Recent Development of Monolithic Solution Techniques for Phase-field Crack Problems
Recent Development of Monolithic Solution Techniques for Phase-field Crack Problems
Monday, March 16, 11:30 (HH312)
Monday, March 16, 11:30 (HH312)
In the past decade, the phase-field approach becomes a popular technique to model crack propagation under mechanical and multiphysics loading conditions. Comparing with traditional numerical techniques such as the embedded discontinuity method and the extended finite element method, the phase-field approach can naturally handle complex crack topology without relying on any heuristic tracking strategy. The ongoing research efforts in the phase-field crack modeling community generally aim to accomplish the following two tasks. The first task is to develop better phase-field models that accurately capture various material fracture behaviors under complex loading conditions. The second task is to develop efficient and robust solution techniques that can overcome the non-convexity and overwhelming computational cost related to phase-field crack simulations. This talk focuses on the second task by reporting several solution techniques recently developed in my group at uOttawa. First, the limited-memory BFGS (L-BFGS) method is introduced as the monolithic solution scheme for the phase-field crack problems. This method can overcome the convergence difficulties caused by the energy functional non-convexity while avoiding excessive memory usage in the traditional BFGS method. Then, a highly efficient gradient projection approach is built upon the L-BFGS method to rigorously enforce the phase-field irreversibility condition under cyclic loading. Lastly, the developed monolithic solution techniques are extended to fully coupled thermomechanical phase-field crack problems. Through a series of widely adopted benchmark problems, the performances of the developed monolithic scheme are compared with the counterparts based on several staggered schemes under the same hardware and software environments. The developed monolithic scheme offers a general solution framework to solve multiphysics crack problems.
References:
[1] T. Jin, “Gradient projection method for enforcing crack irreversibility as box constraints in a robust monolithic phase-field scheme”, Comput. Methods Appl. Mech. Engrg., https://doi.org/10.1016/j.cma.2024.117622, (2025).
[2] T. Jin, Z. Li, K. Chen, “A novel phase-field monolithic scheme for brittle crack propagation based on the limited-memory BFGS method with adaptive mesh refinement”, Internat. J. Numer. Methods Engrg., https://doi.org/10.1002/nme.7572, (2024).