Efficient co‐solution of time step size and independent state in simulations of fluid‐driven fracture propagation with embedded meshes

• Published in: International journal for numerical methods in engineering 2022-05, Vol.123 (10), p.2262-2289
• Main Authors: Ren, Guotong, Younis, Rami M.
• Format: Article
• Language: English
• Subjects: Crack propagation; elasticity; Exact solutions; extended finite element method; Finite element method; fracture; Fracture mechanics; implicit; Mathematical analysis; Mechanical systems; nonlinear solvers; Propagation; Robustness (mathematics); Stress intensity factors; Stress propagation; time integration
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.6935

We present an efficient time‐continuation scheme for fluid‐driven fracture propagation problems in the extended finite element method framework. The approach applies a monolithic solution strategy to a fully coupled and implicit approximation of hydro‐mechanical systems in conjunction with simultaneous linear elastic propagation of multiple fractures. At the end of each time step, the process ensures that the weakest fracture tip is in an equilibrium propagation regime. Furthermore, the solution process provides an initialization procedure for the newly created fracture spaces and an a priori estimate of the stress intensity factor growth rate, improving simulation robustness, and efficiency. The solution process is validated using the Kristianovich‐Geertsma‐de Klerk analytical solution under the toughness‐ and viscosity‐dominated regimes. It is also extended to and demonstrated on problems with multiple fractures undergoing simultaneous propagation with stress shadow interactions. Numerical examples demonstrate that the solution process can reduce the required computational cost by one order of magnitude compared to other existing methods.