Non-uniform extension of a non-linear viscoelastic slab

Abstract

The non-uniform extension of a slab of a non-linear viscoelastic solid is studied. Two boundary value problems are solved, one with deformation prescribed at the upper boundary and the other with the traction prescribed. The formulation uses the deformation in the direction of the slab thickness as the dependent variable, which is found by solving a non-linear integro-differential equation. The numerical calculation is such that at each time step, the problem is equivalent to a fourth order non-linear ordinary differential equation for the current coordinate in the direction of the slab thickness. This equation is then integrated by the same numerical procedure as in the corresponding elastic problem.