Self-activated fragmentation

We explore the consequences of a point of view stating that fracture in strained brittle solids results from the action of mechanically activated random fluctuations. As opposed to thermally activated fracture, the energy reservoir feeding the crack progression is given by the mean elastic energy stored in the cracked region, itself a sub-sample of the strained material. The crack and the material bulk exchange self-consistently energy and momentum via random elastic waves, which are themselves produced by the fracture progression. The statistics of the fluctuating energy, and of the random force directing the fracture are derived, as well as the corresponding Langevin dynamics of the crack position. The role of pre-existing defects in the material is shown to be secondary. We examine in particular the case of a bent beam, for which we determine the distributions of breakup times, fragments number and lengths as a function of its initial deformation and of the material elastic and cohesion properties. The corrections due to plasticity, the effect of a transiently applied load, and the special case of liquids are discussed as well.