Two interacting ellipsoidal inhomogeneities: Applications in geoscience

We developed a method and presented it as a Mathematica code to calculate the stress and strain fields inside and outside of two interacting ellipsoidal inhomogeneities with arbitrary orientation with respect to each other, using the Eshelby technique. The Eshelby technique can be used to determine the elastic fields in and around these inhomogeneities. Assuming same material properties for one of the inclusions and the surrounding matrix, this code can be also used for the single inhomogeneity problem. Different geological features like faults and aquifers can be modeled as inhomogeneous inclusions. We start by reviewing Eshelby's solution for a single inclusion, a single inhomogeneity and a double inhomogeneity problem with the required formulation to calculate Eshelby tensors. Then, we describe our code structure and validate it with existing solutions in the literature and present numerical solutions.