This paper presents a new point-to-face contact algorithm for contacts between two polyhedrons with planar boundaries. A new discrete numerical method called three-dimensional discontinuous deformation analysis (3-D DDA) is used and formulations of normal contact submatrices based on the proposed algorithm are derived. The presented algorithm is a simple and efficient method and it can be easily coded into a computer program. This approach does not need to use an iterative algorithm in each time step to obtain the contact plane, unlike the 'Common-Plane' method applied in the existing 3-D DDA. In the present 3-D DDA method, block contact constraints are enforced using the penalty method. This approach is quite simple, but may lead to inaccuracies that may be large for small values of the penalty number. The penalty method also creates block contact overlap, which violates the physical constraints of the problem. These limitations are overcome by using the augmented Lagrangian method that is used for normal contacts in this research. This point-to-face contact model has been programmed and some illustrative examples are provided to demonstrate the new contact rule between two blocks. A comparison between results obtained by using the augmented Lagrangian method and the penalty method is presented as well.
The original (i.e. first order) discontinuous deformation analysis (DDA) formulation has two main shortcomings. First, a linear function is used to represent the displacement field in the blocks. This formulation implies that the state of stress (and strain) within each block is constant. Second, the material within each block is assumed as linear elastic. These two major limitations can often render the original DDA analysis method unrealistic and significantly inaccurate. In the modified DDA approach introduced in this study, these two limitations have been addressed. The authors have used the finite element method (FEM) to discretise each block in the DDA formulation using an automatic mesh generation algorithm to determine the distributions of stress and strain within each block to a desired accuracy. In addition, the Mohr-Coulomb elastic-plastic yield criterion is incorporated within the modified DDA analysis method using a time marching algorithm to account for the possibility of material failure. This allows the plastic behaviour (i.e. yielding) of the material within each block be included in the analysis, which is a significant improvement over the original DDA method. The numerical implementation of the Mohr-Coulomb criterion involves trials using initial elastic stress increment and comparisons with the yield criterion within each element. The proposed DDA formulation including the Mohr-Coulomb failure criterion (termed here as the MC-DDA method) is validated against selected analytical solutions, numerical solutions from FLAC verification problems and field measurements.
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