  A model of ice floe breakup under ocean wave forcing in the marginal ice zone
(MIZ) is proposed to investigate how floe size distribution (FSD) evolves under
repeated wave breakup events. A three-dimensional linear model of ocean wave
scattering by a finite array of compliant circular ice floes is coupled to a
flexural failure model, which breaks a floe into two floes provided the
two-dimensional stress field satisfies a breakup criterion. A closed-feedback
loop algorithm is devised, which (i)~solves wave scattering problem for a given
FSD under time-harmonic plane wave forcing, (ii)~computes the stress field in
all the floes, (iii)~fractures the floes satisfying the breakup criterion and
(iv)~generates an updated FSD, initialising the geometry for the next iteration
of the loop.The FSD after 50 breakup events is uni-modal and near normal, or
bi-modal. Multiple scattering is found to enhance breakup for long waves and
thin ice, but to reduce breakup for short waves and thick ice. A breakup front
marches forward in the latter regime, as wave-induced fracture weakens the ice
cover allowing waves to travel deeper into the MIZ.
