Elastic forces that do no work and the dynamics of fast cracks.

Elastic singularities such as crack tips, when in motion through a medium that is itself vibrating, are subject to forces orthogonal to the direction of motion and thus impossible to determine by energy considerations alone. This fact is used to propose a universal scenario, in which three dimension-ality is essential, for the dynamic instability of fast cracks in thin brittle materials. The dynamics of crack tips is of particular relevance to the fracture of materials[1] and to earthquake rupture[2]. In addition, recent improvements in instrumenta-tion techniques have revealed unstable crack dynamic behaviour reminiscent of what is observed in other physical systems driven far from equilibrium[3, 4, 5, 6]. These experiments have taken a close quantitative look at the crack-tip velocity fluctuations, ultrasound emission and surface heterogeneities in glass and plexi-glass associated with long standing puzzles in the tensile cracking of very brittle solids[7]. The theoretical effort directed at an understanding of these phenomena has been largely based on two dimensional modelling. It includes analysis based on a continuum approach that considers a cohesive region at the crack tip[8] and numerical computations using lattice[9] as well as molecular dynamics[10] techniques. However, ultrasound[4, 5], surface topography[3, 5] and velocity fluctuation[3, 5] measurements clearly involve length scales comparable or smaller than sample thickness, strongly suggesting that three dimensionality cannot be 1