• Rapid Communication

Autonomy and singularity in dynamic fracture

Eran Bouchbinder
Phys. Rev. E 82, 015101(R) – Published 12 July 2010

Abstract

The recently developed weakly nonlinear theory of dynamic fracture predicts 1/r corrections to the standard asymptotic linear elastic 1/r displacement gradients, where r is measured from the tip of a tensile crack. We show that the 1/r singularity does not automatically conform with the notion of autonomy (autonomy means that any crack tip nonlinear solution is uniquely determined by the surrounding linear elastic 1/r fields) and that it does not automatically satisfy the resultant Newton’s equation in the crack parallel direction. We show that these two properties are interrelated and that by requiring that the resultant Newton’s equation is satisfied, autonomy of the 1/r singular solution is retained. We further show that the resultant linear momentum carried by the 1/r singular fields vanishes identically. Our results, which reveal the physical and mathematical nature of the solution, are in favorable agreement with recent near-tip measurements.

  • Figure
  • Figure
  • Received 13 May 2010

DOI:https://doi.org/10.1103/PhysRevE.82.015101

©2010 American Physical Society

Authors & Affiliations

Eran Bouchbinder

  • Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 82, Iss. 1 — July 2010

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×