水平集和无网格耦合法在裂纹扩展中的应用

Coupling of level set and meshless method and its application to crack propagation

提出了一种模拟裂纹扩展的水平集和无网格耦合方法。由于水平集和无网格方法都是建立在离散节点上,因而可以很自然地实现耦合。在该方法中,两个在裂尖处相互正交的水平集不仅用于描述裂纹的几何形态和裂尖位置,而且用于建立无网格伽辽金法(简称EFGM)不连续近似函数中的Heaviside跳跃项和裂尖处的Westergaard扩展项。当裂纹扩展时,则由水平集更新算法确定新裂纹的位置。水平集和无网格耦合法无需使用可视法、衍射法或透明法,克服了这些方法在裂尖处人为引入的不连续且能很好地再生r奇异场;而且节点影响域不受裂纹线切割的影响,在计算中往往使用较小的影响域,保持了整体刚度矩阵的带状、稀疏性;另外,水平集简化了扩展节点的选取和附加函数的建立,其更新过程无需求解演化方程,实现简单且易于编程。数值算例表明本文方法具有较高的计算精度,其模拟的裂纹扩展路径与试验结果吻合得很好,从而验证了本文方法的正确性和可行性。

A new method which couples the level set method with meshless method to simulate crack growth is presented.The coupling of level set and meshless method can achieve naturally because they all set up based on the discrete nodal data.Two level sets that are orthogonal to one another at the crack tip are used to represent the geometry of crack and the location of crack tip,and to construct the Heaviside skip function and the Westergaard enriched function near the crack tip in the element-free Galerkin method（EFGM） discontinuous approximation.New crack tips are defined by the update algorithm of level set easily when the crack is growing.The coupling method does not use the visibility method,the diffraction method or the transparency method.The singularity is reproduced very well;and the convergence for elastic problems is improved.The passage of crack has no influence on the nodal domain.Smaller domain is used to calculation,which keeps the band and sparsity of the over all stiffness matrix.In addition,the level set makes the selection of enriched nodes and the establishment of additional function simply;and its update process needs no evolution equations.The numerical results show that the presented method has higher computational accuracy;and the simulated expanding path of crack is coincided with the tested curve.So,the results verify the validity and accuracy of the presented method.