Boundary element method for solid materials with multiple types of inclusions

The boundary element method is developed for solving the problems of solid materials containing multiple types of inclusions, such as pores or cavities, elastic inclusions, rigid inclusions, as well as fluid inclusions. In fact, such a kind of problem can be seen as a boundary integral equation (BIE) problem for a multiply connected domain, but it cannot be solved directly for lack of adequate boundary conditions, i.e., both the displacements and tractions on the inner boundaries of the multiply connected domain are unknown quantities. The so-called incidence matrices are established between the tractions and displacements on the inclusion–matrix interfaces, and it happens that they are just the complementary boundary conditions that are missing for solving the algebraic systems arising from the BIEs, and consequently the problems become solvable. The numerical examples apply the method to the analysis of problems with multiple types of inclusions, and the results indicate that this boundary element method scheme is effective and useful for such problems. Furthermore, the present scheme can be used to investigate the equivalent mechanical properties of composite materials containing multiple types of inclusions.