Discrete Eshelby technique for modeling elastic response of unbounded media to eigenstrains

Summary This paper presents a novel Eshelby inclusion-based technique for modeling heterogeneities within unbounded elastic formations as regions of stress-free transformational strains (eigenstrains). It is assumed that the geometrical shape of the regions is known, but the eigenstrains are only available at a number of discrete points. The region of interest is discretized using a triangulation procedure in which the points with known data are made to be located at the vertices of the triangles. It is assumed that the eigenstrain distribution inside each triangle is uniform, but different from that inside other triangles. The value of that uniform eigenstrain is evaluated by constructing a linear interpolating function from the values at the triangle vertices and by finding the average of that function over the area of the triangle. The elastic fields and the components of the Eshelby tensor both inside and outside of each triangle of the region of interest are obtained from exact complex variables-based integral representations for the relevant fields. The technique is validated by comparisons with the reported benchmark results for problems involving circular inclusions subjected to prescribed nonuniform eigenstrains and with those involving inclusions of arbitrary shapes subjected to prescribed uniform eigenstrains. A numerical example illustrates the potential of the technique in handling problems involving arbitrary-shaped inclusions subjected to nonuniform eigenstrains whose values are only available at a discrete number of points.