Research on Thermal Mechanical Properties of Rubber Like Materials Based on Numerical Simulation

2011 ◽  
Vol 704-705 ◽  
pp. 811-816
Author(s):  
Jian Bin Sang ◽  
Wen Ying Yu ◽  
Bo Liu ◽  
Xiao Lei Li ◽  
Tie Feng Liu
Keyword(s):  
Finite Element ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Mechanical Analysis ◽  
Nonlinear Finite Element ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Rubber Seal ◽  
Thermal Mechanical Analysis

This paper start with a discussion on various types of strain energy functions of rubber like materials. Theoretical analysis based on the strain energy function given in by Y.C.Gao in 1997 is proposed. The material parameters of strain energy function were curve-fitted from the uniaxial tensile test. The selected constitutive relation of rubber like materials was implemented into a finite element code MSC.Marc as a user material subroutine to analyze the thermal and mechanical behavior of rubber seal under the plane strain conditions. Contact force and distribution of the contact stress between lip seal and shaft are analyzed and coupled thermal mechanical analysis of rubber seal was proposed. The contact pressure distribution is readily obtainable from the nonlinear finite element analysis and the coupled thermal mechanical analyses results indicate that the thermal stress only have minor influence on the deformed shape of rubber seal, which will be a useful technique for predicting the properties of rubber seal and providing reference for engineering design. Keywords:rubber like materials, nonlinear finite element, contact analysis, thermal mechanical analysis

scholarly journals DEVELOPMENT OF OPEN SOURCE FINITE ELEMENT SOLVER “LD-FEM’ FOR MODELING AND SIMULATION OF RUBBER MATERIALS

ROTASI ◽  
2014 ◽  
Vol 16 (3) ◽  
pp. 10
Author(s):  
Sugeng Waluyo
Keyword(s):  
Finite Element ◽  
Open Source ◽  
Large Deformation ◽  
Strain Energy ◽  
Nonlinear Behavior ◽  
Strain Energy Function ◽  
Numerical Approach ◽  
Uniaxial Tensile ◽  
Material Stiffness ◽  
Loading Tests

“LD-FEM” is an open source computer program working on the basis of finite element method (FEM) which is aimed to model and simulate large deformation in rubber materials. The kinematics of large deformation on the basis of the Total Lagrange framework is applied to linear 4-nodes tetrahedral element and then solved with Newton-Raphson iterative scheme. Furthermore, to obtain the material tangent stiffness directly from strain energy density functions, the Gill-Murray theory of numerical second derivative is used in LD-FEM. Finally, by using the Mooney-Rivlin strain energy function, the performance of LD-FEM is addressed for uniaxial tensile, shear and torsion loading tests. The results confirm the capability of LD-FEM to capture nonlinear behavior of the large deformation either with analytical or numerical approach on the material stiffness derivation with error less than 2%.

An Extended Tube-Model for Rubber Elasticity: Statistical-Mechanical Theory and Finite Element Implementation

1999 ◽  
Vol 72 (4) ◽  
pp. 602-632 ◽  
Author(s):  
M. Kaliske ◽  
G. Heinrich
Keyword(s):  
Finite Element ◽  
Parameter Identification ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Rubber Elasticity ◽  
Experimental Investigations ◽  
Structural Level ◽  
Tube Model ◽  
Starting Point

Abstract A novel model of rubber elasticity—the extended tube-model—is introduced. The model considers the topological constraints as well as the limited chain extensibility of network chains in filled rubbers. It is supplied by a formulation suitable for an implementation into a finite element code. Homogeneous states of deformation are evaluated analytically to yield expressions required e.g., for parameter identification algorithms. Finally, large scale finite element computations compare the extended tube-model with experimental investigations and with the phenomenological strain energy function of the Yeoh-model. The extended tube-model can be considered as an interesting approach introducing physical considerations on the molecular scale into the formulation of the strain energy function which is on the other hand the starting point for the numerical realization on the structural level. Thus, the gap between physics and numerics is bridged. Nevertheless, this study reveals the importance of a proper parameter identification and adapted experiments.

