Stresses in Anisotropic Cylinders

Axisymmetrical stresses in an infinitely long hollow isotropic circular cylinder (plane strain) quickly approach their asymptotic values as the external radius increases. This is not the case if the cylinder is even slightly anisotropic -asymptotic solutions (for an infinitely large external radius) do not exist. We find the mechanical meaning of this disparity by using formulas for radial and hoop stresses in a cylindrically anisotropic cylinder with constant finite stresses at the boundaries: (a) The internal stresses increase infinitely with increasing external radius, if the cylinder is stiffer in the radial direction than in the tangential direction. (b) At any fixed point inside the cylinder, the stresses approach zero as the outer radius increases, if the cylinder is stiffer in the tangential direction than in the radial direction. We call the former effect "stress amplification", and the latter one "stress shielding." Both effects are closely related to the decay of boundary conditions and, in general, to the problem of applicability of SaintVenant's principle to anisotropic solids.