Viscoelastic Model of Finitely Deforming Rubber and Its Finite Element Analysis

[+] Author and Article Information
Seung Jo Kim, Kyeong Su Kim, Jin Yeon Cho

Department of Aerospace Engineering, Seoul National University, San 56-1, Shillim-Dong, Kwanak-Ku, Seoul 151-742, Republic of Korea

J. Appl. Mech 64(4), 835-841 (Dec 01, 1997) (7 pages) doi:10.1115/1.2788989 History: Received August 29, 1996; Revised April 10, 1997; Online October 25, 2007


A viscoelastic model of finitely deforming rubber is proposed and its nonlinear finite element approximation and numerical simulation are carried out. This viscoelastic model based on continuum mechanics is an extended model of Johnson and Quigley’s one-dimensional model. In the extended model, the kinematic configurations and measures based on continuum mechanics are rigorously defined and by using these kinematic measures, constitutive relations are introduced. The obtained highly nonlinear equations are approximated by the nonlinear finite element method, where a mixture of the total and updated Lagrangian descriptions is used. To verify the theory and the computer code, uniaxial stretch tests are simulated for various stretch rates and compared with actual experiments. As a practical example, an axisymmetric rubber plate under various time-dependent pressure loading conditions is analyzed.

Copyright © 1997 by The American Society of Mechanical Engineers
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