A fast multipole BEM with higher-order elements for 3-D composite materials

The present work is to develop the FMBEM with quadratic elements to the analysis of 3-D linear elastic structures containing subdomains. To the numerical integration, an adaptive method with subdivision of elements is applied. The BEM formulation for perfectly bonded subdomains, in which interface traction forces are eliminated from the system of equations is implemented. The method is applied to problems of solids with spherical inclusions: a single inclusion, two interacting inclusions, many regularly distributed inclusions and randomly distributed inclusions. Different values of volume fraction of inclusions, up to 0.5 for the cubic arrangement of inclusions, and contrast in elastic properties between the matrix and inclusions, up to 1000 for the ratio of Young's moduli of the constituents, are considered. Stresses or effective elastic constants are computed. The results are compared to analytical models and a good agreement is observed. The proposed method shows a perspective of modelling 3-D composites efficiently.