Some modifications to the process of discontinuous deformation analysis

This paper presents a modified method of discontinuous deformation analysis (DDA). In the presented method, open-close iteration may not be needed, small penetration is permitted among blocks, and springs are added between contacting block pairs only when a penetration takes place. The three contact patterns (i.e. sliding, locking and opening) in original DDA method are not involved, and the recognition of these contact patterns and treatment of transformation among patterns are not required either, significantly saving the computing time. In a convex to concave contact, there are two candidate entrance edges which may cause uncertainty. In this case, we propose the angle bisector criterion to determine the entrance edge. The spring stiffness is much larger than Youngʹs modulus in the original DDA, however we find that the correct results can still be obtained when it is much smaller than Youngʹs modulus. Finally, the penetrations by using penalty method and augmented Lagrangian method are compared. Penetration of the latter is 1/4 of the former. The range of spring stiffness for the latter is wider than the former, being 0.01–1 of the former. Both methods can lead to correct contact forces.