多裂纹扩展的数值流形法

数值流形法的求解体系建立在两套覆盖(包括数学覆盖和物理覆盖) 和接触环路的基础之上,实现了对连续和非连续问题的统一求解. 在处理裂纹问题时,数学覆盖无需与裂纹重合,方便岩体破坏过程的模拟. 通过在裂纹尖端影响区域内的物理片上增加用于模拟应力奇异性的增强位移函数,发展了扩展的数值流形法. 在此基础上,提出一种多裂纹扩展的控制算法,并给出了裂纹扩展过程中材料体的整体响应. 针对典型的线弹性断裂力学问题, 给出的数值算例表明所建议的方法是正确有效的. 

MULTIPLE CRACK PROPAGATION BASED ON THE NUMERICAL MANIFOLD METHOD

The numerical manifold method based on the two covers (mathematical cover and physical cover) and contact loop have been used to solve the continuum and discontinuum problems in a unified way. The mathematical cover is not enforced to coincide with the cracks when dealing with the discontinuous problem, facilitating the simulation of failure in rock mass. An enriched numerical manifold method is developed by adding the enriched displacement functions used for simulating the stress singularity to the physical patches around the crack tip. And on this base, a new algorithm of the multiple crack propagation is proposed; the overall response of the material is given during the crack propagation. Numerical examples with NMM for the classic linear elastic fracture mechanics problems are presented, suggesting that the proposed procedure is accurate and efficient.