### Tuesday, 12 October 2004 - 1:25 PM

### This presentation is part of : Rajagopal Symposium

### Dynamic Solution of a Nonlinear Viscoelastic Spherical Membrane

**Yi-chao Chen**, University of Houston, Department of Mechanical Engineering, Houston, TX 77204 and Alan Wineman, University of Michigan, Department of Mechanical Engineering, 1231 Beal Avenue, Ann Arbor, MI 48109.
The Dynamic solution of a nonlinear viscoelastic spherical membrane subject to internal pressure is studied. The constitutive equation is of an integral form with the relaxation function generated by the constitutive function of a nonlinear elastic material. The instantaneous response of the viscoelastic material is the same as the generating elastic material. For spherically symmetric motions, the equation of motion is a nonlinear integro-differential equation. This equation is converted to a system of nonlinear differential equations. A phase space analysis is carried out to study the properties of the solutions (trajectories). For the constitutive model generated from the Mooney-Rivlin materials, a numerical analysis is performed, with special attention paid to the transition from bounded solutions to unbounded solutions. Such a transition corresponds to, for equilibrium solutions, the bifurcation from the stable equilibrium deformations to unstable equilibrium deformations.

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