Nonlinear Constitutive Equation and Elastic Constant of Rubber Material

2011 ◽  
Vol 415-417 ◽  
pp. 2267-2274 ◽  
Author(s):  
Chen Li ◽  
Li Zhao
Keyword(s):  
Constitutive Equation ◽  
Elastic Constants ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Compressible Material ◽  
Experiment Data ◽  
Rubber Material ◽  
Nonlinear Constitutive Equation ◽  
Depth Study ◽  
Material Constitutive Equation

In-depth study of compressible material constitutive equation, using incompressible condition, the nonlinear incompressible elastic solid’s complete irreducible constitutive equation and strain energy function expressed in invariants are derived in this essay. The elastic constants of rubber material are given by fitting the experiment data that was carried out by Treloar with the equation. Then we got evelen exact value of the elastic constants.

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.

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.

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.

Thermal Elastic Constitutive Equation of Orthotropic Materials

2017 ◽  
Vol 863 ◽  
pp. 93-101
Author(s):  
Chen Li ◽  
Hai Ren Wang ◽  
Yan An Miao ◽  
Li Zhao
Keyword(s):  
Constitutive Equation ◽  
Elastic Constant ◽  
Elastic Constants ◽  
Representation Theorem ◽  
Constitutive Equations ◽  
Orthotropic Materials ◽  
Tensor Function ◽  
Tensor Method ◽  
Scalar Invariant ◽  
Depth Study

In the finite deformation range, the numbers of orthotropic 2n order elastic constants are studied on the basis of tensor function and of its representation theorem. On the basis of elastic constant research, the elastic orthotropic constitutive equation is derived by using the tensor method. Based on orthotropic elastic constitutive equations an in-depth study on the constitutive theory of orthotropic nonlinear thermal elasticity is carried out, and by considering the deformation produced by the coupling of temperature and load, nonlinear orthotropic thermoelastic constitutive equation is further derived with representation of the tensor invariant and scalar invariant. The constitutive equations could be used very convenient to the application in reality.

Constitutive Equation of Lung Tissue Elasticity

1979 ◽  
Vol 101 (1) ◽  
pp. 38-45 ◽  
Author(s):  
D. L. Vawter ◽  
Y. C. Fung ◽  
J. B. West
Keyword(s):  
Constitutive Equation ◽  
Lung Tissue ◽  
Strain Energy ◽  
Biaxial Loading ◽  
Strain Energy Function ◽  
Lung Mechanics ◽  
Theoretical Formula ◽  
Published Data ◽  
Biaxial Test ◽  
Tissue Elasticity

A constitutive equation for the lung tissue elasticity is formulated under the hypotheses of a simplified alveolar geometry and a pseudo-strain-energy function for the interalveolar septa. The resulting equation contains four material constants. The theoretical result has been tested against published data on uniaxial and triaxial loadings, and is tested critically here with respect to new experimental results on biaxial loading. Comparison between theory and experiments shows that a general agreement is obtained in an approximate sense. The model fits our biaxial experimental data with most correlation coefficients above 0.995. Some details not predicted by the theory are discussed. Since the theory is derived for triaxial loading and the biaxial test is a severe one, the formula should be applicable to the triaxial case at least to the same degree of approximation. The form of the theoretical formula is convenient to use in analytic studies of lung mechanics. Additional key words: mechanical behavior of the lung; stress-strain relationship; strain energy; alveolus model; distortion; interdependence; pressure volume curves.

Mechanical power and hyperelasticity

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Mechanical Power ◽  
Elastic Materials ◽  
Cyclic Motion

This chapter covers the notion of hyperelasticity—the concept that stress is derived from a strain—energy function–by invoking an analogy between elastic materials and springs. Alternatively, it can be derived by invoking a work inequality; the notion that work is required to effect a cyclic motion of the material.

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.

Mechanical characterization of a woven multi-layered hyperelastic composite laminate under uniaxial loading

2021 ◽  
pp. 002199832110115
Author(s):  
Shaikbepari Mohmmed Khajamoinuddin ◽  
Aritra Chatterjee ◽  
MR Bhat ◽  
Dineshkumar Harursampath ◽  
Namrata Gundiah
Keyword(s):  
Composite Materials ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Mechanical Tests ◽  
Stress Strain ◽  
Aerospace Applications ◽  
Envelope Material ◽  
The Individual ◽  
High Dielectric

We characterize the material properties of a woven, multi-layered, hyperelastic composite that is useful as an envelope material for high-altitude stratospheric airships and in the design of other large structures. The composite was fabricated by sandwiching a polyaramid Nomex® core, with good tensile strength, between polyimide Kapton® films with high dielectric constant, and cured with epoxy using a vacuum bagging technique. Uniaxial mechanical tests were used to stretch the individual materials and the composite to failure in the longitudinal and transverse directions respectively. The experimental data for Kapton® were fit to a five-parameter Yeoh form of nonlinear, hyperelastic and isotropic constitutive model. Image analysis of the Nomex® sheets, obtained using scanning electron microscopy, demonstrate two families of symmetrically oriented fibers at 69.3°± 7.4° and 129°± 5.3°. Stress-strain results for Nomex® were fit to a nonlinear and orthotropic Holzapfel-Gasser-Ogden (HGO) hyperelastic model with two fiber families. We used a linear decomposition of the strain energy function for the composite, based on the individual strain energy functions for Kapton® and Nomex®, obtained using experimental results. A rule of mixtures approach, using volume fractions of individual constituents present in the composite during specimen fabrication, was used to formulate the strain energy function for the composite. Model results for the composite were in good agreement with experimental stress-strain data. Constitutive properties for woven composite materials, combining nonlinear elastic properties within a composite materials framework, are required in the design of laminated pretensioned structures for civil engineering and in aerospace applications.

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