Steady-state thermoelasticity for initially stressed bodies

Abstract

An elastic body, deformed from a state of zero stress and strain and uniform temperature by a large deformation and steady-state temperature distribution, is subsequently subjected to small displacements and steady-state temperature distributions. After a general analysis of the problem the work is specialized to the case when the initial large deformation is homogeneous at constant temperature. A general solution of the equations for the small superposed deformation and steady-state temperature distribution is obtained in terms of three stress functions valid for some regions of space including the half space and thick uniform plate, when two perpendicular extension ratios of the initial homogeneous deformation are equal. Applications are made to problems of a plane circular (penny-shaped) crack in an infinite medium and to half-space problems.