A Simple Transversely Isotropic Hyperelastic Constitutive Model Suitable for Finite Element Analysis of Fiber Reinforced Elastomers

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Leslee W. Brown ◽  
Lorenzo M. Smith
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Material Model ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
Material Tests

A transversely isotropic fiber reinforced elastomer’s hyperelasticity is characterized using a series of constitutive tests (uniaxial tension, uniaxial compression, simple shear, and constrained compression test). A suitable transversely isotropic hyperelastic invariant based strain energy function is proposed and methods for determining the material coefficients are shown. This material model is implemented in a finite element analysis by creating a user subroutine for a commercial finite element code and then used to analyze the material tests. A useful set of constitutive material data for multiple modes of deformation is given. The proposed strain energy function fits the experimental data reasonably well over the strain region of interest. Finite element analysis of the material tests reveals further insight into the materials constitutive nature. The proposed strain energy function is suitable for finite element use by the practicing engineer for small to moderate strains. The necessary material coefficients can be determined from a few simple laboratory tests.

Finite Element Analysis by Using Hyper-Elastic Properties for Rubber Component

2011 ◽  
Vol 488-489 ◽  
pp. 190-193
Author(s):  
Chang Su Woo ◽  
Hyun Sung Park ◽  
Wae Gi Shin
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Element Analysis ◽  
Energy Functions ◽  
Hyper Elastic ◽  
Rubber Component ◽  
Strain Energy Functions

The material modeling of hyper-elastic properties in rubber is generally characterized by the strain energy function. The strain energy functions have been represented either in term of the strain in variants that are functions of the stretch ratios, or directly in terms of the principal stretch. Successful modeling and design of rubber components relies on both the selection of an appropriate strain energy function and an accurate determination of material constants in the function. Material constants in the strain energy functions can be determined from the curve fitting of experimental stress-strain data. The uniaxial tension, equi-biaxial tension and pure shear test were performed to acquire the constants of the strain energy functions which were Mooney-Rivlin and Ogden model. Nonlinear finite element analysis was executed to evaluate the behavior of deformation and strain distribute by using the commercial finite element code. Also, the fatigue tests were carried out to obtain the fatigue failure. Fatigue failure was initiated at the critical location was observed during the fatigue test of rubber component, which was the same result predicted by the finite element analysis.

Nonlinear Finite Element Analysis of Crack Tip of Rubber-Like Material

2007 ◽  
Vol 353-358 ◽  
pp. 1013-1016
Author(s):  
Jian Bing Sang ◽  
Su Fang Xing ◽  
Xiao Lei Li ◽  
Jie Zhang
Keyword(s):  
Finite Element ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Elastic Behavior ◽  
Element Analysis ◽  
Finite Element Program ◽  
User Subroutine ◽  
Element Program ◽  
Notch Tip

It has been well known that rubber-like material can undergo large deformation and exhibit large nonlinear elastic behavior. Because of the geometrically nonlinear of rubber like material, it is more difficult to analyze it with finite element near the notch tip. What is more, because there are varieties of the strain energy functions, implementation of these models in a general finite element program to meet the need of industry applications can be time consuming. In order to make use of the constitutive equation of Y.C. Gao in 1997 and analyze the notch tip of rubber-like material, a framework to implement the rubber-like material model is established within the general-purpose finite element program MSC.Marc. It will be very convenient to implement this isotropic hyperelastic model into the program with a user subroutine. This paper starts with the theoretical analysis based on the strain energy function given by Y.C. Gao in 1997. A user subroutine is programmed to implement this strain energy function into the program of MSC.Marc, which offer a convenient method to analyze the stress and strain of rubber-like material with the strain energy function that is needed. Though analysis with MSC.Marc, it is found that the result with finite element is consistent with the analytical result that given by Y.C. Gao in 1997, which testify that analyzing rubber like material with this method is reasonable and convenient.

On the Ogden Strain-Energy Function

1997 ◽  
Vol 70 (2) ◽  
pp. 175-182 ◽  
Author(s):  
O. H. Yeoh
Keyword(s):  
Regression Analysis ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Material Model ◽  
Nonlinear Regression Analysis ◽  
Element Analysis ◽  
Strain Data ◽  
Predicting Behavior ◽  
Deformation Modes

Abstract The Ogden strain-energy function for rubber appears to be gaining popularity among users of finite element analysis. This paper discusses some of the special features of this material model. It explains why nonlinear regression analysis of stress-strain data obtained from just one mode of deformation may yield an Ogden strain-energy function that is unsatisfactory for predicting behavior in other deformation modes. It suggests the regression analysis be constrained such that some of the coefficients are chosen based upon the known behavior of rubbery materials.

