Contact-Stress-Based Stress Recovery Methods for Discontinuous Deformation Analysis

Abstract

Discontinuous deformation analysis (DDA) has been widely applied for the simulation of block systems that have many discontinuous surfaces. The penalty method is utilized to ensure that there are no penetrations between blocks. A linear polynomial function for displacement leads to a constant stress for a block, which cannot precisely describe the stress field within the block. Therefore, a high-order polynomial displacement function and a fine mesh are always used to improve the precision of the stress field. However, these means are not practical for simulating block systems that have many contacts. In this paper, the contact-stress-based stress recovery methods are proposed for DDA. High-precision solutions for the contact stresses on the boundaries of the blocks are utilized. The first-order Gaussian point of a block is the block’s centroid, where the constant stress obtained via DDA is of higher precision. The high-precision solutions for the stresses are utilized in the least squares method to recover a single block’s inner stress field. The proposed methods enhance the resolution of the stress field inside a single block without increasing the computational effort in the main iterative process for displacement in DDA. Numerical examples are simulated using both the finite element method (FEM) with a fine mesh and the proposed DDA program. The recovered DDA results can accurately describe the distribution of the stresses in a single block and, in some areas, have the same precision as the FEM results. Moreover, the precision of the proposed methods improves as the gradient of the contact stress on the boundary decreases.