An approximate continuum theory was developed to effectively handle the problem of interaction between dislocations and inhomogeneity of any shape and properties. The inhomogeneity is, based upon the Eshelby equivalent inclusion theory, equivalent to a homogenous one with a transformation strain. The interaction force between dislocation and the inhomogeneity could then be evaluated from the work done by the dislocation stress field during the transformation. The proposed continuum theory was applicable to a variety of inhomogeneities, such as pore, gas bubble, shear band and plastically deformed zone. It could be reduced to the classical continuum theory for some special cases.

An Approximate Continuum Theory for Interaction Between Dislocation and Inhomogeneity of Any Shape and Properties. Z.Li, Y.Li, J.Sun, X.Q.Feng: Journal of Applied Physics, 2011, 109[11], 113529