Numerical study on rheology of two-dimensional dry foam

We study the mechanical response of two-dimensional aqueous foams subjected to an oscillating shear strain using numerical simulations based on the immersed boundary method. Foams have unique rheological properties ranging from solid-like to fluid-like. They have an elastic property under a small strain with a linear stress-strain relationship. As the strain increases, the foams undergo topological rearrangements with a sudden release of energy and stress. Then the energy-strain and stress-strain curves exhibit hysteresis behaviors under the oscillating shear strain, and the macroscopic response of foams changes from a viscoelastic solid to a viscoelastic fluid. These wide-ranging dynamical responses of foams result from avalanches of topological rearrangements which are concentrated in a single localized region. This is called a shear localization, and we investigate the effect of the topological rearrangements and the shear localization on the rheology of foams.