Title

On the tangent modulus tensor in hyperelasticity

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.

Publication Date

1-1-1998

Publication Title

Acta Mechanica

Volume

131

Issue

1-2

Number of Pages

121-132

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/BF01178249

Socpus ID

0032291885 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0032291885

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