Direct Evaluation of Singular Integrals in a Hole/Inclusion Boundary Element for Modeling Micro-Heterogeneous Material

Abstract

In this work, the integration of singular kernels in a specially
developed hole or inclusion boundary element is accomplished by the
direct method. These elements are custom tailored for modeling
two-dimensional microstructures containing cylindrical holes and/or
inclusions, so that each micro-heterogeneity is represented by a
single element. The traditional discretization in several boundary
elements is then avoided. Using the direct method, all strongly
singular integrals present in the element matrices are
regularized. The convergence behavior of the proposed scheme is
analyzed for several quadrature orders.