数学网格和物理网格分离的有限单元法(II):粘聚裂纹扩展问题中的应用

强化有限单元法将物理网格与数学网格分离开来,可以方便地描述非连续变形;粘聚区域模型是模拟断裂过程区作用最简单有效的方法,且可以避免裂纹尖端的应力奇异性.本文以平面问题为例,将强化有限单元法与粘聚区域模型相结合,利用富集数学节点描述任意粘聚裂纹扩展过程中的非连续变形问题,提出了裂纹扩展过程中数学节点富集和数学单元定义的方法.本文还导出了与平面4～8节点平面等参单元对应的8～16节点粘聚裂纹单元列武.最后,通过三点弯梁的裂纹扩展过程模拟验证了本文提出的粘聚裂纹扩展模拟方法的有效性.

An enhanced finite element method with separate mathematical and physical mesh

Basing on separation between mathematical meshes and physical meshes, the enhanced finite element method (FEM⁺⁺) makes it easy to describe discontinuous deformation. The cohesive zone model (CZM) which can avoid the stress singularity at the crack tip is one of the most effective and simplest model to simulate the interaction within fracture process zone. FEM⁺⁺ and CZM are applied to simulate the propagation of arbitrary cohesive crack by enriching mathematical node in this paper. The rule of mathematical node enrichment and mathematical element definition are also summarized, and an 8-16 node CZM element is proposed for cohesive crack. At last, three point bending beam is analyzed to illuminate the efficiency of the proposed method.