离散大块体断裂破坏分析方法研究

一般离散单元计算方法(包括DDA方法)受离散块体低阶线性位移近似的限制,在模拟开裂过程时,需要将大部分实际上连续的区域离散化,离散方式对分析结果有显著影响。为了建模时利用真实结构面来构造块体系统,提高大块体位移应力分析精度,有必要引进新的位移近似假设。本项研究在块体内引入无网格法位移模式,以离散节点位移自由度代替原基本块体自由度,并在此基础上进行块体内非贯穿裂纹扩展和强度破坏分析。为此建立的无网格法裂纹扩展分析算法,采用满足单位分解条件的特殊增强型函数表达裂纹周围应力场的非连续、奇异特性,将对应的扩展自由度动态映射到裂纹周围的节点上,统一按DDA法隐式迭代方式求解,实现块体裂纹扩展和强度分析,相关算例结果显示该算法是合理有效的。

On a numerical method for analyzing large discrete blocks’ fracture and breakage

Restricted by the assumption of low-order linear displacement approximation in each block,Discrete Element Methods(including DDA) often have to mesh many continuum parts of the problem domain into small discrete blocks when simulating crack propagation problems,and the result is very sensitive to the very way that divides the domain.In order to construct the block system with physical structural planes as consistently as possible and improve precision of displacements and stresses results,it is indispensable to introduce new efficient displacement approximations.This method newly introduces meshfree approximations,meshfree nodal displacements are taken as the degrees of freedom instead of block rigid movements and strains.Based on this improvement,analysis of cracks’ propagation inside blocks can be conducted.The detailed algorithm on analyzing cracks exploration inside blocks is: enriched approximations which describe singular crack tips fields and discontinuous crack faces are employed under the Partition of Unity theory;the enriched nodes surrounding crack tips or faces are respectively mapped with corresponding enriched degrees of freedom,and the solution of all these degrees of freedom is uniformly proceeded by the implicit iteration algorithm of DDA,then fracture and breakage of DDA blocks can be analyzed.The numeric examples show this algorithm is rational and efficient.