Expansion of a Spherical Cavity in an Infinite Dilatant Medium Obeying the Drucker–Prager Yield Criterion and a Non-Associated Plastic Flow Rule

The distributions of the principal stresses, the radial velocity, and the relative density are determined in an infinite dilatant medium in which a spherical cavity expands from a zero radius. The medium obeys the Drucker–Prager yield criterion. The plastic potential is also of Drucker–Prager type but differs from the yield criterion. Moreover, it involves the relative density and results in the incompressibility equation at a certain relative density value. A detailed analysis of the solution is provided for a specific dependence of the plastic potential on the relative density. It is shown that the qualitative behavior of the solution near the cavity’s surface depends on a constitutive parameter involved in this dependence. A numerical example illustrates the general solution.