三维简单变形体离散元方法

针对小应变、大位移和大转动的块体系统提出了三维简单变形体离散元数值模型(3SDEM)。首先基于牛顿定理推导出了包含块体刚体运动和变形的整体运动和变形方程,同时提出了在小变形条件下,块体的运动和变形可分解为块体刚体运动和变形的叠加,从而分别推导出基于刚体平移、转动和变形的方程。此外针对块体的变形,3SDEM选取了几组简单的变形模态,将块体的变形用选定的变形模态来表示,并给出了各个变形模态互相解耦的条件。本模型采用了显式的时步步进的求解格式,因此是一种模拟不连续介质力学行为的有效数值分析方法,尤其适用于求解非连续、大变形以及动力问题。该模型克服了三维复杂变形体离散元(3DEC)需要对块体内部细分网格导致计算量急剧上升的缺点,具有高效、仿真和可变形的特点。算例表明:这种数值模型能够给出合理的结果,并具有良好数值稳定性。

3-D simple deformable distinct element method

Aimed at the block system with small strain,large displacement and rotation,3-D simple deformable distinct element method(3SDEM) was presented,and it was an efficient numerical method for simulating mechanical behaviors of discontinuums.It was suitable to be used to analyze nonlinear,large deformation and dynamic problems due to its explicit finite-difference scheme and automatic contact detection method.First,the equation of motion and deformation was established basedon the Newtonian Laws.Second,under the small deformation condition,the kinematic equation of blocks could be decomposed into rigid motion and deformation.Third,based on several deformation modes,the deformation of blocks could be expressed by the combination of deformation modes,which could be decoupled under specifical conditions.In 3SDEM,each block was an element,avoiding the increase of grid points of the block as what happened in 3DEC.So the computation cost was less than 3DEC.At last,two numerical examples were calculated with 3SDEM,and the reasonable results and the good computation stability were obtained.