The expression for the free energy which was related to the Eshelby-Kröner inelastic inclusion problem was simplified by using the theory of irreducible representations. This method greatly simplified problems, especially those involving moving boundaries, which required energy derivatives. As an application, the stability of a dislocation loop under an applied stress was studied. A new interpretation of the critical shear stress in single crystals was proposed. Another application was the grain-size effect in polycrystalline elasticity. The yield stress was found to obey a reciprocal square root dependence upon grain size at small grain sizes (equivalent to the classic Hall-Petch relationship). At large grain sizes, the grain-size power-law exponent was -1 rather  than -½.

Constrained and Unstable Expansion of Dislocation Loops using an Invariant Formulation of the Free Energy I.Aubert, M.Berveiller: Mechanics of Materials, 1997, 26[4], 127-37