- New
- Research Article
- 10.1016/j.ijsolstr.2026.113980
- Jun 1, 2026
- International Journal of Solids and Structures
- Congjie Wei + 3 more
- New
- Research Article
- 10.1016/j.ijsolstr.2026.113882
- Jun 1, 2026
- International Journal of Solids and Structures
- Aniket Gopa Chanda + 3 more
- New
- Research Article
- 10.1016/j.ijsolstr.2026.113974
- Jun 1, 2026
- International Journal of Solids and Structures
- Flavien Loiseau + 1 more
The variational approach to fracture, particularly through its regularization as a phase-field model, has become a widely used tool for simulating the quasi-static propagation of cracks in structures. However, classic incremental loading can induce unstable crack growth, violating the quasi-static assumption, and in some cases, leads to a loss of force balance, preventing self-consistency and the estimation of dissipated energy during snapback instabilities. To address this challenge, path-following methods are investigated. Their aim is to adjust the applied load so that it stays at the propagation threshold, thereby preserving the quasi-static assumption and ensuring equilibrium solutions. In this work, we apply and evaluate multiple path-following methods within the framework of variational phase-field fracture models, which are developed to regularize linear elastic variational sharp crack evolution problems. Our study pursues two objectives. First, we review several existing path-following methods, with a focus on partitioned strategies based on the displacement field, which decouple the path-following control equation from the rest of the system, facilitating easier integration with staggered solvers. In addition, we introduce a new path-following method whose particularity is to limit the maximum strain increment outside the cracked regions. Second, we use the Γ -convergence to the sharp crack model to evaluate these methods across three crack propagation problems of increasing complexity. The comparison demonstrates that the proposed path-following method offers a simple yet highly effective approach to capture the equilibrium path in phase-field fracture simulations. This method robustly maintains the quasi-static assumption, ensuring physically meaningful results. By enabling accurate estimation of the energy dissipated during snapback instabilities, it paves the way for the rational design of more resistant heterogeneous materials. • Identification of generic path-following methods compatible with staggered solvers. • A new method based on the strain outside the cracked zone offers improved performance. • Evaluation by testing the Γ -convergence to sharp crack model through examples of increasing complexity. • Toward numerically robust, self-consistent evaluation of equilibrium crack propagation paths. • Toward rational design of microstructures for enhanced fracture toughness.
- New
- Research Article
- 10.1016/j.ijsolstr.2026.113950
- Jun 1, 2026
- International Journal of Solids and Structures
- Yingbin Zhang + 4 more
- New
- Research Article
- 10.1016/j.ijsolstr.2026.113992
- Jun 1, 2026
- International Journal of Solids and Structures
- Gianluca Auteri + 3 more
- New
- Research Article
- 10.1016/j.ijsolstr.2026.113972
- Jun 1, 2026
- International Journal of Solids and Structures
- Jinxin Pan + 5 more
- New
- Research Article
- 10.1016/j.ijsolstr.2026.113997
- Jun 1, 2026
- International Journal of Solids and Structures
- Haoran Jiang + 2 more
- New
- Research Article
- 10.1016/j.ijsolstr.2026.113969
- Jun 1, 2026
- International Journal of Solids and Structures
- J.a Clarkson + 1 more
- New
- Research Article
- 10.1016/j.ijsolstr.2026.113975
- Jun 1, 2026
- International Journal of Solids and Structures
- Yuan Li + 3 more
- New
- Research Article
- 10.1016/s0020-7683(26)00158-7
- Jun 1, 2026
- International Journal of Solids and Structures