A New Elastic Potential Function for Rubbery Materials

Blatz, P. J.; Sharda, S. C.; Tschoegl, N. W.

doi:10.1073/pnas.70.11.3041

Cited by 14 publications

(1 citation statement)

References 4 publications

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“…Obviously, for a = 2 the Lagrangian strain tensor is reduced to E. The a-measure of strain was introduced by Seth33 and has been applied by OgdenZ0 and independently by Blatz et al 23 for the description of the elastic large deformation behavior of rubber-like solids. The generalized strain measure has recently been applied to nonhomogeneous deformations in rubber-like solids.…”

Section: Generalized Strain Measurementioning

confidence: 99%

An extension of the penalty function formulation to incompressible hyperelastic solids described by general measure of strain

Kakavas

Chang

1995

J of Applied Polymer Sci

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SYNOPSISThe penalty function formulation for incompressible hyperelastic solids was first proposed about 30 years ago. Since then all studies have been limited to invariant type formulation of the strain energy function, although it is well known that this formulation does not correctly describe the behavior of a real material. On the other hand more realistic constitutive equations, based on general measures of the strain only, have been incorporated to mixed finite element algorithms. In this article, a penalty function formulation is proposed for the analysis of stress field in materials with constitutive equations based on the general measure of strain. The reduced integration method is used to weaken the penalty constraint in order to obtain meaningful numerical results. The incremental equilibrium equations are solved using the regular Newton-Raphson algorithm. The method is applied to evaluate the stress field in materials subjected to plane strain conditions. Satisfactory agreements have been obtained with analytical solutions when available. 0 1995 John Wiley & Sons, Inc.

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Section: Generalized Strain Measurementioning

confidence: 99%

An extension of the penalty function formulation to incompressible hyperelastic solids described by general measure of strain

Kakavas

Chang

1995

J of Applied Polymer Sci

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A new development of the strain energy function for hyperelastic materials using a logarithmic strain approach

Kakavas¹

2000

J. Appl. Polym. Sci.

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ABSTRACT:The development of a new strain energy function for hyperelastic solids based on the logarithmic strain measure is the objective of the present article. For all possible types of deformation it was shown that the proposed energy function is based on three independent material parameters. Using available experimental data for rubber-like materials from the literature, one may determined the materials parameters by a nonlinear fitting. The available domain of the strain energy function can be determined by plotting the third invariant of logarithmic strain vs the second one. The numerical integration of the experimental data of true stress as a function of the logarithmic strain for various types of deformation yields the strain energy function W, for rubber-like solids. The proposed model involves only one parameter that must be determined by fitting with the experimental data.

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The elastic potential function of slightly compressible rubberlike materials

Peng

1979

J. Polym. Sci. Polym. Phys. Ed.

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In order to obtain an analytical expression for the stored energy function W of slightly compressible rubberlike materials, two recent results are used to obtain a unified expression where Γi are a new set of invariants, and H(Γ1,Γ2) is the shear part of the stored energy function which is now assumed to be a separate symmetric function of the modified stretch ratio, λ = λi/I, i.e., Various analytical forms of h(λ) are proposed. Also, a straightforward transformation technique is formulated such that one can easily relate the stress‐strain relation in terms of modified stretch ratio λ to the new invariants Γi. Thus, by a combination of the above equations and the transformation technique, one may readily determine the elastic strain energy function of slightly compressible materials from careful measurements of the volume change in multiaxial deformations.

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A New Elastic Potential Function for Rubbery Materials

Cited by 14 publications

References 4 publications

An extension of the penalty function formulation to incompressible hyperelastic solids described by general measure of strain

An extension of the penalty function formulation to incompressible hyperelastic solids described by general measure of strain

A new development of the strain energy function for hyperelastic materials using a logarithmic strain approach

The elastic potential function of slightly compressible rubberlike materials

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