A Novel Constitutive Formulation for Rubberlike Materials in Thermoelasticity

2013 ◽  
Vol 81 (4) ◽  
Author(s):  
Zhu-Ping Huang
Keyword(s):  
Energy Function ◽  
Strain Energy ◽  
Coupling Effect ◽  
Constitutive Relations ◽  
Strain Energy Function ◽  
Mechanical Coupling ◽  
Material Parameters ◽  
Incompressible Materials ◽  
Gent Model ◽  
Rubberlike Materials

The objective of this paper is to present a new framework to formulate thermoelastic constitutive relations for initially isotropic rubberlike materials undergoing finite deformations. The strain-energy function for incompressible materials is extended to include the effects of compressibility and temperature changes. The novelty of this framework is that only a few material functions and material parameters to be fitted with the experimental data are required, and these functions and parameters have clear physical meaning. In order to validate the proposed formulation, the Gent–Gent model for incompressible rubbers is chosen as an illustrative example. A new expression of the Helmholtz free energy of rubberlike materials, which takes into account the material compressibility and thermal effect, is then derived. In this generalized Gent–Gent model, only one material function and six material parameters are introduced. It is shown that the generalized Gent–Gent model can be used to predict the stress-strain behavior over the entire range of deformation. Even for incompressible materials, the strain-energy function in this paper is different from that given by Gent himself. The generalized Gent–Gent model can also adequately describe the thermal-mechanical coupling effect, in which thermoelastic inversion phenomena occur.

scholarly journals Modelling the Inflation and Elastic Instabilities of Rubber-Like Spherical and Cylindrical Shells Using a New Generalised Neo-Hookean Strain Energy Function

2021 ◽  
Author(s):  
Afshin Anssari-Benam ◽  
Andrea Bucchi ◽  
Giuseppe Saccomandi
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Limit Point ◽  
Strain Energy ◽  
Cylindrical Shells ◽  
Strain Energy Function ◽  
Model Parameters ◽  
Wide Range ◽  
Cylindrical Tubes ◽  
Gent Model

AbstractThe application of a newly proposed generalised neo-Hookean strain energy function to the inflation of incompressible rubber-like spherical and cylindrical shells is demonstrated in this paper. The pressure ($P$ P ) – inflation ($\lambda $ λ or $v$ v ) relationships are derived and presented for four shells: thin- and thick-walled spherical balloons, and thin- and thick-walled cylindrical tubes. Characteristics of the inflation curves predicted by the model for the four considered shells are analysed and the critical values of the model parameters for exhibiting the limit-point instability are established. The application of the model to extant experimental datasets procured from studies across 19th to 21st century will be demonstrated, showing favourable agreement between the model and the experimental data. The capability of the model to capture the two characteristic instability phenomena in the inflation of rubber-like materials, namely the limit-point and inflation-jump instabilities, will be made evident from both the theoretical analysis and curve-fitting approaches presented in this study. A comparison with the predictions of the Gent model for the considered data is also demonstrated and is shown that our presented model provides improved fits. Given the simplicity of the model, its ability to fit a wide range of experimental data and capture both limit-point and inflation-jump instabilities, we propose the application of our model to the inflation of rubber-like materials.

A note on the finite plane-strain equations for isotropic incompressible materials

1955 ◽  
Vol 51 (2) ◽  
pp. 363-367 ◽  
Author(s):  
J. E. Adkins
Keyword(s):  
Differential Equations ◽  
Plane Strain ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Theory Of Elasticity ◽  
Finite Plane ◽  
Incompressible Materials ◽  
Stress Components ◽  
Strain Invariants

For elastic deformations beyond the range of the classical infinitesimal theory of elasticity, the governing differential equations are non-linear in form, and orthodox methods of solution are not usually applicable. Simplifying features appear, however, when a restriction is imposed either upon the form of the deformation, or upon the form of strain-energy function employed to define the elastic properties of the material. Thus in the problems of torsion and flexure considered by Rivlin (4, 5, 6) it is possible to avoid introducing partial differential equations into the analysis, while in the theory of finite plane strain developed by Adkins, Green and Shield (1) the reduction in the number of dependent and independent variables involved introduces some measure of simplicity. Some further simplification is achieved when the strain-energy function can be considered as a linear function of the strain invariants as postulated by Mooney(2) for incompressible materials. In the present paper the plane-strain equations for a Mooney material are reduced to symmetrical forms which do not involve the stress components, and some special solutions of these equations are derived.

Application and Research of Numerical Simulation for Rubber Like Material with MSC.Marc

2008 ◽  
Vol 575-578 ◽  
pp. 854-858
Author(s):  
Jian Bing Sang ◽  
Bo Liu ◽  
Zhi Liang Wang ◽  
Su Fang Xing ◽  
Jie Chen
Keyword(s):  
Numerical Simulation ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Stress And Strain ◽  
Perfect Agreement ◽  
Energy Functions ◽  
Material Parameters ◽  
User Subroutine ◽  
Strain Energy Functions

This paper starts with a discussion on the theory of finite deformation and various types strain energy functions of rubber like material, the material parameter of elastic law of Gao[3] is estimated by experiment and numerical simulation. Because there are various types of strain energy functions, a user subroutine is programmed to implement the strain energy function of Gao[3] into the program of MSC.Marc, which offers a convenient method to analyze the stress and strain of rubber-like material with the strain energy function that is needed. Two examples will be presented in this paper to demonstrate the use of the framework for rubber like materials. One is to simulate a foam tube in compression. The other one is to simulate a rectangle board with a circular hole. After numerical analysis, it is proved the numerical results based on Gao model are in perfect agreement with the results based on Mooney model and the estimated material parameters are valid.

