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]

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Finding the Constitutive Relation for a Specific Elastomer

Journal of Electronic Packaging ◽

10.1115/1.2909336 ◽

1993 ◽

Vol 115 (3) ◽

pp. 329-336 ◽

Cited By ~ 7

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.

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Neural Network Based Constitutive Model for Rubber Material

Rubber Chemistry and Technology ◽

10.5254/1.3547822 ◽

2004 ◽

Vol 77 (2) ◽

pp. 257-277 ◽

Cited By ~ 19

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.

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Methodical fitting for mathematical models of rubber-like materials

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2016.0811 ◽

2017 ◽

Vol 473 (2198) ◽

pp. 20160811 ◽

Cited By ~ 38

Author(s):

Michel Destrade ◽

Giuseppe Saccomandi ◽

Ivonne Sgura

Keyword(s):

Experimental Data ◽

Mathematical Models ◽

Nonlinear Elasticity ◽

Strain Energy ◽

Nonlinear Response ◽

Energy Functions ◽

Nonlinear Elasticity Theory ◽

Polymeric Chains ◽

Strain Energy Functions ◽

Global Fitting

A great variety of models can describe the nonlinear response of rubber to uniaxial tension. Yet an in-depth understanding of the successive stages of large extension is still lacking. We show that the response can be broken down in three steps, which we delineate by relying on a simple formatting of the data, the so-called Mooney plot transform. First, the small-to-moderate regime, where the polymeric chains unfold easily and the Mooney plot is almost linear. Second, the strain-hardening regime, where blobs of bundled chains unfold to stiffen the response in correspondence to the ‘upturn’ of the Mooney plot. Third, the limiting-chain regime, with a sharp stiffening occurring as the chains extend towards their limit. We provide strain-energy functions with terms accounting for each stage that (i) give an accurate local and then global fitting of the data; (ii) are consistent with weak nonlinear elasticity theory and (iii) can be interpreted in the framework of statistical mechanics. We apply our method to Treloar's classical experimental data and also to some more recent data. Our method not only provides models that describe the experimental data with a very low quantitative relative error, but also shows that the theory of nonlinear elasticity is much more robust that seemed at first sight.

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

International Journal of Applied Mechanics ◽

10.1142/s1758825119500844 ◽

2019 ◽

Vol 11 (09) ◽

pp. 1950084 ◽

Cited By ~ 5

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.

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