Some examples involving uniform, compressible isotropic materials

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Plane Strain ◽  
Analytical Solutions ◽  
Strain Energy ◽  
Three Dimensional ◽  
Energy Functions ◽  
Isotropic Materials ◽  
Strain Energy Functions ◽  
Compressible Materials

This chapter details analytical solutions for unconstrained materials using tractable strain–energy functions. Three-dimensional and plane–strain deformations are illustrated. These include a formulation of the cavtitation problem in compressible materials and a discussion of so-called Harmonic materials.

Strain energy functions for filled elastomers

1965 ◽  
Vol 9 (7) ◽  
pp. 2565-2579 ◽  
Author(s):  
M. Shinozuka ◽  
A. M. Freudenthal
Keyword(s):  
Strain Energy ◽  
Energy Functions ◽  
Filled Elastomers ◽  
Strain Energy Functions

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]

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 Methodical fitting for mathematical models of rubber-like materials

2017 ◽  
Vol 473 (2198) ◽  
pp. 20160811 ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document