscosity ratio (0.8) are used with two different friction Weissenberg numbers (50 and 100). We then first find that the corresponding achieved drag reduction, in the range of friction Reynolds numbers used in this work (180-590), is insensitive to the Reynolds number (in accordance to previous work). The obtained drag reduction is at the level of $49\%\;and\;63\%$, for the friction Weissenberg numbers 50 and 100, respectively. The largest value is substantially higher than any of our previous simulations, performed at more moderate levels of viscoelasticity (i.e. higher viscosity ratio and smaller extensibility parameter values). Therefore, the maximum extensional viscosity exhibited by the modeled system and the friction Weissenberg number can still be considered as the dominant factors determining the levels of drag reduction. These can reach high values, even for of dilute polymer solution (the system modeled by the FENE-P model), provided the flow viscoelasticity is high, corresponding to a high polymer molecular weight (which translates to a high extensibility parameter) and a high friction Weissenberg number. Based on that and the changes observed in the turbulent structure and in the most prevalent statistics, as presented in this work, we can still rationalize for an increasing extensional resistance-based drag reduction mechanism as the most prevalent mechanism for drag reduction, the same one evidenced in our previous work: As the polymer elasticity increases, so does the resistance offered to extensional deformation. That, in turn, changes the structure of the most energy-containing turbulent eddies (they become wider, more well correlated, and weaker in intensity) so that they become less efficient in transferring momentum, thus leading to drag reduction. Such a continuum, rheology-based, mechanism has first been proposed in the early 70s independently by Metzner and Lamley and is to be contrasted against any molecularly based explanations.

• Restorative Dentistry and Endodontics
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• 제29권6호
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• pp.489-497
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• 2004

Objective: The purpose of this study was to investigate the viscoelastic properties related to handling characteristics of composite resins, Methods: A custom designed vertical oscillation rheometer (VOR) was used for rheological measurements of composites. The VOR consists of three parts: (1) a measuring unit, (2) a deformation induction unit and (3) a force detecting unit, Two medium viscous composites, Z100 and Z250 and two packable composites, P60 and SureFil were tested. The viscoelastic material function, including complex modulus $E^{*}$ and phase angle ${\delta}$, were measured. A dynamic oscillatory test was used to evaluate the storage modulus (E'), loss modulus (E") and loss tangent ($tan{\delta}$) of the composites as a function of frequency ($\omega$) from 0.1 to 20 Hz at $23^{\circ}C$. Results: The E' and E" increased with increasing frequency and showed differences in magnitude between brands. The $E^{*}s$ of composites at ${\omega}{\;}={\;}2{\;}Hz$, normalized to that of Z100, were 2.16 (Z250), 4,80 (P60) and 25.21 (SureFil). The magnitudes and patterns of the change of $tan{\delta}$ of composites with increasing frequency were significantly different between brands. The relationships between the complex modulus $E^{*}$, the phase angle ${\delta}$ and the frequency \omega were represented by frequency domain phasor form, $E^{*}{\;}(\omega){\;}={\;}E^{*}e^{i{\delta}}{\;}={\;}E^{*}{\angle}{\delta}$. Conclusions: The viscoelasticity of composites that influences handling characteristics is significant different between brands, The VOR is a relatively simple device for dynamic, mechanical analysis of high viscous dental composites. The locus of frequency domain phasor plots in a complex plane is a valuable method of representing the viscoelastic properties of composites.

• 한국게임학회 논문지
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• 제15권5호
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• pp.143-152
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• 2015

일반적인 입자 기반 유체 폭발 시뮬레이션과는 다르게 탄성을 지닌 유체의 폭발을 시뮬레이션 하는 경우 물질의 사실적인 변형을 표현하기 위한 여러 가지 특수한 방법이 필요하다. 기존 입자 기반의 점탄성체 연구에서는 물체가 힘을 받아 압축이 되었을 때 한계치 이상의 힘을 받으면 변형되는 최대 변형에너지 이론과 물체의 부피가 일정 수준 이상 줄어들었을 때 변형되는 최대 전단응력 이론을 이용하여 진흙이나 페인트 같이 소성변형을 하는 물체의 변형을 다루었지만 실리콘이나 탄성이 강한 고무줄과 같이 한계치 이상의 힘을 받았을 때 여러 부분으로 쪼개지는 취성변형을 표현하지는 못하였다. 본 논문은 물체가 받은 힘을 변형된 길이나 부피로 표현한 기존의 입자 기반 시뮬레이션과 달리, 힘을 받았을 때 물체에 발생하는 최대응력이 물체의 파단응력에 도달하였을 때 항복이 일어난다는 취성 변형에 적합한 쿨롱-모어 이론을 제안한다. 쿨롱-모어 이론을 적용한 강한 탄성을 가진 반유동체가 힘을 받은 경계면이 파단응력에 도달하였을 때 물체가 현실감 있게 파괴되는 과정을 표현할 수 있음을 확인하였다. 반유동체가 지면에 부딪혀 힘을 받았을 때 쿨롱-모어 이론을 적용하여 물체의 파괴를 표현하였다.

