A new integral formula for the variation of matrix elastic energy of heterogeneous materials

This work presents a new integral formula for the variation of matrix elastic energy caused by the inclusion, which only contains the displacements on the interface between inclusion and matrix. Compared with the existing formula, the present formula avoids the corner point problems in the implementation of the boundary element method (BEM) so that it can conveniently deal with the complex shape inclusion problems. In numerical calculation, 3-node (8-node) quadratic boundary elements for two (three) dimensional problems are used to discretize the interface between inclusion and matrix. Numerical results are compared with the analytical solutions available.