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.

The Cosserat Point Element as an Accurate and Robust Finite Element Formulation for Implicit Dynamic Simulations

2019 ◽  
Vol 17 (01) ◽  
pp. 1844006
Author(s):  
Mahmood Jabareen ◽  
Yehonatan Pestes
Keyword(s):  
Finite Element ◽  
Energy Function ◽  
Strain Energy ◽  
Three Dimensional ◽  
Nonlinear Dynamic Analysis ◽  
Strain Energy Function ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Dynamic Simulations ◽  
Cosserat Point

The reliability of numerical simulations manifested the need for an accurate and robust finite element formulation. Therefore, in the present study, an eight node brick Cosserat point element ( CPE ) for the nonlinear dynamic analysis of three-dimensional (3D) solids including both thick and thin structures is developed. Within the present finite element formulation, a strain energy function is proposed and additively decoupled into two parts. One part is characterized by any 3D strain energy function, while the other part controls the response to inhomogeneous deformations. Several example problems are presented, which demonstrate the accuracy and the robustness of the developed CPE in modeling the dynamic response of elastic structures.

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.

A Simplified Strain Energy Function to Represent the Mechanical Behavior of the Annulus Fibrosus

2009 ◽  
Author(s):  
Jose J. García ◽  
Christian Puttlitz
Keyword(s):  
Finite Element ◽  
Mechanical Behavior ◽  
Energy Function ◽  
Annulus Fibrosus ◽  
Strain Energy ◽  
Degrees Of Freedom ◽  
Strain Energy Function ◽  
Efficient Simulation ◽  
Matrix Interactions ◽  
Complex Functions

Models to represent the mechanical behavior of the annulus fibrosus are important tools to understand the biomechanics of the spine. Many hyperelastic constitutive equations have been proposed to simulate the mechanical behavior of the annulus that incorporate the anisotropic nature of the tissue. Recent approaches [1,2] have included terms into the energy function which take into account fiber-fiber and fiber-matrix interactions, leading to complex functions that cannot be readily implemented into commercial finite element codes for an efficient simulation of nonlinear realistic models of the spine (which are generally composed of 100,000+ degrees of freedom). An effort is undertaken here to test the capability of a relatively simple strain energy function [3] for the description of the annulus fibrosus. This function has already been shown to successfully represent the mechanical behavior of the arterial tissue and can be readily implemented into existing finite element codes.

3D Mechanical Properties of the Layered Esophagus: Experiment and Constitutive Model

2006 ◽  
Vol 128 (6) ◽  
pp. 899-908 ◽  
Author(s):  
W. Yang ◽  
T. C. Fung ◽  
K. S. Chian ◽  
C. K. Chong
Keyword(s):  
Constitutive Model ◽  
Fiber Orientation ◽  
Strain Energy ◽  
Physiological State ◽  
Three Dimensional ◽  
Strain Energy Function ◽  
Esophageal Wall ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Esophageal Diseases

The identification of a three dimensional constitutive model is useful for describing the complex mechanical behavior of a nonlinear and anisotropic biological tissue such as the esophagus. The inflation tests at the fixed axial extension of 1, 1.125, and 1.25 were conducted on the muscle and mucosa layer of a porcine esophagus separately and the pressure-radius-axial force was recorded. The experimental data were fitted with the constitutive model to obtain the structure-related parameters, including the collagen amount and fiber orientation. Results showed that a bilinear strain energy function (SEF) with four parameters could fit the inflation data at an individual extension very well while a six-parameter model had to be used to capture the inflation behaviors at all three extensions simultaneously. It was found that the collagen distribution was axial preferred in both layers and the mucosa contained more collagen, which were in agreement with the findings through a pair of uniaxial tensile test in our previous study. The model was expected to be used for the prediction of stress distribution within the esophageal wall under the physiological state and provide some useful information in the clinical studies of the esophageal diseases.

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