Finite Deformation Analysis and Numerical Simulation of Arterial Wall

2013 ◽  
Vol 300-301 ◽  
pp. 1636-1639
Author(s):  
Jian Bing Sang ◽  
Li Fang Sun ◽  
Lan Lan Ge ◽  
Zhong Kai Zhang ◽  
Dong Ling Zhang ◽  
...  
Keyword(s):  
Theoretical Analysis ◽  
Energy Function ◽  
Finite Deformation ◽  
Radial Stress ◽  
Strain Energy ◽  
Arterial Wall ◽  
Circumferential Stress ◽  
Strain Energy Function ◽  
Deformation Analysis ◽  
Gent Model

Based on Gent model, a new strain energy function is developed for the description of mechanical response of arterial wall, which fulfills the requirement that in the rigid condition and will thansform into Gent model when . By utilizing the modified strain energy function, inflation of arterial wall by internal pressure is researched. Stress distribution through the deformed arterial wall at cylindrical system is achieved based finite deformation theory. In order to analyze the deformation and stress field of arterial wall at different blood pressure, a user subroutine is programmed to implement the modified strain energy function from Gent into the program of MSC.Marc,. The results show that maximum radial stress and maximum circumferential stress all appear at inside wall. In the meanwhile, radial stress and circumferential stress become smaller along the wall thickness from inside to outside. It can seen the results of finite element analysis of arterial wall are accordant to the result of theoretical analysis, which approves that theoretical analysis is correct.

Application of Finite Elastic Theory to the Behavior of Rubberlike Materials

1963 ◽  
Vol 36 (5) ◽  
pp. 1459-1496 ◽  
Author(s):  
Paul J. Blatz
Keyword(s):  
Energy Function ◽  
Strain Energy ◽  
Mechanical Response ◽  
Finite Elasticity ◽  
Strain Energy Function ◽  
Elastic Theory ◽  
Mechanical Parameters ◽  
Molecular Interpretation ◽  
Rubberlike Materials

Abstract A brief review of the theory of finite elasticity is presented. The theory is applied to the characterization of the mechanical response parameters of a polyurethan foam. The incorporation of compressibility and anisotropy effects into the strain energy function are discussed. An example of the behavior of a composite or filled foam is presented. Finally some of the problems associated with the molecular interpretation of mechanical parameters are discussed.

MULTIAXIAL STRAIN ENERGY FUNCTIONS OF RUBBERLIKE MATERIALS: AN EXPLICIT APPROACH BASED ON POLYNOMIAL INTERPOLATION

2014 ◽  
Vol 87 (1) ◽  
pp. 168-183 ◽  
Author(s):  
Xiao-Ming Wang ◽  
Hao Li ◽  
Zheng-Nan Yin ◽  
Heng Xiao
Keyword(s):  
Energy Function ◽  
Strain Energy ◽  
Polynomial Interpolation ◽  
Strain Energy Function ◽  
Shear Plane ◽  
Unknown Parameters ◽  
Energy Functions ◽  
Explicit Approach ◽  
Strain Energy Functions ◽  
Rubberlike Materials

ABSTRACT We propose an explicit approach to obtaining multiaxial strain energy functions for incompressible, isotropic rubberlike materials undergoing large deformations. Via polynomial interpolation, we first obtain two one-dimensional strain energy functions separately from uniaxial data and shear data, and then, from these two, we obtain a multiaxial strain energy function by means of direct procedures based on well-designed logarithmic invariants. This multiaxial strain energy function exactly fits any given data from four benchmark tests, including uniaxial and equibiaxial extension, simple shear, plane–strain extension, and so forth. Furthermore, its predictions for biaxial stretch tests provide good accord with test data. The proposed approach is explicit in a sense without involving the usual procedures both in deriving forms of the multiaxial strain energy function and in estimating a number of unknown parameters.

An Anisotropic Hyperelastic Constitutive Model With Fiber-Matrix Shear Interaction for the Human Annulus Fibrosus

2005 ◽  
Vol 73 (5) ◽  
pp. 815-824 ◽  
Author(s):  
X. Q. Peng ◽  
Z. Y. Guo ◽  
B. Moran
Keyword(s):  
Constitutive Model ◽  
Energy Function ◽  
Annulus Fibrosus ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Material Parameters ◽  
The Matrix ◽  
Fiber Matrix ◽  
Matrix Shear ◽  
Fiber Interaction

Based on fiber reinforced continuum mechanics theory, an anisotropic hyperelastic constitutive model for the human annulus fibrosus is developed. A strain energy function representing the anisotropic elastic material behavior of the annulus fibrosus is additively decomposed into three parts nominally representing the energy contributions from the matrix, fiber and fiber-matrix shear interaction, respectively. Taking advantage of the laminated structure of the annulus fibrosus with one family of aligned fibers in each lamella, interlamellar fiber-fiber interaction is eliminated, which greatly simplifies the constitutive model. A simple geometric description for the shearing between the fiber and the matrix is developed and this quantity is used in the representation of the fiber-matrix shear interaction energy. Intralamellar fiber-fiber interaction is also encompassed by this interaction term. Experimental data from the literature are used to obtain the material parameters in the constitutive model and to provide model validation. Determination of the material parameters is greatly facilitated by the partition of the strain energy function into matrix, fiber and fiber-matrix shear interaction terms. A straightforward procedure for computation of the material parameters from simple experimental tests is proposed.

scholarly journals Importance of material parameters and strain energy function on the wall stresses in the left ventricle

2017 ◽  
Vol 20 (11) ◽  
pp. 1223-1232 ◽  
Author(s):  
Sareh Behdadfar ◽  
Laurent Navarro ◽  
Joakim Sundnes ◽  
Molly M. Maleckar ◽  
Stéphane Avril
Keyword(s):  
Left Ventricle ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Material Parameters
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