Gradient distributions of material properties are taken into account in phase-field model of fracture and the adaptive consistent element-free Galerkin method (EFG) for the fracture analysis of functionally graded materials (FGMs) is presented. Considering the fact that both the moving least-square approximation and the consistent integration scheme contribute to producing the accurate stress fields, the phase-field model of fracture for FGMs is numerically solved by the consistent EFG method in this paper. The corresponding adaptive criterion is established and 2D and 3D crack propagation of FGMs is simulated. Numerical results indicate that the proposed method can accurately reflect the influence of different distributions of material parameters on the crack propagation and has high efficiency compared with the standard EFG method and linear FEM. At some level, the fracture mechanism that crack propagation is driven by both the strain energy history and the critical energy release rate is revealed using phase-field model.

在断裂的相场模型中考虑了材料特性的梯度分布，并提出了用于功能梯度材料（FGM）断裂分析的自适应一致无元素Galerkin方法（EFG）。考虑到移动最小二乘逼近和一致积分方案都有助于产生精确的应力场，本文采用一致EFG方法对FGM的断裂相场模型进行了数值求解。建立了相应的自适应准则，并模拟了FGM的2D和3D裂纹扩展。数值结果表明，与标准的EFG法和线性有限元法相比，该方法能准确反映材料参数的不同分布对裂纹扩展的影响，具有较高的效率。