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.

中文翻译：

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基于接触应力的应力恢复方法，用于不连续变形分析

不连续变形分析（DDA）已广泛用于模拟具有许多不连续表面的块系统。惩罚方法用于确保块之间没有穿透。位移的线性多项式函数导致一个块的应力恒定，这无法精确描述该块内的应力场。因此，始终使用高阶多项式位移函数和精细网格来提高应力场的精度。但是，这些方法对于模拟具有许多触点的块系统不切实际。本文提出了基于接触应力的应力恢复方法。利用了针对块边界上的接触应力的高精度解决方案。块的一阶高斯点是块的质心，通过DDA获得的恒定应力具有更高的精度。最小二乘法使用高精度的应力解决方案来恢复单个块的内部应力场。所提出的方法提高了单个块内应力场的分辨率，而没有增加DDA位移的主要迭代过程中的计算量。数值示例使用具有精细网格的有限元方法（FEM）和提出的DDA程序进行了仿真。恢复的DDA结果可以准确地描述单个块中的应力分布，并且在某些区域中具有与FEM结果相同的精度。此外，所提出方法的精度随着边界上接触应力梯度的减小而提高。