• Title/Summary/Keyword: Force relaxation function

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Nonlinear rheology of linear polymer melts: Modeling chain stretch by interchain tube pressure and Rouse time

  • Wagner, Manfred H.;Rolon-Garrido, Victor H.
    • Korea-Australia Rheology Journal
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    • v.21 no.4
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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.

Structural analysis of cracked R.C. members subjected to sustained loads and imposed deformations

  • Mola, F.;Gatti, M.C.;Meda, G.
    • Structural Engineering and Mechanics
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    • v.11 no.6
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    • pp.637-650
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    • 2001
  • A structural analysis of cracked R.C. members under instantaneous or sustained loads and imposed displacements is presented. In the first part of the paper the problem of deriving feasible moment-curvature diagrams for a long term analysis of R.C. sections is approached in an exact way by using the Reduced Relaxation Function Method in state I uncracked and the method suggested by CEB in state II cracked. In both states the analysis of the main parameters governing the problem has shown that it is possible to describe the concrete creep behaviour in an approximate way by using the algebraic formulation connected to the Effective Modulus Method. In this way the calculations become quite simple and can be applied in design practice without introducing significant errors. Referring to continuous beams, the structural analysis is then approached in a general way, applying the Force Method and the Principle of Virtual Works. Finally, considering single members, the structural analysis is performed by means of a graphical procedure based on the application of feasible moment-rotation diagrams which allow to easily solve various structural problems and to point out the most interesting aspects of the long term behaviour of cracked R.C. members with rigid or elastically deformable redundant restraints.

Mechanical Behavior of the Soleus Aponeuroses during Voluntary Contraction Using Magnetic Resonance Imaging Technique (자기공명 영상기법을 이용한 인체 가자미근 건막의 기계학적 특성 연구)

  • Lee, Hae-Dong
    • Korean Journal of Applied Biomechanics
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    • v.17 no.1
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    • pp.121-127
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    • 2007
  • Muscle force produced by muscle fibers is transmitted to bones via tendinous structures(aponeuroses and tendon), resulting in joint(s) movement. As force-transmitting elements, mechanical behavior of aponeuroses and tendon are closely related with the function of muscle-tendon complex. The purpose of this study was to determine strain characteristics of aponeuroses for in-vivo human soleus muscle during submaximal voluntary contractions using an advanced medical imaging technique, velocity-encoded phase-contrast magnetic resonance imaging (VE-PC MRI). VE-PC MRI of the soleus muscle-tendon complex was acquired during submaximal isometric plantarflexion contraction-relaxation cycle (n = 7), using 3.0T Trio MRI scanner(Siemens AG, Malvern, MA). From the VE-PC MRI containing the tissue velocity in superior-inferior direction, twenty regions of interest(20 ROI; 10 on the anterior aponeurosis and 10 on the posterior aponeurosis) were tracked. During the isometric plantarflexion contraction-relaxation cycle, velocity and displacement profiles were different between the anterior and posterior aponeuroses, indicating heterogeneous strain behavior along the length of the leg. The anterior aponeurosis elongated while the posterior aponeurosis shortened during the initial phase of the contraction. Moreover, strain behavior of the posterior aponeurosis was different from that of the Achilles tendon. Possible explanation for the observed variations in strain behavior of aponeuroses was investigated with morphological assessment of the soleus muscle and it was found that the intramuscular tendinous structures significantly vary among subjects. In conclusion, the heterogeneous mechanical behavior of the soleus aponeuroses and the Achilles tendon suggests that the complexity of skeletal muscle-tendon complex should be taken into consideration when modeling the complex for better understanding of its functions.

Time-Dependent Differential Equation of PSC Flexural Member with Constant Eccentricity (직선배치 긴장재를 갖는 PSC 휨 부재의 시간종속적 지배미분방정식)

  • 강병수;김택중;조용덕;이용학
    • Proceedings of the Korea Concrete Institute Conference
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    • 2002.05a
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    • pp.303-308
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    • 2002
  • A governing differential equation (GDE) of PSC flexural member with constant eccentricity considering the long-term losses including concrete creep, shrinkage, and PS steel relaxation is derived based on the two approaches. The first approach utilizes the force and moment equilibrium equations derived based on the geometry of strains of the uniform and curvature strains while the second one utilizes the principle of minimum total potential energy formulation. The identity of the two GDE's is verified by comparing the coefficients consisting of the GDE's. The boundary conditions resulting from the functional analysis of the variational calculus are investigated. Rayleigh-Ritz method provides a way to get the explicit form of the continuous deflection function in which the total potential energy is minimized with respect to the unknown coefficients consisting of the trial functions. As a closure, the analytically calculated results are compared with the experiments and show good agreements.

