Dynamic fracture analysis of the linearly uncoupled and coupled physical phenomena by the variable-node multiscale XFEM. (September 2021) - Yin, Shuohui; Zhang, Ning; Liu, Peng; Liu, Jingang; Yu, Tiantang; Gu, Shuitao; Cong, Yu
Highlights: The variable-node multiscale extended finite element method (V-XFEM) is elaborated for the dynamic crack analysis of the linearly uncoupled and coupled physical phenomena in a compact formula. The numerical results of the linearly elastic and piezoelectric problems considered as illustrated examples show that the V-XFEM has a higher accuracy and more and efficiency than standard XFEM. For piezoelectric structures, numerical results show that the normalized dynamic intensity factors have a significant dependence on the poling direction and electrical impact loading. Because of a unified way for all single and coupled linear phenomena, the proposed V-XFEM has the potential to simulate all the linearly physical phenomena. Abstract: This paper aims to develop a variable-node multiscale extended finite element method (V-XFEM) for dynamic fracture analysis of the linearly uncoupled and coupled physical phenomena in a compact formula. The general governing equations for the linearly uncoupled and coupled physical phenomena are presented in a compact form. The local mesh refinement technique for modeling cracks is used to improve the accuracy and efficiency, in which variable-node elements without modifying the system matrix or impose additional boundary conditions are taken to connect/link different scale elements. In addition, the time-dependent equations are solved by the unconditionally stable implicit Newmark time integration method, and the dynamic intensity factors (DIFs) are derived from the domain forms of the interaction integrals. Numerical results of the linearly elastic and piezoelectric problems show that V-XFEM is an efficient numerical approach to simulate the dynamic fracture problems of the linearly uncoupled and coupled physical phenomena.