弹塑性体脆断相场模型的一致性无单元伽辽金法

Consistent element-free Galerkin method for phase-field model of brittle fracture in elasto-plastic solids

采用无单元伽辽金法(EFG)对弹塑性体脆性断裂的相场模型进行了数值实现。利用无单元法便于构建高阶近似函数的优势,位移和相场均采用二阶移动最小二乘(MLS)近似。刚度阵的数值积分采用更为高效的二阶一致三点积分格式QC3(Quadratically Consistent 3-point integration scheme)。本构算法采用Newton-Raphson迭代和弹塑性一致性切线模量。数值结果表明了本文方法模拟弹塑性体脆性断裂的有效性。

This work presents the numerical implementation of the phase-field model of brittle fracture in elasto-plastic solids by using the Element-free Galerkin(EFG)method.Second-order moving least-squares approximation for both the displacement and the phase field is employed by taking full use of the convenience of the EFG method in constructing high-order approximation functions.The stiffness matrix is evaluated by the efficient Quadratically Consistent 3-point(QC3)integration scheme.Newton-Raphson iteration and consistent elasto-plastic modulus are employed in the constitutive algorithm.Numerical results demonstrate the validity of the presented method in modeling the brittle fracture of elasto-plastic solids.