• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.10 s.253
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• pp.1227-1234
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• 2006

Up to now, several mathematical theories based on strain energy functions have been developed for rubber materials. These theories, coupled with the finite element method, can be used very effectively by engineers to analyze and design rubber components. However, due to the complexities of the mathematical formulations and the lack of general guidelines available fur the analysis of rubber components, it is a formidable task for an engineer to analyze rubber components. In this paper a method for predicting strain energy functions - Neo-Hookean model and Mooney-Rivlin model - from the hardness using the empirical equation without any experiment is discussed. First based on the elasticity theories of rubber, the relation between stress and strain is defined. Then for the butyl rubbers, the model constants of Neo-Hookean model and Mooney-Rivlin model are calculated from uniaxial tension tests. From the results, the usefulness of the empirical equation to estimate elastic modulus from hardness is confirmed and, fur Mooney-Rivlin model, the predicted and the experimental model constants are compared and discussed.

• Elastomers and Composites
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• v.48 no.2
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• pp.148-155
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• 2013

The crosslinking density of polymer can be quantitatively calculated by the Flory-Rehner equation using the swelling experimental data and the lattice constant ${\beta}_1$ of interaction parameter (${\chi}$) in this equation should be chosen have used cautiously. This ${\beta}_1$ is the experimental data by rule of thumb, and researchers have used little different values respectively. Generally, the average molecular weight between crosslink points $M_c$ in the Flory-Rehner equation and the Mooney-Rivlin equation have the same value, and ${\beta}_1$ can be calculated when the $M_c$ in the Flory-Rehner equation is given. Therefore, in this research, firstly we calculated the $M_c$ using the selected ${\beta}_1$ (=0.34) and the swelling experimental data of 1,2,3-triazole polymer from the Flory-Rehner equation, secondly the $M_c$ from the Mooney-Rivlin equation is calculated by the tensile experimental data, and finally two $M_c$ were compared. As a result, two $M_c$ values were almost the same, and it was proved that the ${\beta}_1$ (=0.34) was selected properly.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.12
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• pp.14-24
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• 2018

Several typical hyper-elastic constitutive models that encompass both conventional and advanced ones were investigated for the application of instability problems, including the biaxial tension of a rubber patch and inflation of spherical or cylindrical balloons. The material models included the neo-Hookean model, Mooney-Rivlin model, Gent model, Arruda-Boyce model, Fung model, and Pucci-Saccomandi model. Analyses can be done using membrane equations with particular strain energy density functions. Among the typical strain energy density functions, Kearsley's bifurcation for the Treloar's patch occurs only with the Mooney-Rivlin model. The inflation equation is so generalized that a spherical balloon and tube balloons can be taken into account. From the analyses, the critical material parameters and limit points were identified for material models in terms of the non-dimensional pressure and inflation volume ratio. The bifurcation was then identified and found for each material model of a balloon. When the finite element method was used for the structural instability problems of rubber-like materials, some careful treatments required could be suggested. Overall, care must be taken not only with the analysis technique, but also in selecting constitutive models, particularly the instabilities.

• Elastomers and Composites
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• v.33 no.5
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• pp.315-323
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• 1998

The purpose of this study was to investigate the crosslinking density and reinforcement of rubber compounds with various carbon black loadings, cure systems and cure temperatures. Bound rubber content increased with volume fraction of carbon black in rubber compounds, but total crosslinking density decreased with increasing the bound rubber content. Rate constant of cure reaction was changed significantly by cure system and cure temperature, especially it showed strong dependence on the cure temperature. High activation energys of cure reaction were shown in the rubber compound with high loading of carbon black under EC system and in the rubber compound with low loading of carbon black under CC system. High total crosslinking density of vulcanized compounds appeared in the rubber compound with low loading of carbon black and CC system among cure systems. Typical change of total crosslinking density by EC system was not shown. The highest elastic constant by Mooney-Rivlin equation was shown in the rubber compound with low loading of carbon black and SEC system. Modulus increased as increasing the loading of carbon black in the rubber compounds and showed the order of SEC, CC, and EC system for cure system.

