Interaction of nonhomogeneous shear, nonlinear viscoelasticity, and yield of a solid polymer

Abstract

AbstractA constitutive equation for small strain viscoelastic response is considered in which stress relaxation. occurs faster as strain increases. The constitutive equation is of single integral type and has a psuedo‐ or material time function which is calculated from a strain dependent shift function. First, it is shown that such a constitutive equation can account for yield as observed in polymers for a number of different stress and strain histories. Next, the constitutive equation is used in the analysis of the problem in which a hollow cylinder is fixed at its inner surface and a moment history is applied to its outer surface. This causes the cylindrical surfaces to rotate about the central axis, thereby inducing a radial shear strain distribution. It is shown that there is a time when the material near the inner support begins to yield and a layer of large shear strain gradient begins to grow rapidly. It is also shown that the stress or strain history at a material element will generally not be one of the standard histories used to study yield.