A Parametric Investigation on the Neo-Hookean Material Constant

2014 ◽  
Vol 915-916 ◽  
pp. 853-857 ◽  
Author(s):  
Siti Hajar Mohd Yusop ◽  
Mohd Nor Azmi Ab Patar ◽  
Anwar P.P. Abdul Majeed ◽  
Jamaluddin Mahmud
Keyword(s):  
Constitutive Equation ◽  
Material Properties ◽  
Parametric Study ◽  
Strain Energy ◽  
Deformation Behaviour ◽  
Strain Energy Function ◽  
Material Constant ◽  
Hyperelastic Materials ◽  
Material Parameters ◽  
To Come

This paper assesses the Neo-Hookean material parameters pertaining to deformation behaviour of hyperelastic material by means of numerical analysis. A mathematical model relating stress and stretch is derived based on Neo-Hookeans strain energy function to evaluate the contribution of the material constant, C1, in the constitutive equation by varying its value. A systematic parametric study was constructed and for that purpose, a Matlab programme was developed for execution. The results show that the parameter (C1) is significant in describing material properties behaviour. The results and findings of the current study further enhances the understanding of Neo-Hookean model and hyperelastic materials behaviour. The ultimate future aim of this study is to come up with an alternative constitutive equation that may describe skin behaviour accurately. This study is novel as no similar parametric study on Neo-Hookean model has been reported before.

scholarly journals Generalized shear deformations for isotropic incompressible hyperelastic materials

1977 ◽  
Vol 20 (2) ◽  
pp. 129-141 ◽  
Author(s):  
James M. Hill
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Shear Deformations ◽  
Partial Differential ◽  
Hyperelastic Materials ◽  
Restricted Form ◽  
Consistent Solution

AbstractFor isotropic incompressible hyperelastic materials the single function characterizing generalized shear deformations or as they are sometimes called anti-plane strain deformations must satisfy two distinct partial differential equations. Knowles [5] has recently given a necessary and sufficient condition for the strain–energy function of the material which if satisfied ensures that the two equations have consistent solutions. It is shown here for the general material not satisfying Knowles' criterion that the only possible consistent solution of the two partial differential equations are those which are already known to exist for all strain–energy functions. More general types of generalized shear deformations for such meterials are shown to exist only for special or restricted form ot the strain-energy function. In derving these results we also obtain an alternative derivation of Knowles' criterion.

On the Development of Volumetric Strain Energy Functions

1999 ◽  
Vol 67 (1) ◽  
pp. 17-21 ◽  
Author(s):  
S. Doll ◽  
K. Schweizerhof
Keyword(s):  
Strain Energy ◽  
Volumetric Strain ◽  
Strain Energy Function ◽  
Material Behavior ◽  
Additional Material ◽  
Energy Functions ◽  
Material Parameters ◽  
Physical Conditions ◽  
Starting Point ◽  
Strain Energy Functions

To describe elastic material behavior the starting point is the isochoric-volumetric decoupling of the strain energy function. The volumetric part is the central subject of this contribution. First, some volumetric functions given in the literature are discussed with respect to physical conditions, then three new volumetric functions are developed which fulfill all imposed conditions. One proposed function which contains two material parameters in addition to the compressibility parameter is treated in detail. Some parameter fits are carried out on the basis of well-known volumetric strain energy functions and experimental data. A generalization of the proposed function permits an unlimited number of additional material parameters.  Dedicated to Professor Franz Ziegler on the occasion of his 60th birthday. [S0021-8936(00)00901-6]

Finite Bending and Straightening of Hyperelastic Materials: Analytical Solution and FEM

2019 ◽  
Vol 11 (09) ◽  
pp. 1950084 ◽  
Author(s):  
Sara Sheikhi ◽  
Mohammad Shojaeifard ◽  
Mostafa Baghani
Keyword(s):  
Finite Element ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Optimization Procedure ◽  
Element Analysis ◽  
Energy Functions ◽  
Hyperelastic Materials ◽  
Finite Bending ◽  
Strain Energy Functions ◽  
Analytical Approaches

In this research, an incompressible, isotropic, nonlinear elastic rectangular block and a circular cylindrical sector are studied under bending and straightening moments, respectively. Analytical approaches are presented on implementing of the left Cauchy–Green tensor and Cauchy stresses. In addition, finite element analysis of both problems is carried out using UHYPER user-defined subroutine in ABAQUS to verify the analytical methods. Four different invariant-based strain energy functions, including neo-Hookean, Mooney–Rivlin, Arruda–Boyce, and recently proposed polynomial Exp-Exp models, are examined, and the results are compared. Material parameters of silicon rubber for the strain energy functions are identified by applying an optimization procedure. Finite element method results confirmed the analytical approach with great compatibility. Results showed that the length of the unbent beam does not affect the stress. Likewise, the initial angle of curved structure does not affect the unbending moment and stresses. Moreover, the Exp-Exp model had a slightly different result rather than other strain energies, which means that this model is more conservative than its counterparts. Furthermore, the Exp-Exp strain energy function is calibrated for tissue-like phantom and is compared with experimental data.

