The dynamics of rapid fracture:

instabilities, nonlinearities and

length scales

Eran Bouchbinder1, Tamar Goldman2 and Jay Fineberg2

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

2 The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel

E-mail: jay@mail.huji.ac.il

Received 9 May 2013, revised 21 October 2013

Accepted for publication 9 December 2013

Published 19 March 2014

Invited by Paul Chaikin

Abstract

The failure of materials and interfaces is mediated by cracks, almost singular dissipative structures

that propagate at velocities approaching the speed of sound. Crack initiation and subsequent

propagation—the dynamic process of fracture—couples a wide range of time and length scales.

Crack dynamics challenge our understanding of the fundamental physics processes that take place

in the extreme conditions within the almost singular region where material failure occurs. Here, we

first briefly review the classic approach to dynamic fracture, namely linear elastic fracture

mechanics (LEFM), and discuss its successes and limitations. We show how, on the one hand,

recent experiments performed on straight cracks propagating in soft brittle materials have

quantitatively confirmed the predictions of this theory to an unprecedented degree. On the other

hand, these experiments show how LEFM breaks down as the singular region at the tip of a crack is

approached. This breakdown naturally leads to a new theoretical framework coined ‘weakly

nonlinear fracture mechanics’, where weak elastic nonlinearities are incorporated. The stronger

singularity predicted by this theory gives rise to a new and intrinsic length scale, lnl. These

predictions are verified in detail through direct measurements. We then theoretically and

experimentally review how the emergence of lnl is linked to a new equation for crack motion,

which predicts the existence of a high-speed oscillatory crack instability whose wavelength is

determined by lnl. We conclude by delineating outstanding challenges in the field.