A family of hole boundary elements for modeling materials with cylindrical voids

In this paper, a boundary element formulation for modeling two-dimensional microstructures containing cylindrical voids is presented. Each void is inserted in a standard boundary element mesh in a efficient way using a single special hole element. The traditional discretization in several boundary elements is then avoided. Trigonometric functions are used as base for the element shape functions. A family of hole elements with 3, 4, 5 and 6 nodes is proposed. The numerical integration of the strongly singular kernels found in the element implementation is accomplished by the direct method, resulting in a regularized element. The convergence behavior of the proposed approach is analyzed for several quadrature orders. A static condensation scheme is performed on the system of equation to further improve the formulation. The accuracy of proposed method is illustrated with some examples.