Solutions for a viscoelastic axisymmetric plane problem involving time-dependent boundary regions under mixed boundary condition

摘要

The stress and displacement fields for a viscoelastic axisymmetric plane problem involving time-dependent boundary regions under mixed boundary condition are presented in this paper. The viscoelastic fields are determined by solving two unknown functions; one is governed by a resulting second kind Volterra integral equation from the stress condition at the outer radius of an annular region, which is dependent on the other by the displacement condition at the inner radius. The integral equation has an analytical solution for the case of an infinite region with large enough outer radius while it can be solved using a numerical integral method for the case of a finite region. Numerical examples for the Boltzmann viscoelastic model are given, and the responses of the displacement and stresses are presented in detail to illustrate the effects of velocity of change in the inner radius and the magnitude of the outer radius. Meanwhile, the effect of the aspect ratio (void concentration parameter) on the viscoelastic fields is presented. When the ratio of the outer radius to the inner radius is large enough, the responses can be evaluated by directly adopting the resulting analytical solution to avoid a complex numerical procedure. The resulting solutions and computational results are helpful to a better understanding of mechanical behaviors for (large) excavation or finite void growth in viscoelastic media.