  Quasistatic simple shearing flow of random monodisperse soap froth is
investigated by analyzing Surface Evolver simulations of spatially periodic
foams. Elastic-plastic behavior is caused by irreversible topological
rearrangements (T1s) that occur when Plateau's laws are violated; the first T1s
occur at the elastic limit and at large strains frequent cascades of T1s,
composed of one or more individual T1s, sustain the yield-stress plateau. The
stress and shape anisotropy of individual cells is quantified by $Q$, a scalar
measure derived from the interface tensor that gauges each cell's contribution
to the global stress. During each T1 cascade, the connected set of cells with
decreasing $Q$, called the \textit{stress release domain}, is network-like and
highly non-local. Geometrically, the network-like nature of the stress release
domains is corroborated through morphological analysis using the Euler
characteristic. The stress release domain is distinctly different from the set
of cells that change topology during a T1 cascade. Our results highlight the
unique rheological behavior of foams, where complex large-scale cooperative
rearrangements of foam cells are observed as a consequence of distinctly local
events.
