New Strain Energy Function for Acoustoelastic Analysis of Dilatational Waves in Nearly Incompressible, Hyper-Elastic Materials

2005 ◽  
Vol 72 (6) ◽  
pp. 843-851 ◽  
Author(s):  
H. Kobayashi ◽  
R. Vanderby
Keyword(s):  
Wave Propagation ◽  
Energy Function ◽  
Strain Energy ◽  
Constitutive Models ◽  
Strain Energy Function ◽  
Deformation Tensor ◽  
Energy Functions ◽  
Dilatational Wave ◽  
Hyper Elastic ◽  
Strain Energy Functions

Acoustoelastic analysis has usually been applied to compressible engineering materials. Many materials (e.g., rubber and biologic materials) are “nearly” incompressible and often assumed incompressible in their constitutive equations. These material models do not admit dilatational waves for acoustoelastic analysis. Other constitutive models (for these materials) admit compressibility but still do not model dilatational waves with fidelity (shown herein). In this article a new strain energy function is formulated to model dilatational wave propagation in nearly incompressible, isotropic materials. This strain energy function requires four material constants and is a function of Cauchy–Green deformation tensor invariants. This function and existing (compressible) strain energy functions are compared based upon their ability to predict dilatational wave propagation in uniaxially prestressed rubber. Results demonstrate deficiencies in existing functions and the usefulness of our new function for acoustoelastic applications. Our results also indicate that acoustoelastic analysis has great potential for the accurate prediction of active or residual stresses in nearly incompressible materials.

Finite Element Analysis by Using Hyper-Elastic Properties for Rubber Component

2011 ◽  
Vol 488-489 ◽  
pp. 190-193
Author(s):  
Chang Su Woo ◽  
Hyun Sung Park ◽  
Wae Gi Shin
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Element Analysis ◽  
Energy Functions ◽  
Hyper Elastic ◽  
Rubber Component ◽  
Strain Energy Functions

The material modeling of hyper-elastic properties in rubber is generally characterized by the strain energy function. The strain energy functions have been represented either in term of the strain in variants that are functions of the stretch ratios, or directly in terms of the principal stretch. Successful modeling and design of rubber components relies on both the selection of an appropriate strain energy function and an accurate determination of material constants in the function. Material constants in the strain energy functions can be determined from the curve fitting of experimental stress-strain data. The uniaxial tension, equi-biaxial tension and pure shear test were performed to acquire the constants of the strain energy functions which were Mooney-Rivlin and Ogden model. Nonlinear finite element analysis was executed to evaluate the behavior of deformation and strain distribute by using the commercial finite element code. Also, the fatigue tests were carried out to obtain the fatigue failure. Fatigue failure was initiated at the critical location was observed during the fatigue test of rubber component, which was the same result predicted by the finite element analysis.

Finding the Constitutive Relation for a Specific Elastomer

1993 ◽  
Vol 115 (3) ◽  
pp. 329-336 ◽  
Author(s):  
Yun Ling ◽  
Peter A. Engel ◽  
Wm. L. Brodskey ◽  
Yifan Guo
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Strain Energy ◽  
Pure Shear ◽  
Strain Energy Function ◽  
Invariant Polynomial ◽  
Energy Functions ◽  
Finite Element Program ◽  
Biaxial Extension ◽  
Strain Energy Functions

The main purpose of this study was to determine a suitable strain energy function for a specific elastomer. A survey of various strain energy functions proposed in the past was made. For natural rubber, there were some specific strain energy functions which could accurately fit the experimental data for various types of deformations. The process of determining a strain energy function for the specific elastomer was then described. The second-order invariant polynomial strain energy function (James et al., 1975) was found to give a good fit to the experimental data of uniaxial tension, uniaxial compression, equi-biaxial extension, and pure shear. A new form of strain energy function was proposed; it yielded improved results. The equi-biaxial extension experiment was done in a novel way in which the moire techniques (Pendleton, 1989) were used. The obtained strain energy functions were then utilized in a finite element program to calculate the load-deflection relation of an electrometric spring used in an electrical connector.

