Transient response of a case-bonded nonlinear viscoelastic cylinder.

Abstract

The problem of a rapidly pressurized, infinitely long, thick-walled viscoelastic cylinder bonded to a thin elastic shell is considered. The plane strain solution is obtained when the strain e and deformation rate d in the viscoelastic cylinder are such that terms of order three and higher in e and d can be neglected in comparison with e and d. The strains in the shell, however, are restricted to magnitudes for which infinitesimal elasticity theory applies. The effect of inertia of the viscoelastic cylinder is included in the analysis. The cylinder is internally pressurized by two types of pressure programs: a step pressure and a ramp pressure with four different rise-times. For these loadings the Eulerian strain and circumferential stress response at the inner and outer radii of the viscoelastic cylinder are obtained using a second-order constitutive relation in which the stress depends only on the displacement and velocity gradients.