IGABEM of 2D and 3D liquid inclusions

Randomly distributed liquid inclusions in elastic matrix exist in nature, biology, material science and other fields. In this paper, the isogeometic analysis boundary element method (IGABEM) is applied to study the mechanical properties of the elastic matrix with liquid inclusions, in which the liquid inclusion is assumed to be linearly compressible and the interface tension is neglected. Singularity subtraction technique (SST) and Tells transformation method are respectively used to solve the strongly and weakly singular integrals in two-dimensional (2D) problems, while the power series expansion method is used to carry out various singular integrals in three-dimensional (3D) problems. The oriented bounding box (OBB) is adopted to generate the randomly distributed liquid inclusions, which can be formed easily by the control points of the IGA. Numerical examples show the accuracy and effectiveness of the present method in the study of liquid inclusions.