• Transactions of the Korean Society of Automotive Engineers
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• v.7 no.5
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• pp.141-153
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• 1999

A finite element procedure for the analysis of rubber-like hyperelastic material is developed. The volumetric incompressiblity conditions of the rubber deformation is included in the formulation by using penalty method. In this paper, the behavior of the rubber deformation is represented by hyperelastic constitutive relations based on a generalized Mooney-Rivlin model. The principle of virtual work is used to derive nonlinear finite element equation for the large displacement problem and presented in total-Lagrangian description. The finite element procedure using analytic differentiation resulted in very close solution to the result of the well known commercial packages NISAII AND ABAQUS. Numerical tests show that the results from the numerical differentiation method coincide very well with those from the analytic method and the well known commercial packages in static analysis. The convergency of rubber usingν iteration method is also discussed.

• The Korean Journal of Rheology
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• v.11 no.1
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• pp.18-27
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• 1999

Predicting the deformation behaviors of sheets in thermoforming processes has been a daunting challenge due to the strong nonlinearities arising from very large deformations, mold-polymer contact condition and hyperelasticity constitutive equations. Nonlinear numerical analysis is always required to face this challenge especially for realistic processing conditions. In this study a 3-D algorithm and the membrane approximation are developed for thermoforming processes. The constitutive equation is expressed in terms of the 2nd Piola-Kirchhoff stress tensor and the Cauchy-Green deformation tensor. The 2-term Mooney-Rivlin model is used for the material model equation. The algorithm is established by the finite element formulation employing the total Lagrangian coordinate. The deformation behavior and the stress distribution results of 3-D algorithm with various point boundary conditions are compared to those of the membrane approximation algorithm. Also, the slip boundary condition and the no-slip boundary condition are applied for the systems that have molds. Finally, the effect of sheet temperatures on the final thickness distribution is investigated for the ABS material.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2009.04a
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• pp.108-108
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• 2009

The main object of this research is to minimize the shock effects which frequently result in fatal damage in wind met mast on impact of barge. The collision between wind met mast and barge is generally a complex problem and it is often not practical to perform rigorous finite element analyses to include all effects and sequences during the collision. LS-dyna generally purpose explicit finite element code, which is a product of ANSYS software, is used to model and analyze the non-linear response of the met mast due to barge collision. A significant part of the collision energy is dissipated as strain energy and except for global deformation modes, the contribution from elastic straining can normally be neglected. On applying impact force of a barge to wind met mast, the maximum acceleration, internal energy and plastic strain were calculated for each load cases using the finite element method and then compare it, varying to the velocity of barge, with one varying to the thickness of rubber fender conditions. Hence, we restrict the present research mainly to the wind met mast and also parametric study has been carried out with various velocities of barge, thickness of wind met mast, thickness and Mooney-Rivlin coefficient of rubber fender with experimental data. The equation of motion of the wind met mast is derived under the assumption that it was ignored vertical movement effect of barge on sea water. Such an analyzing method which was developed so far, make it possible to determine the proper size and material properties of rubber fender and the optimal moving conditions of barge, and finally, application method can be suggested in designing process of rubber fender considering barge impact.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.706-710
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• 2008

The experiment of dome port cover under shock impact is performed with shock tube. The dome port cover blocked intake air duct up from the solid propellant during air breathing vehicle speed reach Mach 2.0. When the air breathing vehicle reach Mach 2.0, the inlet cover is removed and the dome port cover is broken to pieces by detonator or pressure of inlet air. Thus the dome port cover not only must stand the pressure of combustion chamber but also easy to break from the RAM pressure. In this study, a fracture evaluation on the $Al_2O_3$ ceramic spherical dome and circular plate port under impact has been presented. Ceramic were supported by the rigid body and a couple of O-ring. The Mooney-Rivlin model have been used to describe behaviors of both O-ring. And spherical dome and circular plate fracture results of the LS-DYNA code using Johnson-Holmquist(JH-2) constitutive equation was compared.

• Transactions of the Korean Society of Automotive Engineers
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• v.15 no.4
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• pp.10-16
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• 2007

A rubber seal for wheel bearing which has been mainly applied to car wheel supporting device is required to have both high sealing performance and drag torque. Because of severe operational conditions like infiltration of mud or splashed water, the importance of rubber seal which is aimed for leakage prevention of grease and effective blocking of foreign substances has been increasing continuously. The sealing performance of this seal depends on several factors such as materials of seal, friction conditions of contact regions and geometry of seals and so on. We have focused on the effects of geometric characteristics such as the angle of main lip, interference between lip edge and inner metallic ring. In this study, the optimization of geometric variables was performed using the finite element analysis. For the sake of finite element analysis, uniaxial tensile tests were conducted and several constants for Mooney-Rivlin's equation were obtained. According to the results of this study, mock-up bearing was made. To verify this study, drag torque and mud spray test were preformed.