• 호남수학학술지
• /
• 제41권2호
• /
• pp.369-380
• /
• 2019

Inspired by the problem of finding hyperelastic curves in a Riemannian manifold, we present a study on the variational problem of a hyperelastic curve in Lie group. In a Riemannian manifold, we reorganize the characterization of the hyperelastic curve with appropriate constraints. By using this equilibrium equation, we derive an Euler-Lagrange equation for the hyperelastic energy functional defined in a Lie group G equipped with bi-invariant Riemannian metric. Then, we give a solution of this equation for a null hyperelastic Lie quadratic when Lie group G is SO(3).

• Advances in concrete construction
• /
• 제13권5호
• /
• pp.377-384
• /
• 2022

The present paper deals with nonlinear deflection analysis of hyperelastic plates rested on elastic foundation and subject to a transverse point force. For modeling of hyperelastic material, three-parameter Ishihara model has been employed. The plate formulation is based on classic plate theory accounting for von-Karman geometric nonlinearity. Therefore, both material and geometric nonlinearities have been considered based on Ishihara hyperelastic plate model. The governing equations for the plate have been derived based on Hamilton's rule and then solved via Galerkin's method. Obtained results show that material parameters of hyperelastic material play an important role in defection analysis. Also, the effects of foundation parameter and load location on plate deflections will be discussed.

• Journal of applied mathematics & informatics
• /
• 제33권3_4호
• /
• pp.261-273
• /
• 2015

We consider the hyperelastic rod equation describing nonlinear dispersive waves in compressible hyperelastic rods. We investigate the existence of certain traveling wave solutions to this equation. We also determine whether two other equations(the b-family equation and the modified Camassa-Holm equation) have our solution type.

• Structural Engineering and Mechanics
• /
• 제59권4호
• /
• pp.601-619
• /
• 2016

In this study, developments of an efficient visco-hyperelastic constitutive equation for describing the time dependent material behavior accurately in dynamic and impact loading and finding related materials constants are considered. Based on proposed constitutive model, behaviour of a hollow cylinder elastomer bushing under different dynamic and impact loading conditions is studied. By implementing the developed visco-hyperelastic constitutive equation to LS-DYNA explicit dynamic finite element software a three dimensional model of the bushing is developed and dynamic behaviour of that in axial and torsional dynamic deformation modes are studied. Dynamic response and induced stress under different impact loadings which is rarely studied in previous researches have been also investigated. Effects of hyperelastic and visco-hyperelastic parameters on deformation and induced stresses as well as strain rate are considered.

• Tribology and Lubricants
• /
• 제35권5호
• /
• pp.267-273
• /
• 2019

Wheel bearings are important automotive parts that bear the vehicle weight and translate rotation motion; in addition, their seals are components that prevent grease leakage and foreign material from entering from the outside of the bearings. Recently, as the need for electric vehicles and eco-friendly vehicles has been emerging, the reduction in fuel consumption and $CO_2$ emissions are becoming the most important issues for automobile manufacturers. In the case of wheel bearings, seals are a key part of drag torque. In this study, we investigate the prediction of the drag torque taking into consideration the hyperelastic and viscoelastic material properties of automotive wheel bearing seals. Numerical analysis based on the finite element method is conducted for the deformation analyses of the seals. To improve the reliability of the rubber seal analysis, three types of rubber material properties are considered, and analysis is conducted using the hyperelastic material properties. Viscoelastic material property tests are also conducted. Deformation analysis considering the hyperelastic and viscoelastic material properties is performed, and the effects of the viscoelastic material properties are compared with the results obtained by the consideration of the hyperelastic material properties. As a result of these analyses, the drag torque is 0.29 Nm when the hyperelastic characteristics are taken into account, and the drag torque is 0.27 Nm when both the hyperelastic and viscoelastic characteristics are taken into account. Therefore, it is determined that the analysis considering both hyperelastic and viscoelastic characteristics must be performed because of its reliability in predicting the drag torque of the rubber seals.

• Steel and Composite Structures
• /
• 제45권1호
• /
• pp.39-49
• /
• 2022

This research investigates a rotary disk with variable cross-section and incompressible hyperelastic material with functionally graded properties in large hyperelastic deformations. For this purpose, a power relation has been used to express the changes in cross-section and properties of hyperelastic material. So that (m) represents the changes in cross-section and (n) represents the manner of changes in material properties. The constants used for hyperelastic material have been obtained from experimental data. The obtained equations have been solved for different m, n, and (angular velocity) values, and the values of radial stresses, tangential stresses, and elongation have been compared. The results show that m and n have a significant impact on disk behavior, so the expected behavior of the disk can be obtained by an optimal selection of these two parameters.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2001년도 춘계학술대회논문집A
• /
• pp.698-703
• /
• 2001

This paper is concerned with the nonlinear hyperelastic problem fur the incompressible characteristics of the rubber. Tension sensor is a strain gage type load cell element for a fence intrusion detection system and consists of the sensing part and the rubber housing. The analysis includes an elastic analysis and a hyperelastic analysis of a tension sensor for the deformed shape and variation of the maximum strain on the sensing part with respect to the vertical load. Numerical results show that the hyperelastic model is stiffer and less deformed than the elastic model. Comparing with the experimental test data, we know the hyperelastic model is the better approximation than the elastic model.

• Geomechanics and Engineering
• /
• 제7권4호
• /
• pp.335-353
• /
• 2014

The softening hyperelastic model based on the strain energy limitation is of clear concepts and simple forms to describe the failure of materials. In this study, a linear and a nonlinear softening hyperelastic model are proposed to characterize the deformation and the failure in granular materials by introducing a softening function into the shear part of the strain energy. A method to determine material parameters introduced in the models is suggested. Based on the proposed models the numerical examples focus on bearing capacity and strain localization of granular materials. Compared with Volokh softening hyperelasticity and classical Mohr-Coulomb plasticity, our proposed models are able to capture the typical characters of granular materials such as the strain softening and the critical state. In addition, the issue of mesh dependency of the proposed models is investigated.

• Structural Engineering and Mechanics
• /
• 제24권2호
• /
• pp.227-245
• /
• 2006

The performance of a three dimensional non-linear finite element model for hyperelastic material considering the effect of compressibility is studied by analyzing rubber blocks under different modes of deformation. It includes simple tension, pure shear, simple shear, pure bending and a mixed mode combining compression, shear and bending. The compressibility of the hyperelastic material is represented in the strain energy function. The nonlinear formulation is based on updated Lagrangian (UL) technique. The displacement model is implemented with a twenty node brick element having u, ${\nu}$ and w as the degrees of freedom at each node. The results obtained by the present numerical model are compared with the analytical solutions available for the basic modes of deformation where the agreement between the results is found to be satisfactory. In this context some new results are generated for future references since the number of available results on the present problem is not sufficient enough.

• 융복합기술연구소 논문집
• /
• 제7권2호
• /
• pp.13-16
• /
• 2017

The design of sealing mechanisms of a manual pressure valve was analyzed with FE analysis for a hydrogen fuels charge and discharge system of FCEV. The damage prediction of the O-ring with respect to the material models of rubbers was calculated by the gap analysis of the backup ring and O-ring according to the internal pressure. Two kinds of the rubber material characteristic models were adopted to the O-ring. One was the linear elastic and the other was hyperelastic of Ogden $3^{rd}$ order model. The experimental data of urethane of Shore hardness 90 was utilized to the curve fitting of hyperelastic properties. It was found that the contact pattern of the backup ring was different in two models and the sealing mechanism was better in the case of the hyperelastic characteristic model.