Local plastic deformation in sheared highly polydisperse foams

We simulate the shear of dense two-dimensional foams using the Durian bubble model with a Lees-Edwards boundary condition. In particular, we study highly polydisperse systems with the largest bubble diameters being as much as ten times the smallest diameter. The high polydispersity requires us to rethink the conventional ideas that are applied to study the local plastic deformation of systems with comparable sizes of droplets, such as D²_min which highlights locally nonaffine motion (Falk & Langer, PRE 1998). We modify the conventional definition of "local" in the calculation of D²_min to consider the existence of big droplets and study how the "local" rearrangements differ for large and small droplets. More specifically, we find the large droplets follow the mean shear, while the small droplets have significant nonaffine motions and move more erratically. We demonstrate an optimal definition of local that best distinguishes the local nonaffine motions from the bulk shear.