Improved double-phase-field algorithm based on scaled boundary finite element method for rock-like materials

The study of cracking analysis algorithms for rock-like materials is an important branch in the development of solid mechanics, and the related results have received extensive attention from researchers around the world. To broaden the generalizability of the phase-field method, an improved double-phase-field (DPF) algorithm based on the Scaled Boundary Finite Element Method (SBFEM) is presented. Firstly, the main governing equations are deduced and interpreted based on the nonlinear SBFEM framework. Secondly, the flexible polygon class library, data structure and solving framework for DPFM are designed by object-oriented programming. Subsequently, the presented algorithm is integrated in the self-developed finite element software GEODYNA. Thirdly, the precision is demonstrated by three classic examples, and its efficiency and practicality for complex mixed-mode fractures are validated with three case studies. Obviously, the tensile and compressive-shear mixed-mode fracture mode can be reproduced realistically, and the efficient quadtree grids can be utilized directly, making the efficiency to be optimized by more than 75% in representative cases. More potential for practical applications would be further elucidated with extending the proposed method to three-dimensional.