Transient Stresses in Nonhomogeneous Viscoelastic (Maxwell) Materials

Abstract

This paper determines the transient-stress distribution, due to imposed strain rates, which exists in bars made of a linear nonhomogeneous viscoelastic (Maxwell) material. The cases of constant and exponentially decreasing strain-rate histories are solved. The particular nonhomogeneity is an exponential variation of the fluidity in the thickness coordinate. I t is shown that this fluidity variation can be the result of a steady linear temperature gradient. One-dimensional strength of materials assumptions are made for the problems of axial extension and bending. I t is further assumed that all of the initial stresses due to heating have vanished prior to load application. I t is found in the case of constant strain rate that the stress distribution approaches the configuration associated with a purely viscous material after one relaxation time of the cold face. In addition, an approximate solution to the problem of constant load is given in Appendix A.