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.