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A One-Pass Standard Cell Placement Algorithm Using Multi-Stage Graph Model (다단 그래프 모델을 이용한 빠른 표준셀 배치 알고리즘)

  • 조환규;경종민
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.24 no.6
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    • pp.1074-1079
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    • 1987
  • We present a fast, constructive algorithm for the automatic placement of standard cells, which consists of two steps. The first step is responsible for cell-row assignment of each cell, and converts the circuit connectivity into a multi-stage graph under to constraint that sum of the cell-widths in each stage of the multi-state graph does not exceed maximum cell-row width. Generatin of feed-through cells in the final layout was shown to be drastically reduced by this step. In the second step, the position of each cell within the row is determined one by one from left to right so that the cost function such as the local channel density is minimized. Our experimental result shows that this algorithm yields near optimal results in terms of the number of feed-through cells and the horizontal tracks, while running about 100 times faster than other iterative procedures such as pairwise interchange and generalized force directed relaxation method.

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Response of temperature dependence of an elastic modulus in microstretch generalized thermoelasticity

  • Kumar, Rajneesh;Gupta, Rajani Rani
    • Structural Engineering and Mechanics
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    • v.30 no.5
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    • pp.577-592
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    • 2008
  • Laplace-Fourier transform techniques are used to investigate the interaction caused by mechanical, thermal and microstress sources in a generalized thermomicrostretch elastic medium with temperature-dependent mechanical properties. The modulus of elasticity is taken as a linear function of reference temperature. The integral transforms are inverted using a numerical technique to obtain the normal stress, tangential stress, tangential couple stress, microstress and temperature distribution. Effect of temperature dependent modulus of elasticity and thermal relaxation times have been depicted graphically on the resulting quantities. Comparisons are made with the results predicted by the theories of generalized thermoelasticity. Some particular cases are also deduced from the present investigation.

Analysis of Creep Crack Growth at High-Temperature Components by Diffusive Growth Model of Grain Boundary Cavities (I)-Effect of Grain Boundary Cavitation on Stress Field and Crack Growth Rate- (입계기공의 확산성장 모델을 이용한 고온기기의 크립균열전파해석(1)-응력장 및 균열전파속도에 미치는 입계기공의 영향-)

  • Jeon, Jae-Young
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.20 no.4
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    • pp.1177-1185
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    • 1996
  • The crack growth under creep condition is one of the major damage mechanisms which determines remaining life of the component operating at high temperatures. In this paper, the creep crack growth by grain boundary cavitation is studied, which is frequently observed failure mechanism for creep brittle materials. As a result of diffusive growth of creep cavities, it is shown that the crack-tip stress field is modified from the original stress distribution by the amount of singularity attenuation parameter which is function of crack growth rate and material properties. Also, the stress relaxation at crack-tip results in the extension of cavitating area by the load dump effect to meet the macroscopic force equilibrium conditdion.

The Effect of Applying the Muscle Energy Technique to Neck Muscles on the Forward Head Posture (목 근육에 대한 근에너지기법 적용이 전방머리자세에 미치는 영향)

