Mathematical model reveals why cracks sharpen during rapid rubber fracture

A research group from the University of Osaka, Zen University, and the University of Tokyo has mathematically uncovered the mechanism that causes crack tips to sharpen during the rapid fracture of rubber.

The bursting of rubber balloons or tire blowouts is caused by rapid fracture, a phenomenon in which a small crack propagates instantaneously. During this process, the crack tip sharpens, accelerating the fracture. However, the reason behind this sharpening had long remained unexplained. Traditionally, it was believed to result from the material’s complex nonlinear effects.

The research group—comprising Hokuto Nagatakiya, a doctoral student; Shunsuke Kobayashi, assistant professor; and Ryuichi Tarumi, professor at the University of Osaka; along with Naoyuki Sakumichi, associate professor at Zen University and project associate professor at the University of Tokyo—has mathematically solved the problem of crack propagation. They derived equations that describe both the shape of the crack and the overall deformation of the material.

This breakthrough, now published in Physical Review Research, demonstrates that crack tip sharpening in polymer materials such as rubber arises solely from their fundamental property of viscoelasticity. Furthermore, the team mathematically proved the viscoelastic trumpet theory—proposed nearly 30 years ago by Nobel Laureate in Physics, Pierre-Gilles de Gennes—based on the fundamental equations of continuum mechanics.

These findings lay a theoretical foundation for controlling fractures in a wide range of viscoelastic materials—from tires to medical products—contributing to improved durability, accident prevention, and reduced environmental impact through longer product lifespans.