A Microstructurally Based Orthotropic Hyperelastic Constitutive Law

2002 ◽  
Vol 69 (5) ◽  
pp. 570-579 ◽  
Author(s):  
J. E. Bischoff ◽  
E. A. Arruda ◽  
K. Grosh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Constitutive Model ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Entropy Change ◽  
Constitutive Law ◽  
Elastic Behavior ◽  
The Finite Element Method

A constitutive model is developed to characterize a general class of polymer and polymer-like materials that displays hyperelastic orthotropic mechanical behavior. The strain energy function is derived from the entropy change associated with the deformation of constituent macromolecules and the strain energy change associated with the deformation of a representative orthotropic unit cell. The ability of this model to predict nonlinear, orthotropic elastic behavior is examined by comparing the theory to experimental results in the literature. Simulations of more complicated boundary value problems are performed using the finite element method.

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.

Extending Marlow’s general first-invariant constitutive model to compressible, isotropic hyperelastic materials

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Florian Hüter ◽  
Frank Rieg
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Test Data ◽  
Curve Fitting ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Content Type ◽  
Hyperelastic Materials ◽  
Fitting Procedures

Purpose A general first-invariant constitutive model has been derived in literature for incompressible, isotropic hyperelastic materials, known as Marlow model, which reproduces test data exactly without the need of curve-fitting procedures. This paper aims to describe how to extend Marlow’s constitutive model to the more general case of compressible hyperelastic materials. Design/methodology/approach The isotropic constitutive model is based on a strain energy function, whose isochoric part is solely dependent on the first modified strain invariant. Based on Marlow’s idea, a principle of energetically equivalent deformation states is derived for the compressible case, which is used to determine the underlying strain energy function directly from measured test data. No particular functional of the strain energy function is assumed. It is shown how to calibrate the volumetric and isochoric strain energy functions uniquely with uniaxial or biaxial test data only. The constitutive model is implemented into a finite element program to demonstrate its applicability. Findings The model is well suited for use in finite element analysis. Only one set of test data is required for calibration without any need for curve-fitting procedures. These test data are reproduced exactly, and the model prediction is reasonable for other deformation modes. Originality/value Marlow’s basic concept is extended to the compressible case and applied to both the volumetric and isochoric part of the compressible strain energy function. Moreover, a novel approach is described on how both compressive and tensile test data can be used simultaneously to calibrate the model.

Stress Analysis of a Tire Under Vertical Load by a Finite Element Method

1977 ◽  
Vol 5 (2) ◽  
pp. 102-118 ◽  
Author(s):  
H. Kaga ◽  
K. Okamoto ◽  
Y. Tozawa
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computer Program ◽  
Temperature Rise ◽  
Strain Energy ◽  
Internal Stresses ◽  
Vertical Load ◽  
The Finite Element Method ◽  
Internal Temperature ◽  
Element Method

Abstract An analysis by the finite element method and a related computer program is presented for an axisymmetric solid under asymmetric loads. Calculations are carried out on displacements and internal stresses and strains of a radial tire loaded on a road wheel of 600-mm diameter, a road wheel of 1707-mm diameter, and a flat plate. Agreement between calculated and experimental displacements and cord forces is quite satisfactory. The principal shear strain concentrates at the belt edge, and the strain energy increases with decreasing drum diameter. Tire temperature measurements show that the strain energy in the tire is closely related to the internal temperature rise.

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.

Structural Stiffness of Tire Calculated From Strain Energy

2015 ◽  
Author(s):  
Namcheol Kang ◽  
Jong-Jin Bae ◽  
Jong Beom Suh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Energy Method ◽  
Strain Energy ◽  
Vertical Force ◽  
Structural Stiffness ◽  
Contribution Ratio ◽  
The Finite Element Method ◽  
Vertical Stiffness ◽  
Strain Energy Method

The vertical stiffness of a tire is the ratio of the vertical force to the deflection; it can be expressed as the summation of the structural stiffness and air stiffness. However, the calculation of the structural stiffness is a challenging topic. This paper presents a new methodology for extracting the structural stiffness from the strain energy of a regular tire. In order to verify our proposed method, the vertical force-deflection results from the finite element method is compared with those from the strain energy method at zero air pressure. Also the results for an inflated tire are compared to calculate the structural stiffness. Finally, we calculated the contribution ratio of the tire components and used an alternative way of extracting the structural stiffness based on changing the Young’s modulus.

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

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