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  • Letter
  • Open Access

Analytical expression for fracture profile in viscoelastic crack propagation

Hokuto Nagatakiya1,*, Naoyuki Sakumichi2,3,*,†, Shunsuke Kobayashi1, and Ryuichi Tarumi1,‡

  • 1Graduate School of Engineering Science, The University of Osaka, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan
  • 2Faculty of Social Informatics, ZEN University, 3-12-11 Shinjuku, Zushi, Kanagawa 249-0007, Japan
  • 3Department of Chemistry and Biotechnology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

  • *These authors contributed equally to this work.
  • †Contact author: sakumichi@gel.t.u-tokyo.ac.jp
  • ‡Contact author: tarumi.ryuichi.es@osaka-u.ac.jp
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Phys. Rev. Research 7, L042001 – Published 1 October, 2025

DOI: https://doi.org/10.1103/4gnw-ys42

Abstract

We derive an analytical expression for the strain field during steady-state crack propagation in viscoelastic solids described by the standard linear solid (Zener) model. This expression reveals three regions in the fracture profile and in the strain field ahead of the crack tip, each distinguished by power-law exponents that evolve with distance from the crack tip. These features explain the experimentally observed crack-tip sharpening in rubbers and gels as the crack-propagation velocity increases, often associated with catastrophic failure triggered by a velocity jump. Furthermore, we establish de Gennes’ viscoelastic trumpet on a continuum-mechanical foundation, previously based only on a scaling argument.

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References (39)

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Phys. Rev. Research 7, L042001– Published 1 October, 2025
  • Received 12 December 2023
  • Accepted 4 August 2025
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