Abstract：A numerical method combining finite element sub-partition and substructure is developed to simulate crack extension. In this method, crack is allowed to enter or separate an element or to extend along element side. Therefore, crack can extend along any path without the limitation of original mesh. The elements involving one crack are sub-partitioned according to the crack path and they are constructed a sub-structure. The size of substructure expands when the crack propagates. The additional freedoms introduced by element sub-partition are expressed by the freedoms of original mesh nodes via agglomeration of stiffness matrix. Therefore the total freedom dimension keeps constant whether cracks extend or new cracks appear. The crack initiation and extension laws are suggested based upon this sub-partition algorithm. This method is used to calculate the crack tip fields of central crack in infinite plane for both mono-material and bi-material to investigate its accuracy. It is further used to simulate micro-scale crack extension in particle, matrix and particle/matrix interface in a particle reinforced composite to prove its adaptability for simulating of complex path cracking.
2013, Vol. 34 
