http://dx.doi.org/10.1007/bf01178249

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Title

On the tangent modulus tensor in hyperelasticity

Authors

Authors

D. W. Nicholson;B. Lin

Comments

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Abbreviated Journal Title

Acta Mech.

Keywords

FINITE-ELEMENT ANALYSIS; RUBBER; Mechanics

Abstract

The tangent modulus tensor, denoted as D, plays a central role in nonlinear finite element simulation of elastomeric components such as seals. It is derived from the strain energy function w for isotropic elastomers. Using Kronecker product notation, a compact expression for D has been derived in Nicholson [1] and Nicholson and Lin [2] for invariant-based strain energy functions such as the Mooney-Rivlin model. In the current investigation, a corresponding expression is derived for stretch ratio-based strain energy functions such as the Ogden model. Compressible, incompressible and near-incompressible elastomers are addressed. The derived expressions are considerably more elaborate than their counterparts for invariant based models. As illustration, D is evaluated and presented for the torsion of a natural rubber shaft described by a three term Ogden model, using coefficients reported by Treloar.

Journal Title

Acta Mechanica

Volume

131

Issue/Number

1-2

Publication Date

1-1-1998

Document Type

Article

Language

English

First Page

121

Last Page

132

WOS Identifier

WOS:000076166000008

ISSN

0001-5970

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