Elastic Field in a Semi-Infinite Solid due to Thermal Expansion or a Coherently Misfitting Inclusion

Abstract

It is shown that the elastic field due to nonuniform temperature or a coherently misfitting inclusion in a semi-infinite region can be derived simply from the corresponding field in an infinite region. This follows from the work of Mindlin and Cheng [J. Appl. Phys. 21 , 931 (1950)] but it is not necessary to calculate the thermoelastic potential itself. In particular, the displacement of the free surface is the same as that of the equivalent plane in an infinite solid, increased by a factor of 4(1−ν). The change in volume associated with the distortion of the surface is reduced by a factor of 2(1+ν)/3 from the free expansion of the inclusion. A rectangular inclusion is used to illustrate the theory.