An analysis of the volterra problem for the steady state creep material using complex stress and pseudo-stress functions

Abstract

A stress solution for a steady state creep material described by the power law is obtained by applying the pseudo-complex stress function which satisfies the biharmonic equation. The relation between the complex stress and the pseudo-stress function is established. The stress function or the stress components can be obtained from the known pseudo stress function. Two specific cases are investigated: 1) the stress field is presumed to contian σ x , σ y and σ xy and 2) the stress field contains only shearing stress, σ xz and σ yz . Both cases presume plane strain, incompressibility and an isothermal condition. Using the solutions obtained from the analysis two boundary value problems are illustrated: 1) the creep continuum is dislocated in the radial direction with constant velocity and 2) the media is dislocated in the axial direction with a constant velocity. If the constant velocity term in the analysis presented herein is replaced with a constant displacement term, then these linear elastic continuum problems are known as Volterra problems. If the problem is reduced to the problem for a perfectly viscous material (m=1.0), the solution for the stress expression is shown to be identical to existing classical solutions.