A simple dynamical generalization of the electrical random fuse model for rupture in random media is introduced in which fuses are heated locally by a generalized Joule effect. When their temperature reaches a given threshold, the fuses burn out irreversibly and become insulators. In one limit, the rupture dynamics is spontaneously attracted to the critical state of the bond percolation model. In another limit, it recovers the ‘‘static’’ random fuse model previously studied in the literature. In between these two extremes, the existence of a novel dynamical memory effect produces a rich phenomenology of fractal rupture patterns, which are sensitively dependent upon the input current.

• Received 30 September 1991

DOI:https://doi.org/10.1103/PhysRevLett.68.612