  We study the dynamics of a local load sharing fiber bundle model in two
dimensions, under an external load (which increases with time at a fixed slow
rate) applied at a single point. Due to the local load sharing nature, the
redistributed load remains localized along the boundary of the broken patch.
The system then goes to a self-organized state with a stationary average value
of load per fiber along the (increasing) boundary of the broken patch (damaged
region) and a scale free distribution of avalanche sizes and other related
quantities are observed. In particular, when the load redistribution is only
among nearest surviving fiber(s), the numerical estimates of the exponent
values are comparable with those of the Manna model. When the load
redistribution is uniform along the patch boundary, the model shows a simple
mean-field limit of this self-organizing critical behaviour, for which we give
analytical estimates of the saturation load per fiber values and avalanche size
distribution exponent. These are in good agreement with numerical simulation
results.
