AI summary · arXiv: 2111.10649v1 · math.NA
A robust monolithic solver for phase-field fracture integrated with fracture energy based arc-length method and under-relaxation
The essentials
- The phase-field fracture free-energy functional is a mathematical model used to simulate fractures in materials.
- Conventional solvers like the Newton-Raphson method face challenges due to the non-convexity of the functional.
- Alternate minimization (staggered) solvers are more robust for phase-field based fracture simulations.
- Staggered solvers require a large number of iterations to converge.
- The authors propose a robust monolithic solver for the phase-field fracture problem.
- The solver incorporates a fracture energy-based arc-length method and an adaptive under-relaxation scheme.
- The arc-length method allows overcoming critical points during specimen loading.
- An under-relaxation scheme helps stabilize the solver by preventing divergence caused by an ill-behaving stiffness matrix.
- Efficiency is enhanced through an adaptive mesh refinement scheme based on PHTsplines within the framework of isogeometric analysis.
- Numerical examples demonstrate the efficacy of the proposed solver.
- All codes and data sets will be made available on GitHub (https://github.com/rbharali/IGAFrac).
- The research presents a novel approach to solving the phase-field fracture problem, addressing issues related to nonconvexity and convergence.
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