Non-rigid disk-based DDA with a new contact model

In this paper, a new disk-based DDA formulation is presented. In the original disk-based DDA, disks are considered to be rigid and the penalty method is used to enforce disk contact constraints. In order to improve the accuracy of the disk-based DDA, new formulations of stiffness and force matrices for non-rigid disks using a new efficient contact model are presented in this paper. Blocks are considered deformable without need to do more computations for contact detection. In the proposed contact model, disk–disk and disk–boundary contacts are transformed into the form of point-to-line contacts and normal spring, shear spring and frictional force sub-matrices are derived by vector analysis. The penalty method is quite simple to implement, but has some major disadvantages. In the presented contact model, not only the simplicity of the penalty method is retained but also the limitations are overcome by using the augmented Lagrangian method. Moreover, unlike the contact model used in the original disk-based DDA, reference line can be obtained directly by using only coordinates of disk centers and their radii, and no more computations are needed. The validity and capability of the new disk-based DDA formulation are demonstrated by several illustrative examples.