Numerical solution of 3D elastostatic inclusion problems using the volume integral equation method Original Research Article

A volume integral equation technique developed by Lee and Mal (J. Appl. Mech. Trans. ASME 64 (1997) 23) has been extended to investigate three-dimensional stress problems with multiple inclusions of various shapes. Based on the volume integral formulation, displacement continuity and traction equilibrium along the interfaces between the matrix and the inclusions are automatically satisfied. While the embedding matrix is represented by an integral formulation, only the inclusion parts are discretized into finite elements (isoparametric quadratic 10-node tetrahedral or 20-node hexahedral elements are used in the present study). A number of numerical examples are given to show the accuracy and effectiveness of the proposed method.