This code determines the stress and strain fields of multiple spherical /circular inhomogeneities by Equivalent Inhomogeneous Inclusion Method (EIIM). EIIM is an inverse of Equivalent Inclusion Method and simulates the subdomains of matrix with known strains with equivalent inhomogeneous inclusions. The stress and strain fields of multiple inhomogeneities are decomposed into the superposition of matrix under applied load and each solitary inhomogeneous inclusion with polynomial eigenstrains by the iteration of EIIM. 

There are two programs in the attachment. Codes for 2D EIIM deals with multiple circular inhomogeneity problems, and codes for 3D EIIM deals with multiple spherical inhomogeneity problems. We recommend the readers the papers Multiple ellipsoidal/elliptical inhomogeneities embedded in infinite matrix by equivalent inhomogeneous inclusion method for a better understanding of the programs. 

main_2D（3D）
The two programs start with main_2D and main_3D, respectively.

Residual_Elastic_Field_2D (3D)
This subprogram calculates the residual stress and strain fields of multiple inhomogeneities by EIIM.

Polynomial_EigenF_ItoM_2D (3D)
This subprogram transforms the inhomogeneous inclusion with polynomial eigenstress to homogeneous inclusion with polynomial eigenstress, as a homogeneous inclusion with polynomial eigenstrain has analytical solutions.

Equivalent_Eigenstress_2D (3D)
This subprogram evaluates the equivalent eigenstress of the jth inhomogeneity resulted from the ith inhomogeneity. The non-uniform eigenstrain are approximate by polynomials.

Trsform_X_Q_2D(3D)
This subprogram returns the polynomial form of points.

T0_Strainoutside_2D(3D)
This subprogram evaluates the strain outside the incluions with uniform eigenstrain.

T1_Strainoutside_2D(3D)
This subprogram evaluates the strain outside the incluions with linear eigenstrain.

T1_Cell_3D
This subprogram returns Eshelby's tensors of spherical incluison with linear eigensrain.

Dense_area
Much time is occupied by the calculations of stress and strain of nodes. To save time, Dense_area makes the nodes close to the boundary of the fiber become dense while the nodes away from the fibers are spare.

Createfigure
Plot the stress and strain fields of multiple inhomogeneities. The field contours are close to those of Abaqus.

84fiber_positions.xls
An example of 84 fibers embeded in infinite matrix is presented in the paper Multiple ellipsoidal/elliptical inhomogeneities embedded in infinite matrix by equivalent inhomogeneous inclusion method. The position of the 84fibers are stored in this xls file, the first and second columns are, respectively, the x- and y-coordinates of the center of fibers. The EIIM code for circular inhomogeneities can evaluate the stress and strain fields of the 84 fibers.