双材料界面裂纹的改进广义有限差分法  

An Improved Generalized Finite Difference Method for Bimaterial Interfacial Crack Analysis

作　　者：江崧维 谷岩 傅卓佳[2] 屈文镇 Songwei Jiang;Yan Gu;Zhuojia Fu;Wenzhen Qu(School of Mathematics and Statistics,Qingdao University,Qingdao,266071;Hohai University,College of Mechanics and Materials,Nanjing,213022)

机构地区：[1]青岛大学数学与统计学院,青岛266071 [2]河海大学力学与材料学院,南京213022

出　　处：《固体力学学报》2022年第5期541-550,共10页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(11872220,12111530006);山东杰出青年科学基金项目(ZR2021JQ02);德国洪堡基金项目(DFG,ZH15/14-2)资助。

摘　　要：采用数值方法进行断裂力学分析时,裂纹尖端奇异区域处理的好坏直接关系到最终断裂力学参数的求解精度.与传统均匀介质不同,复合材料界面裂纹渐近位移和应力场表现出剧烈的振荡特性,许多用于表征经典的平方根和负平方根物理场渐近性的传统方法也因此失效.论文提出了一种改进的广义有限差分法,该方法基于多元函数泰勒级数展开和移动最小二乘法的思想,将节点变量的各阶导数由相邻点集函数的加权线性累加来近似,具有无网格、无数值积分、数据准备简单、稀疏矩阵快速求解等优点.为提高该方法求解断裂力学问题的计算精度和数值稳定性,论文引入了裂尖奇异区域局部点簇的自动创建技术和一种基于局部点簇几何尺寸的矩阵正则化算法.数值算例表明,所提算法稳定,效率高,在不增加计算量的前提下,显著提高了裂尖近场力学参量和断裂力学参数的求解精度和数值稳定性.Cracks on the interface of a bimaterial result from the manufacturing defects and/or the mismatch between different material properties of the bimaterial. The near-tip asymptotic stress and deformation fields of bimaterial interfacial cracks exhibit oscillatory characteristics, which are very different from those of cracks in homogeneous materials. Due to the oscillatory behavior related to complex eigenvalues, modeling such interfacial cracks by following the conventional solution procedure designed for homogeneous materials is inadequate, and may not lead to accurate solutions by using the well-established and widely applied finite element method(FEM) or boundary element method(BEM), even when a very fine mesh near the crack tip is employed. In the present paper, we document the attempt to apply the generalized finite difference method(GFDM) to the fracture analysis of bimaterials containing interfacial cracks. The main idea of the method is based on the theories of local Taylor series expansion and moving least-squares approximation. Since the method is meshless and no element connectivity is needed, it can be viewed as a competitive alternative for bimaterial interfacial crack analysis. In our calculations, a multi-domain technique is employed to handle the non-homogeneity of dissimilar materials, and the displacement extrapolation method(DEM) is introduced to calculate the complex stress intensity factors(SIFs) for cracked dissimilar materials. An improved GFDM formulation is proposed to further improve the accuracy and stability of the GFDM for fracture mechanics analysis. Two benchmark numerical examples are well studied to demonstrate the accuracy and stability of the present method for interfacial crack analysis of bimaterials. In the work that follows, other interesting and important problems, such as thermal effects, dynamic effects, and crack propagation and arrest should be considered. The present work provides an efficient alternative for bimaterial interfacial crack analysis, and the corresponding

关 键 词：广义有限差分法 界面裂纹 应力强度因子 断裂力学 双材料 

分 类 号：O346.1[理学—固体力学] TB34[理学—力学]