Relaxation of Thick-Walled Cylinders and Spheres

Abstract

Using the nonlinear creep law proposed by Soderberg, closed-form solutions are derived for the relaxation of incompressible thick-walled spheres and cylinders in plane strain. These solutions involve series expressions which, however, converge very quickly. By simply ignoring these series expressions, extremely simple approximate solutions are obtained. Despite their simplicity these approximations possess an accuracy that is superior to approximations currently in use. Finally, several physical aspects related to the relaxation of cylinders and spheres are discussed.