Stresses in rotating spheres grown by accretion

Analytical expressions are obtained for the stress field in a sphere that has grown by accretion while rotating about an axis at a speed which may vary during the accretion process. It is assumed that accretion occurs by the adherence of infinitesimal particles that are stress free at the instant of attachment and that the material of the sphere behaves elastically once it has accreted. The resulting stress field differs significantly from that predicted in a sphere that was manufactured in a stress free state and then set to rotate. The implications of these differences are discussed in the context of the mechanisms for failure in accreted planetary bodies.