Isogeometric analysis of the new integral formula for elastic energy change of heterogeneous materials

In recent years, more and more attention has been paid to isogeometric methods, in which shape functions are used to accurately describe CAD models and approximate unknown fields. The isogeometric boundary element method (IGABEM) realizes the integration on the exact boundary of the region, which means there is no geometric discretization error. In this paper, a more general interface integral formula for elastic energy increment of heterogeneous materials is extended from previous work (Dong, 2018), in which the only unknown variable is the displacement located on the interface between matrix and inclusion. This feature makes it more compatible with boundary element method (BEM) because of none of volume parametrization. However, the geometry discontinuity on the boundary called ‘corner point problem’ increases the difficulty and decreases the accuracy when solving complex numerical examples when heterogeneous structures are considered. The discontinuous element method combined with IGABEM is presented and applied to deal with ‘corner point problem’. In the numerical examples, the interface between matrix and inclusion is discretized by quadratic isogeometric elements. Compared with the analytical solution, the numerical results show that the method has higher accuracy and efficiency.