  • Kim, Hyeon-Su;Lee, Keon-Cheol;Kim, Dae-Jin;Ahn, Jeong-Hoon
    • Journal of The Korean Society of Integrative Medicine
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    • v.9 no.1
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    • pp.173-181
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    • 2021
  • Purpose : The purpose of this study is to compare muscle activity after applying two muscle energy techniques (MET) to subjects with forward head posture to see if the post isometric relaxation (PIR) technique is more effective than the reciprocal inhibition (RI) technique. Methods : The muscle activity was measured using EMG after applying the PIR and RI techniques to 30 adults at K College. Subjects were selected for forward head posture whose ear center was 2.5 ㎝ front of the center of the shoulder. EMG equipment was used to measure muscle activity, and the measurement sites were measured in cervical flexor and extensor muscles. The experiment period was performed once a week for a total of two weeks, and after the pre-measurement was performed for 5 minutes PIR and RI exercise. In the PIR technique, the head is tilted back in a sitting position, and the experimenter applies resistance with the same force for 7~10 seconds and repeats 3-5 times after rest. In the RI technique, in a sitting position, the subject gives the force to bend the head forward, and the experimenter applies resistance with the same force for 7 to 10 seconds, and repeats 3 to 5 times after rest. Results : The result is same as the following. In the comparison of muscle activity, there was a significant decrease in both PIR and RI at 1 and 2 weeks. And there was a greater decrease in muscle activity in PIR. There was no difference in the comparison of decrease in muscle activity at 1 week and 2 week. Conclusion : Both PRI and RI can be said to be effective in improving the function of the forward head posture in the neck muscles. Therefore, the selection of the two techniques in clinical practice should be appropriately performed under the judgment of experts according to the patient's situation.

Study on Damage Reduction of (Ba0.6Sr0.4)TiO3 Thin Films in Ar/CF4 Plasma (Ar/CF4 유도결합 플라즈마에서 식각된 (Ba0.6Sr0.4)TiO3 박막의 손상 감소)

  • 강필승;김경태;김동표;김창일
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.16 no.6
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    • pp.460-464
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    • 2003
  • The barium strontium titannate ((Ba,Sr)TiO$_3$:BST) thin films were etched in an inductively coupled plasma (ICP) as a function of CF$_4$/Ar gas mixing ratio. Under CF$_4$(20%)/Ar(80%), the maximum etch rate of the BST films was 400 $\AA$/min. Etching products were redeposited on the surface of BST and then the nature of crystallinity were varied. Therefore, we investigated the etched surface of BST by X-ray photoelectron spectroscopy (XPS) and atomic force microscopy (AFM). The plasma damages were evaluated in terms of leakage current density by Agilent 4145C and dielectric constant by HP 4192 impedance analyzer. After the BST thin films exposed in the plasma, the leakage current density and roughness increases. After annealing at 600 $^{\circ}C$ for 10 min in $O_2$ ambient, the leakage current density, roughness and nonvolatile etch byproducts reduced. From this results, the plasma induced damages were recovered by annealing process owing to the relaxation of lattice mismatches by Ar ions and the desorption of metal fluorides in high temperature.

Mechanical Properties of Natural Rubber/Acrylonitrile-Butadiene Rubber Blends and Their Adhesion Behavior with Steel Cords (Natural Rubber/Acrylonitrile-Butadiene Rubber 블렌드의 기계적 물성과 강선과의 접착거동)

  • Sohn, Bong-Young;Nah, Chong-Woon
    • Elastomers and Composites
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    • v.36 no.2
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    • pp.111-120
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    • 2001
  • Mechanical properties and their adhesion behavior with zinc- and brass-plated steel cords of natural rubber/acrylonitrile-butadiene blend compounds were investigated as a function of blend ratio. The Mooney viscosity and stress relaxation time were found to be lowered with increasing NBR content. Tensile modulus generally increased with increasing NBR content. Tensile stress at break stayed constant up to about 40 phr and showed minimum at $50{\sim}60 phr$, and thereafter increased with increasing NBR content. Strain at break decreased linearly below 50 phr, and above the level it showed nearly constant value. Based on the abrupt drops in elastic modulus and tan ${\delta}$ peak, the glass transition temperature of NR and NBR were found to be -55 and $-10^{\circ}C$, respectively. In the case of NR/NBR blend compounds, two distinct transition points were observed and each transition position was not affected by NBR level indicating an incompatible nature of NR/NBR blend system. The pullout force and rubber coverage decreased to the level of about 40% to that of pure m compound, when the 50 phr of NR was replaced by NBR. However, the pure NBR compound showed the comparable adhesion performance with NR(${\sim}90%$). The sulfur concentration was found to become lower with the increased NBR content at the adhesion interface based on the Auger spectrometer results, representing a lack of adhesion layer formation, and this was explained for a possible cause of low adhesion performance with adding NBR.

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