Incremental finite element equations for thermomechanical response of elastomers: effect of boundary conditions including contact

    Authors

    D. W. Nicholson;B. Lin

    Comments

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    Abbreviated Journal Title

    Acta Mech.

    Keywords

    MATRIX; Mechanics

    Abstract

    The present investigation concerns the solution of nonlinear finite element equations by Newton iteration, for which the Jacobian matrix plays a central role. In earlier investigations [1], [2], a compact expression for the Jacobian matrix was derived for incremental finite element equations governing coupled thermomechanical response of near-incompressible elastomers. A fully Lagrangian formulation was adopted, with three important restrictions: (a) the traction and heat flux vectors were referred to the undeformed coordinates; (b) Fourier's law for heat conduction was expressed in terms of the undeformed coordinates; and (c) variable contact was not considered. In contrast, in the current investigation, the boundary conditions and Fourier's law of heat conduction are referred to the deformed coordinates, and variable thermomechanical contact is modeled. A thermohyperelastic constitutive equation introduced by the authors [3] is used and is specialized to provide a thermomechanical, near-incompressible counterpart of the two-term Mooney-Rivlin model. The Jacobian matrix is now augmented with several terms which are derived in compact form using Kronecker product notation. Calculations are presented on a confined rubber O-ring seal submitted to force and heat.

    Journal Title

    Acta Mechanica

    Volume

    128

    Issue/Number

    1-2

    Publication Date

    1-1-1998

    Document Type

    Article

    Language

    English

    First Page

    81

    Last Page

    104

    WOS Identifier

    WOS:000072128800007

    ISSN

    0001-5970

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