Lifetime Prediction of Tires with Regard to Oxidative Aging5

2008 ◽  
Vol 36 (1) ◽  
pp. 63-79 ◽  
Author(s):  
L. Nasdala ◽  
Y. Wei ◽  
H. Rothert ◽  
M. Kaliske
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Temperature Distribution ◽  
Superposition Principle ◽  
Accelerated Aging ◽  
Material Model ◽  
Aging Behavior ◽  
Element Analysis ◽  
Material Parameters ◽  
Reaction Processes

Abstract It is a challenging task in the design of automobile tires to predict lifetime and performance on the basis of numerical simulations. Several factors have to be taken into account to correctly estimate the aging behavior. This paper focuses on oxygen reaction processes which, apart from mechanical and thermal aspects, effect the tire durability. The material parameters needed to describe the temperature-dependent oxygen diffusion and reaction processes are derived by means of the time–temperature–superposition principle from modulus profiling tests. These experiments are designed to examine the diffusion-limited oxidation (DLO) effect which occurs when accelerated aging tests are performed. For the cord-reinforced rubber composites, homogenization techniques are adopted to obtain effective material parameters (diffusivities and reaction constants). The selection and arrangement of rubber components influence the temperature distribution and the oxygen penetration depth which impact tire durability. The goal of this paper is to establish a finite element analysis based criterion to predict lifetime with respect to oxidative aging. The finite element analysis is carried out in three stages. First the heat generation rate distribution is calculated using a viscoelastic material model. Then the temperature distribution can be determined. In the third step we evaluate the oxygen distribution or rather the oxygen consumption rate, which is a measure for the tire lifetime. Thus, the aging behavior of different kinds of tires can be compared. Numerical examples show how diffusivities, reaction coefficients, and temperature influence the durability of different tire parts. It is found that due to the DLO effect, some interior parts may age slower even if the temperature is increased.

scholarly journals Finite Element Analysis for Nonlinear Unbonded Circular Fiber-Reinforced Elastomeric Bearings

2021 ◽  
Vol 5 (7) ◽  
pp. 170
Author(s):  
Pablo Castillo Ruano ◽  
Alfred Strauss
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Carbon Fiber ◽  
Seismic Isolation ◽  
Nonlinear Viscoelasticity ◽  
Fiber Reinforcement ◽  
Special Focus ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
Elastomeric Bearings

In recent years, interest in low-cost seismic isolation systems has increased. The replacement of the steel reinforcement in conventional elastomeric bearings for a carbon fiber reinforcement is a possible solution and has garnered increasing attention. To investigate the response of fiber-reinforced elastomeric bearings (FREBs) under seismic loads, it is fundamental to understand its mechanical behavior under combined vertical and horizontal loads. An experimental investigation of the components presents complexities due to the high loads and displacements tested. The use of a finite element analysis can save time and resources by avoiding partially expensive experimental campaigns and by extending the number of geometries and topologies to be analyzed. In this work, a numerical model for carbon fiber-reinforced bearings is implemented, calibrated, and validated and a set of virtual experiments is designed to investigate the behavior of the bearings under combined compressive and lateral loading. Special focus is paid to detailed modeling of the constituent materials. The elastomeric matrix is modeled using a phenomenological rheological model based on the hyperelastic formulation developed by Yeoh and nonlinear viscoelasticity. The model aims to account for the hysteretic nonlinear hyper-viscoelastic behavior using a rheological formulation that takes into consideration hyperelasticity and nonlinear viscoelasticity and is calibrated using a series of experiments, including uniaxial tension tests, planar tests, and relaxation tests. Special interest is paid to capturing the energy dissipated in the unbonded fiber-reinforced elastomeric bearing in an accurate manner. The agreement between the numerical results and the experimental data is assessed, and the influence of parameters such as shape factor, aspect ratio, vertical pressure, and fiber reinforcement orientation on stress distribution in the bearings as well as in the mechanical properties is discussed.

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