Numerical Modeling for the Analysis of Crack-Inclusion Problems by the Eigen Iterative Computational Model

For the numerical modeling of solid materials containing crack-inclusions, the theory of Eshelby’s eigenstrain and equivalent inclusion was incorporated into the boundary integral equations (BIEs). A computation model and an iterative algorithm for the eigen crack opening displacement (COD) and eigenstrain BIEs to address the interaction of crack-inclusions were proposed. Under certain conditions, anisotropic inclusions may be considered as general inclusions. When the elastic modulus of the inclusion is set to zero, the inclusion will degenerate into a hole, and geometrically, with its minimum dimension reduced to zero further it will degenerate into a crack. Thereby, a crack was classified as a special type of inclusion with zero elastic modulus. The discrete form of the boundary integral equation was utilized for the numerical validation of cracks and inclusions, with their boundaries discretized with Gaussian integration points and the boundary point methods, respectively, to conduct stress analysis and investigate the interaction between crack-inclusions. Numerical examples confirm the correctness and feasibility of the eigen iterative model in modeling crack-inclusion problems, demonstrating its high computation accuracy, and providing the theoretical foundation for future large-scale numerical analysis with this computation model.