Numerical simulation of 3-D elastic moduli with elliptical cracks using FM-DBEM

In the paper, the fast multiple dual boundary element method is applied to simulate the model of a elastic three-dimensional (3-D) isotropic solid with elliptical microcracks in various sizes and estimate the global effective elastic moduli of the microcrack-weakened solid. Following the previous simulation of solids with circular microcracks, the present analyses require no interactions of elliptical microcracks, and investigate the relations between the effective elastic moduli and the microcrack density parameter. Some representative elliptical microcrack models (including randomly distributed microcracks and a family of parallel microcracks) are simulated, and compared with some analytic approximate micromechanical solutions. Numerical results shows the elliptical microcracks can be approximated with good accuracy to be circular cracks in the same crack density. Besides, it can also present an alternative simulation method of structure containing elliptical microcracks or microcracks of other shapes in complicate distributing states, and present an accurate effective moduli prediction.