Strain-Gradient Effects Around Cylindrical Inclusions and Cavities in a Field of Cylindrically Symmetric Tension

In this work, it is assumed that the potential energy of an elastic body depends on its strains and strain gradients. Such a potential energy will give rise to both classical and higher-order stress terms. The constitutive law of the body will therefore incorporate additional elastic constants whose dimensions differ from those of the classical moduli by the square of length. A solution to the problem of a cylindrical inclusion and cavity in a field of cylindrically symmetric tension is presented to illustrate some of the new effects contained in the strain-gradient theory.