On the tangent modulus tensor in hyperelasticity

    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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