Estimation of temperature in rubber-like materials using non-linear finiteelement analysis based on strain history

A finite element procedure for hyper-elastic materials such as rubber has b een developed to estimate the temperature rise during cyclic loading. The i rreversible mechanical work developed in rubber has been used to determine the heat generation rate for carrying out thermal analysis. The evaluation of the heat energy is dependent on the strains. The finite element analysis assumes Green-Lagrangian strain displacement relations, Mooney-Rivlin stra in energy density function for constitutive relationship, incremental equil ibrium equations, and Total Lagrangian approach and the stress and strain o f the rubber-like materials are evaluated using a degenerated shell element with assumed strain held technique, considering both material and geometri c non-linearities. A transient heat conduction analysis has been carried ou t to estimate the temperature rise for different time steps in rubber-like materials using Galerkin's formulations. A numerical example is presented a nd the computed temperature values for various load steps agree closely wit h the experimental results reported in the literature. (C) 1998 Elsevier Sc ience B.V. All rights reserved.