Distributed-Spring Edge-to-Edge Contact Model for Two-Dimensional Discontinuous Deformation Analysis

Edge-to-edge contact is a fundamental contact type in blocky systems. In two-dimensional discontinuous deformation analysis (2D DDA, and hereinafter DDA for short), an edge-to-edge contact is transformed into two separated vertex-to-edge contacts by applying two pairs of concentrated springs. Although this simplification facilitates the DDA algorithm, it is not always sufficiently accurate and can even yield irregular results. To solve this problem, a distributed-spring contact model (DSCM) that exerts distributed instead of concentrated forces on contact edges is proposed in this paper for the edge-to-edge contact in DDA. Submatrices for the force matrix and stiffness matrix are obtained by minimizing the potential energy of the distributed contact forces and are incorporated into an improved DDA (I-DDA) code. Four examples are evaluated to illustrate the validations and advantages of the I-DDA. The first example is a single square impacting on a base block. Deformation of the contact area is evaluated by comparison with the theoretical deformation solution, and the results calculated by the I-DDA show better agreement with the analytical solution than the original DDA (O-DDA). The second example is an impact validation, proving that the I-DDA is more adaptable to discrete systems containing blocks of different sizes. Then an example and an experiment about block rebounding are provided, demonstrating that the errors in rotation and rebounding exhibited in the O-DDA results are avoided when using the I-DDA, indicating that the I-DDA provides more realistic solutions. The results of this study suggest that the proposed I-DDA incorporating the DSCM is quite accurate and capable of improving calculation accuracy compared to the O-DDA.