Neural Network Based Constitutive Model for Rubber Material

2004 ◽  
Vol 77 (2) ◽  
pp. 257-277 ◽  
Author(s):  
Y. Shen ◽  
K. Chandrashekhara ◽  
W. F. Breig ◽  
L. R. Oliver
Keyword(s):  
Neural Network ◽  
Curve Fitting ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Phenomenological Approach ◽  
Neural Network Approach ◽  
Energy Functions ◽  
The Neural Network ◽  
Strain Energy Functions

Abstract Rubber hyperelasticity is characterized by a strain energy function. The strain energy functions fall primarily into two categories: one based on statistical thermodynamics, the other based on the phenomenological approach of treating the material as a continuum. This work is focused on the phenomenological approach. To determine the constants in the strain energy function by this method, curve fitting of rubber test data is required. A review of the available strain energy functions based on the phenomenological approach shows that it requires much effort to obtain a curve fitting with good accuracy. To overcome this problem, a novel method of defining rubber strain energy function by Feedforward Backpropagation Neural Network is presented. The calculation of strain energy and its derivatives by neural network is explained in detail. The preparation of the neural network training data from rubber test data is described. Curve fitting results are given to show the effectiveness and accuracy of the neural network approach. A material model based on the neural network approach is implemented and applied to the simulation of V-ribbed belt tracking using the commercial finite element code ABAQUS.

scholarly journals A generalized strain approach to anisotropic elasticity

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
M. H. B. M. Shariff
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Single Variable ◽  
Energy Functions ◽  
Anisotropic Strain ◽  
Strain Energy Functions ◽  
Strain Function

AbstractThis work proposes a generalized Lagrangian strain function $$f_\alpha$$ f α (that depends on modified stretches) and a volumetric strain function $$g_\alpha$$ g α (that depends on the determinant of the deformation tensor) to characterize isotropic/anisotropic strain energy functions. With the aid of a spectral approach, the single-variable strain functions enable the development of strain energy functions that are consistent with their infinitesimal counterparts, including the development of a strain energy function for the general anisotropic material that contains the general 4th order classical stiffness tensor. The generality of the single-variable strain functions sets a platform for future development of adequate specific forms of the isotropic/anisotropic strain energy function; future modellers only require to construct specific forms of the functions $$f_\alpha$$ f α and $$g_\alpha$$ g α to model their strain energy functions. The spectral invariants used in the constitutive equation have a clear physical interpretation, which is attractive, in aiding experiment design and the construction of specific forms of the strain energy. Some previous strain energy functions that appeared in the literature can be considered as special cases of the proposed generalized strain energy function. The resulting constitutive equations can be easily converted, to allow the mechanical influence of compressed fibres to be excluded or partial excluded and to model fibre dispersion in collagenous soft tissues. Implementation of the constitutive equations in Finite Element software is discussed. The suggested crude specific strain function forms are able to fit the theory well with experimental data and managed to predict several sets of experimental data.

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.

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.

On the Choice of Strain Energy Function for Mechanical Characterisation of Soft Biological Tissues

1984 ◽  
Vol 13 (1) ◽  
pp. 11-14 ◽  
Author(s):  
K B Sahay
Keyword(s):  
Energy Function ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Biological Tissues ◽  
Energy Functions ◽  
Soft Biological Tissues ◽  
Mechanical Characterisation ◽  
Strain Energy Functions ◽  
Made In

Constitutive equations that describe stress–strain relations of soft biological tissues require parameters such as the strain energy functions, or certain of their derivatives. An attempt has been made in this paper to examine the suitability of the various strain energy functions reported in the literature. Certain criteria are proposed for the same.

