New point-to-face contact algorithm for 3-D contact problems using the augmented Lagrangian method in 3-D DDA

Abstract

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.

Keywords:

• numerical method
• three-dimensional
• discontinuous deformation analysis
• augmented Lagrangian method
• rock mechanics