Stability of rigid solids embedded in an elastic medium

The stability of a two-dimensional continuum consisting of rigid solids embedded in an elastic homogeneous medium with a fixed boundary is investigated. With each solid is associated the scalar where are balanced dead loads acting at points M of the solid, and where S is the area of the surface of the solid. If is the shear modulus of the elastic medium, it is shown that (i) the inequality +4>0, when it applies to each solid, is a sufficient condition for stability of the continuum; (ii) the inequality +40 is a necessary condition for stability of a single circular solid embedded in an infinite elastic medium.