scholarly journals Residually Stressed Fiber Reinforced Solids: A Spectral Approach

Materials ◽  
2020 ◽  
Vol 13 (18) ◽  
pp. 4076
Author(s):  
Mohd Halim Bin Mohd Shariff ◽  
Jose Merodio
Keyword(s):  
Constitutive Equation ◽  
Energy Function ◽  
Strain Energy ◽  
Finite Strain ◽  
Strain Energy Function ◽  
Spectral Approach ◽  
Fiber Reinforced ◽  
Elastic Solids ◽  
Preferred Direction ◽  
The Right

We use a spectral approach to model residually stressed elastic solids that can be applied to carbon fiber reinforced solids with a preferred direction; since the spectral formulation is more general than the classical-invariant formulation, it facilitates the search for an adequate constitutive equation for these solids. The constitutive equation is governed by spectral invariants, where each of them has a direct meaning, and are functions of the preferred direction, the residual stress tensor and the right stretch tensor. Invariants that have a transparent interpretation are useful in assisting the construction of a stringent experiment to seek a specific form of strain energy function. A separable nonlinear (finite strain) strain energy function containing single-variable functions is postulated and the associated infinitesimal strain energy function is straightforwardly obtained from its finite strain counterpart. We prove that only 11 invariants are independent. Some illustrative boundary value calculations are given. The proposed strain energy function can be simply transformed to admit the mechanical influence of compressed fibers to be partially or fully excluded.

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.

Large Deformation Analysis for Soft Foams Based on Hyperelasticity

2010 ◽  
Vol 26 (3) ◽  
pp. 327-334 ◽  
Author(s):  
G. Silber ◽  
M. Alizadeh ◽  
M. Salimi
Keyword(s):  
Experimental Data ◽  
Constitutive Equation ◽  
Uniaxial Compression ◽  
Compression Test ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Uniaxial Compression Test ◽  
Highly Nonlinear ◽  
Non Linear

AbstractIn Elastomeric foam materials find wide applications for their excellent energy absorption properties. The mechanical property of elastomeric foams is highly nonlinear and it is essential to implement mathematical constitutive models capable of accurate representation of the stress-strain responses of foams. A constitutive modeling method of defining hyperfoam strain energy function by a Simplex Strategy is presented in this work. This study will demonstrate that a strain energy function of finite hyperelasticity for compressible media is applicable to describe the elastic properties of open cell soft foams. This strain energy function is implemented in the FE-tool ABAQUS and proposed for high compressible soft foams. To determine this constitutive equation, experimental data from a uniaxial compression test are used. As the parameters in the constitutive equation are linked in a non-linear way, non-linear optimization routines are adopted. Moreover due to the in homogeneities of the deformation field of the uniaxial compression test, the quality function of the optimization routine has to be determined by an FE-tool. The appropriateness of the strain energy function is tested by a complex loading test.By using the optimized parameters the FE-simulation of this test is in good accordance with the experimental data.

The Nonlinear Material Properties of Liver Tissue Determined From No-Slip Uniaxial Compression Experiments

2006 ◽  
Vol 129 (3) ◽  
pp. 450-456 ◽  
Author(s):  
Esra Roan ◽  
Kumar Vemaganti
Keyword(s):  
Soft Tissue ◽  
Uniaxial Compression ◽  
Material Properties ◽  
Liver Tissue ◽  
Mechanical Response ◽  
Strain Energy Function ◽  
Bovine Liver ◽  
Hyperelastic Material ◽  
Nonlinear Material ◽  
Material Parameters

The mechanical response of soft tissue is commonly characterized from unconfined uniaxial compression experiments on cylindrical samples. However, friction between the sample and the compression platens is inevitable and hard to quantify. One alternative is to adhere the sample to the platens, which leads to a known no-slip boundary condition, but the resulting nonuniform state of stress in the sample makes it difficult to determine its material parameters. This paper presents an approach to extract the nonlinear material properties of soft tissue (such as liver) directly from no-slip experiments using a set of computationally determined correction factors. We assume that liver tissue is an isotropic, incompressible hyperelastic material characterized by the exponential form of strain energy function. The proposed approach is applied to data from experiments on bovine liver tissue. Results show that the apparent material properties, i.e., those determined from no-slip experiments ignoring the no-slip conditions, can differ from the true material properties by as much as 50% for the exponential material model. The proposed correction approach allows one to determine the true material parameters directly from no-slip experiments and can be easily extended to other forms of hyperelastic material models.

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.

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