INCREMENTAL FINITE-ELEMENT EQUATIONS FOR THERMOMECHANICAL RESPONSE OFELASTOMERS - EFFECT OF BOUNDARY-CONDITIONS INCLUDING CONTACT

The present investigation concerns the solution of nonlinear finite el ement equations by Newton iteration, for which the Jacobian matrix pla ys a central role. In earlier investigations [1], [2], a compact expre ssion for the Jacobian matrix was derived for incremental finite eleme nt equations governing coupled thermomechanical response of near-incom pressible 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 hea t 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 condu ction are referred to the deformed coordinates, and variable thermomec hanical 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 Moo ney-Rivlin model. The Jacobian matrix is now augmented with several te rms which are derived in compact form using Kronecker product notation . Calculations are presented on a confined rubber O-ring seal submitte d to force and heat.