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 micro cracks in various sizes and estimate the global effective elastic moduli of the micro crack-weakened solid. Following the previous simulation of solids with circular micro cracks, the present analyses require no interactions of elliptical micro cracks, and investigate the relations between the effective elastic moduli and the micro crack density parameter. Some representative elliptical micro crack models (including randomly distributed micro cracks and a family of parallel micro cracks) are simulated, and compared with some analytic approximate micromechanical solutions. Numerical results shows the elliptical micro cracks 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 micro cracks or micro cracks of other shapes in complicate distributing states, and present an accurate effective moduli prediction.