Constitutive Equations for Isotropic Rubber-Like Materials Using Phenomenological Approach: A Bibliography (1930–2003)

2006 ◽  
Vol 79 (3) ◽  
pp. 489-499 ◽  
Author(s):  
Vahap Vahapoğlu ◽  
Sami Karadeniz
Keyword(s):  
Energy Function ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Isothermal Condition ◽  
Strain Energy Function ◽  
Phenomenological Approach ◽  
Elastic Behavior ◽  
Energy Functions ◽  
Strain Energy Functions

Abstract To describe the elastic behavior of rubber-like materials, numerous specific forms of strain energy functions have been proposed in the literature. This bibliography provides a list of references on the strain energy functions for rubber-like materials on isothermal condition using the phenomenological approach. The published works, either containing the strain energy function proposals or the discussions on such proposals, based upon the phenomenological approach, are classified.

Modeling of Visco-Hyperelastic Behavior of Foams

2008 ◽  
Author(s):  
Y. Anani ◽  
M. Asghari ◽  
R. Naghdabadi
Keyword(s):  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Constitutive Law ◽  
Energy Functions ◽  
Material Constants ◽  
Maxwell Element ◽  
Rate Dependent ◽  
Dependent Behavior ◽  
Strain Energy Functions

In this paper, a new visco-hyperelastic constitutive law for describing the rate dependent behavior of foams is proposed. The proposed model was based on a phenomenological Zener model: a hyperelastic equilibrium spring, which describes the steady-state, long-term response, parallel to a Maxwell element, which captures the ratedependency. A nonlinear viscous damper connected in series to a hyperelastic intermediate spring, controls the ratedependency of the Maxwell element. Therefore, the stress is the sum of equilibrium stress on the equilibrium spring and overstress on the intermediate spring. In hyperelastic theory stress is not calculated directly as in the case of small-strain, linear elastic materials. Instead, stresses are derived from the principle of virtual work using the stored strain energy potential function. In addition, foams are compressible, therefore classic strain energy functions such as the Ogden strain energy function or the Mooney-Rivlin strain energy function are not suitable to describe hyperelastic behavior of foams. So, strain energy functions must include the effect of compressibility. That means the third principal invariant of the deformation gradient tensor F should enter in strain energy functions. For rate-dependent behavior of foams, history integral constitutive law is used. For the equilibrium spring and the intermediate spring, the same strain energy function is employed. In order to use this stain energy function in history integral equation, the kernel function of it is calculated. The effect of compressibility is considered in rate-dependent behavior of foams too. All material constants were obtained from the results of uniaxial tensile tests. Nonlinear regulation was used to find these constants. In these calculations, Average strain rate was employed to find material constants.

A Generalized Strain Approach to Anisotropic Elasticity

2021 ◽  
Author(s):  
M.H.B.M. Shariff
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Single Variable ◽  
Energy Functions ◽  
Anisotropic Strain ◽  
Strain Energy Functions ◽  
Strain Function

Abstract This work proposes a generalized Lagrangian strain function fα (that depends on modified stretches) and a volumetric strain function gα (that depends on the determinant of the deformation tensor) to characterize isotropic/anisotropic strain energy functions. With the aid of a spectral approach, the single-variable strain functions enable the development of strain energy functions that are consistent with their infinitesimal counterparts, including the development of a strain energy function for the general anisotropic material that contains the general 4th order classical stiffness tensor. The generality of the single-variable strain functions sets a platform for future development of adequate specific forms of the isotropic/anisotropic strain energy function; future modellers only require to construct specific forms of the functions fα and gα to model their strain energy functions. The spectral invariants used in the constitutive equation have a clear physical interpretation, which is attractive, in aiding experiment design and the construction of specific forms of the strain energy. Some previous strain energy functions that appeared in the literature can be considered as special cases of the proposed generalized strain energy function. The resulting constitutive equations can be easily converted, to allow the mechanical influence of compressed fibres to be excluded or partial excluded and to model fibre dispersion in collagenous soft tissues. Implementation of the constitutive equations in Finite Element software is discussed. The suggested crude specific strain function forms are able to fit the theory well with experimental data and managed to predict several sets of experimental data.

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