FINITE-ELEMENT METHOD FOR THERMOMECHANICAL RESPONSE OF NEAR-INCOMPRESSIBLE ELASTOMERS

The present study addresses finite element analysis of the coupled the rmomechanical response of near-incompressible elastomers such as natur al rubber. Of interest are applications such as seals, which often inv olve large deformations, nonlinear material behavior, confinement, and thermal gradients. Most published finite element analyses of elastome ric components have been limited to isothermal conditions. A basic qua ntity appearing in the finite element equation for elastomers is the t angent stiffness matrix. A compact expression for the isothermal tange nt stiffness matrix has recently been reported by the first author, in cluding compressible, incompressible, and near-incompressible elastome rs. In the present study a compact expression is reported for the tang ent stiffness matrix under coupled thermal and mechanical behavior, in cluding pressure interpolation to accommodate near-incompressibility. The matrix is seen to have a computationally convenient structure and to serve as a Jacobian matrix in a Newton iteration scheme. The formul ation makes use of a thermoelastic constitutive model recently introdu ced by the authors for near-incompressible elastomers. The resulting r elations are illustrated using a near-incompressible thermohyperelasti c counterpart of the conventional Mooney-Rivlin model. As an applicati on, an element is formulated to model the response of a rubber rod sub jected to force and heat.