The equilibrium shape of an elastically inhomogeneous inclusion

Abstract A method is proposed for determining the equilibrium shape of an elastically inhomogeneous coherent precipitate in an anisotropic medium. Arbitrary eigenstrains and an isotropic interfacial energy density are taken into account. Use is made of Eshelby's notion of a “force on an interface” and boundary integral techniques are employed. Results for the plane strain case of one single inclusion and a regular array of inclusions with dilatational eigenstrains in an orthotropic matrix are presented. We find that the three factors: difference of elastic moduli in matrix and inclusion, interfacial energy and particle-particle interaction can affect the equilibrium shape in much the same way. The elastic inhomogeneity can cause strongly non-convex particle shapes and considerably affects the stability of fourfold symmetric equilibrium shapes.

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