DEM与FEM动态耦合算法研究

离散单元法作为一种有效的数值分析方法,能够模拟脆性材料的裂纹扩展及碎片飞散等破坏特性,但是无法从根本上克服计算效率低下的诟病;传统有限单元法具有计算高效稳定的优点,却难以描述脆性材料冲击破坏过程中连续体向非连续体的转化。本文首先提出一种基于罚函数法的改进型离散单元和有限单元耦合方法,以提高耦合分析精度。在此基础上提出了动态耦合算法:即在初始阶段,模型全部为有限单元,当局部即将发生破坏时,仅使即将发生破坏的有限单元及相邻单元自动转化为离散单元,在离散单元区域研究破坏问题。这种算法充分利用有限单元法计算高效的优点,同时最大限度克服了离散单元法计算效率的不足。最后,通过两个简单算例验证了改进型耦合算法和动态耦合算法的有效性。

Study on dynamic coupling algorithm based on DEM and FEM

The discrete element method (DEM),one of effective numerical methods,can model fracture characteristics of brittle material such as crack propagation and dispersing fragments,but has poor computational efficiency which cannot be overcome essentially.By contrast,the conventional finite element method (FEM),which has advantages of high efficiency and stability,does not effectively simulate the failing procedure.We firstly propose improved coupling method based on penalty function method in order to improve computational accuracy.We develop a dynamic coupling algorithm which is based on improved coupling method:in the initial stage,the whole model is constructed with finite elements and no discrete elements; thereafter if the local damage happens,the finite elements impending to fail and their neighbors will be automatically converted into discrete elements and the glass fracture procedure is simulated in the region of discrete elements.The algorithm not only takes full advantages of the two methods mentioned above,but also overcomes low efficiency of DEM.The effectiveness of two algorithms mentioned before is validated by comparing the results of a few simple cases.