On bounds for primary creep in symmetric pressure vessels

The field equations governing primary creep in spherical and incompressible cylindrical pressure vessels subject to a non-decreasing internal pressure are reduced to a single equation in the effective stress. The effects of elastic strains are included. Using this equation, bounds and monotonicity properties are established for the effective stress at any point in the body at any time. It is also shown that these results imply upper and lower bounds for the displacement. These bounds are stated explicitly for the displacement of the outer surface of the vessel.