Elastic Inclusion Problems in Multi-Phase Materials
Perry H. Leo
Department of Aerospace Engineering and Mechanics
University of Minnesota
We consider two examples where Eshelby’s solution for elastic inclusions is applied to multiphase materials. The first example is of a multiphase microstructure arising from a diffusional phase transformation, such as in nickel-based superalloys. Here the elastic fields influence the kinetics of the transformation process, and so we use numerical methods to track the microstructure as it evolves toward the equilibrium structure. The second example is of a composite material made of ferromagnetic shape memory inclusions. We find the effective properties of the composite by adapting Eshelby’s result that ellipsoidal inclusions in an infinite matrix have uniform strain in their interior. We extend this result to high volume fraction composites with periodic microstructures by finding inclusion shapes that share this uniform strain property.