Micromechanics of hardening of elastic–plastic crystals with elastic inclusions: I – Dilute concentration

We propose a micromechanical model for elastic–plastic deformation of crystals containing elastic inclusions. The model is based on a novel method for calculation of elastic strain energy associated with incompatible deformation in the matrix and in the inclusion, whereby this energy is interpreted as the interaction energy of geometrically necessary dislocation loops (Mesarovic, S.Dj., 2005. Energy, configurational forces and characteristics lengths, associated with the continuum description of geometrically necessary dislocations. Int. J. Plasticity 21, 1855–1889), which are geometrically equivalent to the incompatible strain. The method is general, easily applied to complex geometries and particle interactions, and – it often yields analytic solutions. In this communication, we analyze the simple case of dilute concentration of inclusions. The resulting model is remarkably simple; it falls within the framework of classical crystal plasticity with a specific elastic–plastic constitutive law that accounts for shape of inclusions.