基于NMM的EFG方法及其裂纹扩展模拟

数值流形方法（numerucal manifold method，NMM）通过引入数学覆盖和物理覆盖两套系统来统一处理连续和非连续问题. 通过用移动最小二乘插值（moving least squares interpolation，MLS）中的节点影响域构造数学覆盖，得到了基于数值流形方法的无网格伽辽金法（element free Galerkin，EFG）. 该方法在保证前处理简单的同时，又能方便处理如裂纹等不连续问题. 建立了适用于小变形和大变形的裂纹扩展计算格式，并通过对曲折裂纹（kinked crack）的处理，在不加密的情况下实现了任意小步长的裂纹扩展，大大提高了在固定网格中模拟裂纹扩展的实用性. 大小变形的结果对比表明，按照不考虑构型变化的小变形计算，结果可能偏于危险. 

THE NMM-BASED EFG METHOD AND SIMULATION OF CRACK PROPAGATION

In order to solve continuum and discontinuous problems in a uniform way, the numerical manifold method (NMM) introduces two cover systems, i.e., the mathematical cover (MC) and the physical cover (PC). By constructing the MC with the node influence domains in moving least squares interpolation (MLS) as the mathematical cover, the Element Free Galerkin method in the setting of NMM is proposed, named NMM-EFG. The NMM-EFG can easily deal with continuum and discontinuous problems while the pre-processing becomes very easy. A scheme for simulating crack propagation under the small deformation and the large deformation conditions is developed. By the treatment of kinked cracks, the crack can grow at arbitrarily small step without mesh refinement. Compared with results from large deformation, the results from small deformation might be prone to unsafe evaluation.