BOUNDARY ELEMENT METHOD FOR PROBLEMS WITH MULTIPLE TYPES OF INCLUSIONS

A new boundary element method is presented for solving the problems of 2D solids with multiple types of inclusions such as elastic inclusions, fluid inclusions and pores. Essentially, this problem is also a multi-connected domain problem, but the displacements and tractions on the inner boundaries of the multi-connected domain are unknown quantities, which made the whole problem cannot be solved directly for the lack of adequate boundary conditions. According to the constitutive relations of the different types of inclusions, the so-called incidence matrices are established between the tractions and displacements on the inclusion-matrix interfaces, and they are just the complementary boundary conditions that we are trying to find, consequently the problem can be solved without any difficulty. To verify the validity of the presented method as well as the correctness and the reliability of the program, the examples of plane strain problems are illustrated, in which the solid matrix containing only one or all of the three types of inclusions respectively, and the effective elastic modulus are simulated for a sheet that contains up to 100 randomly distributed elastic inclusions.