3D DDA Based on Variational Inequality Theory and Its Solution Scheme

Abstract

The advantage of 3D discontinuous deformation analysis (3D DDA) is the rigorous contact conditions on the interaction of 3D blocks. These conditions are enforced by the penalty function convention; however, inappropriate penalty parameters easily generate numerical instability. To avoid the introduction of the penalty parameters, the contact conditions in 3D DDA are described as variational inequalities in this study, and the extra-gradient method is employed to solve this new formulation of 3D DDA. The proposed computation scheme is more flexible and dispenses with large scale matrix inversion. Some practical examples originally designed by Shi are analysed, verifying the effectiveness and precision of the new scheme.