• Korea-Australia Rheology Journal
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• 제13권1호
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• pp.29-35
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• 2001

The development of filament stretching extensional rheometers over the past decade has enabled the systematic measurement of the transient extensional stress growth in dilute and semi-dilute polymer solutions. The strain-hardening in the extensional viscosity of dilute solutions overwhelms the perturbative effects of capillarity, inertia & gravity and the kinematics of the extensional deformation become increasingly homogeneous at large strains. This permits the development of a robust open-loop control algorithm for rapidly realizing a deformation with constant stretch history that is desired for extensional rheometry. For entangled fluids such as concentrated solutions and melts the situation is less well defined since the material functions are governed by the molecular weight between entanglements, and the fluids therefore show much less pronounced strain-hardening in transient elongation. We use experiments with semi-dilute/entangled and concentrated/entangled monodisperse polystyrene solutions coupled with time-dependent numerical computations using nonlinear viscoelastic constitutive equations such as the Giesekus model in order to show that an open-loop control strategy is still viable for such fluids. Multiple iterations using a successive substitution may be necessary, however, in order to obtain the true transient extensional viscosity material function. At large strains and high extension rates the extension of fluid filaments in both dilute and concentrated polymer solutions is limited by the onset of purely elastic instabilities which result in necking or peeling of the elongating column. The mode of instability is demonstrated to be a sensitive function of the magnitude of the strain-hardening in the fluid sample. In entangled solutions of linear polymers the observed transition from necking instability to peeling instability observed at high strain rates (of order of the reciprocal of the Rouse time for the fluid) is directly connected to the cross-over from a reptative mechanism of tube orientation to one of chain extension.

• Steel and Composite Structures
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• 제23권5호
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• pp.529-541
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• 2017

In the present study, vibration analysis of functionally graded carbon nanotube reinforced composite (FGCNTRC) plate moving in two directions is investigated. Various types of shear deformation theories are utilized to obtain more accurate and simplest theory. Single-walled carbon nanotubes (SWCNTs) are selected as a reinforcement of composite face sheets inside Poly methyl methacrylate (PMMA) matrix. Moreover, different kinds of distributions of CNTs are considered. Based on extended rule of mixture, the structural properties of composite face sheets are considered. Motion equations are obtained by Hamilton's principle and solved analytically. Influences of various parameters such as moving speed in x and y directions, volume fraction and distribution of CNTs, orthotropic viscoelastic surrounding medium, thickness and aspect ratio of composite plate on the vibration characteristics of moving system are discussed in details. The results indicated that thenatural frequency or stability of FGCNTRC plate is strongly dependent on axially moving speed. Moreover, a better configuration of the nanotube embedded in plate can be used to increase the critical speed, as a result, the stability is improved. The results of this investigation can be used in design and manufacturing of marine vessels and aircrafts.

• Journal of Biosystems Engineering
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• 제37권1호
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• pp.28-35
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• 2012

Purpose: This study performed the oscillatory test using the texture analyzer to characterize the viscoelastic behavior of apples such as the storage modulus (E'), the loss modulus (E"), the complex modulus (${\mid}E^*{\mid}$) and the energy dissipated per cycle ($W_{diss}$). Methods: The sinusoidal deformation with the frequency of 1-10 Hz and the maximum displacement of 0.1 mm were applied to the flesh tissues of Fuji, Golden Delicious and Red Delicious apples. The Lissajous figure was used to measure the phase angle(${\delta}$) between stress and strain curve. Results: Trigger force was critical to the measurement of the phase angle. E', E", ${\mid}E^*{\mid}$ and Wdiss were measured using the Lissajous figure and the phase angle. The complex modulus of Golden Delicious apple was significantly lower than those of Fuji apple and Red Delicious apple. Conclusions: Apple flesh was exhibiting more elasticity at low frequency, and more viscosity at high frequency. Dynamic compressive properties of Fuji apple were similar to those of Red Delicious apple but significantly different from those of Golden Delicious apple.

• 소성∙가공
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• 제12권1호
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• pp.34-42
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• 2003

This paper presents a rigid-plastic finite element method to handle the frictional contact problem between two deformable bodies experiencing large deformation. The variational formulation combined with incremental quasi-static model is employed for treating the contact boundary condition. The frictional behavior of the model obeys Coulomb's law of friction. The proposed contact algorithms are classified into two categories, one for searching contacting nodes and the other for calculating contact forces at the contact surface. A slave node and master contact segment are defined using the geometric condition of finite elements on the contact interface. The penalty parameter is used to limit the penetration between contacting bodies, and the finite elements are coupled with contact boundary elements.us gates and cavity thicknesses. Through this study we have observed that the jetting is related to the die swell of material. This means that the jotting is strongly affected by the elastic flow property rather than the viscous flow property in viscoelastic characteristics of molten polymer. Different resins have different elastic properties, and elastic flow behavior depends on the shear rate of flow, i.e. injection speed. Large die swell would eliminate jetting however, the retardation of die swell would stimulate jetting. In the point of mole design, reducing the thickness ratio of cavity to gate can reduce or eliminate jetting regardless of amount of elasticity of polymer melt.