Displacements Produced by Linearly Varying Eigenstrains with Application to Isoparametric Triangular Inclusion

The planar Eshelby's inclusion model has been widely applied in exploring the micromechanical behavior of fiber-reinforced composites. Based on contour integral formulation, we first present a closed-form solution to the displacement of a polygonal inclusion subjected to linear eigenstrains. In view of isoparametric representation, the resulting contributions from a triangular inclusion are conceived as the elementary solution, which may be regarded as building blocks for analyzing an arbitrarily shaped inclusion with any distributed eigenstrains. The present numerical discretization is merely performed on the inclusion domain, as opposed to the traditional Finite Element Method where the infinitely extended matrix also requires tremendous meshing efforts.