Crack propagation in disordered materials as an elastic line driven in
a random medium 

Anstract.

Crack propagation is the fundamental process leading
to the failure of brittle solids. However, if one goes beyond the
failure of a continuum homogeneous medium and considers more realistic
situations, i.e. solids with inhomogeneous failure properties, the
continuum mechanics approach clearly fails to reproduce the main
features of crack propagation. To capture the role played by the
microstructural disorder, one can add a stochastic term describing the
quenched disordered properties of solids in the equations describing
the motion and the trajectory of cracks in elastic solids. In this new
theoretical framework, the crack front of a fracturing brittle solid
is analogous to an elastic line driven in a random potential. We will
analyze numerically, and sometimes analytically, the main properties
of the solution of these equations that will be used to make
predictions on the motion of cracks. Comparisons with experimental
observations will be finally discussed.