Asymptotic homogenization for effective parameters of unidirectional fiber reinforced composites by isogeometric boundary element method

In this paper, formulations for asymptotic homogenization method based on the boundary element method (BEM) are presented for the estimations for effective parameters of unidirectional fiber reinforced composites in the 2D plane strain case. The boundaries are discretized by shape functions of non-uniform rational B-splines (NURBS) according to the features of isogeometric analysis and the related isogeometric boundary element method is established. The strongly and weakly singular integrals in the boundary integral equations are precisely calculated in direct schemes. Comprehensive comparisons for the obtained effective parameters by the current method are conducted with the existing ones by conventional BEM and the ones by finite element method (FEM). It is found that the estimations in present work are more accurate than the ones by conventional BEM with fewer control points and are also more accurate than the ones by FEM for fibers with more complex geometry. The outperformance of the current method shows competitive potentials in homogenization for the real 3D composites.