1/12/2026
CEE professor Oscar Lopez-Pamies and doctoral student Farhad Kamarei establish universal criteria for when and where fractures will spread once they start, knowledge that will provide greater understanding of fracture to all fields of science and engineering.
Written by
Foundational understanding of fracture is crucial for engineers and scientists across all disciplines. Civil and Environmental Engineering Professor Oscar Lopez-Pamies studies fracture from a variety of different angles and has most recently uncovered the answer to a question that has eluded researchers for decades: when and where do fractures grow in a material under arbitrary quasi-static loads?
Previous research from Lopez-Pamies helped fill in field-wide knowledge gaps about predicting fracture nucleation, revealing the vital role a material’s intrinsic strength plays in how fractures get their start. In a new paper, Lopez-Pamies and CEE doctoral student Farhad Kamarei take that finding one step further and establish universal criteria for evaluating where cracks will grow within a material after forming.
Guided by the mathematical framework used in Kumar, Francfort and Lopez-Pamies’s regularized phase-field theory of fracture, and tested against several classical experiments on glass, they first determined that cracks can only spread through areas of the material where the strength surface has been compromised. This finding follows the same principle as Lopez-Pamies’s earlier work on fracture nucleation, emphasizing that stress must exceed the material’s strength surface value for fractures to not only begin, but also grow.
As for the path they take to spread once formed? It turns out fractures like following the path of least resistance: within the region where the strength surface has been compromised, the cracks will grow in the direction that minimizes both potential and surface energy.
Together, these two criteria provide a standardized explanation for where fractures will grow within a material once they have begun. This work also serves to underscore the central role that strength surface plays in understanding fracture as a whole, something that has previously been overlooked.
With growing appreciation for the strength surface and its importance, Lopez-Pamies’ work provides the foundation for better characterizing, predicting and mitigating fracture, something that will have impacts across all fields of science and engineering.
The full paper “When and where do large cracks grow? Griffith energy competition constrained by material strength” can be read here.
Listen to a podcast breaking down the paper and its impact on Lopez-Pamies’ website.