A crack-length control technique for phase field fracture in FFT homogenization
Pedro Aranda, Javier Segurado
TL;DR
This work tackles instability in microscale fracture modeling by introducing a crack-length control method for phase-field fracture implemented in FFT-based homogenization, enabling monolithic, robust solutions that resolve snap-backs. The authors formulate an energy-dissipation constraint that makes crack growth monotonic in a controlled sense, deriving a non-symmetric Newton–Krylov solver compatible with FFT and, for comparison, a parallel FEM implementation with Lagrange multipliers. They demonstrate equivalence with conventional strain-control approaches in stable regimes and validate the method through FFT–FEM comparisons, Griffith-panel tests, and 2D/3D microstructure examples, including composites and porous materials. The approach yields consistent energy-release rate behavior via J-integrals and provides a practical route to estimate effective fracture toughness, $G_{C\text{eff}}$, from microscale simulations, with clear implications for multiscale material design and analysis. Overall, the crack-length control technique advances high-performance, accurate micromechanical fracture simulations and opens pathways for robust toughness homogenization in complex heterogeneous media.
Abstract
Modeling the propagation of cracks at the microscopic level is fundamental to understand the effect of the microstructure on the fracture process. Nevertheless, microscopic propagation is often unstable and when using phase field fracture poor convergence is found or, in the case of using staggered algorithms, leads to the presence of jumps in the evolution of the cracks. In this work, a novel method is proposed to perform micromechanical simulations with phase field fracture imposing monotonic increases of crack length and allowing the use of monolithic implementations, being able to resolve all the snap-backs during the unstable propagation phases. The method is derived for FFT based solvers in order to exploit its very high numerical performance n micromechanical problems, but an equivalent method is also developed for Finite Elements (FE) showing the equivalence of both implementations. It is shown that the stress-strain curves and the crack paths obtained using the crack control method are superposed in stable propagation regimes to those obtained using strain control with a staggered scheme. J-integral calculations confirm that during the propagation process in the crack control method, the energy release rate remains constant and equal to an effective fracture energy that has been determined as function of the discretization for FFT simulations. Finally, to show the potential of the method, the technique is applied to simulate crack propagation through the microstructure of composites and porous materials providing an estimation of the effective fracture toughness.