Discrete rearranging disordered patterns, part II: 2D plasticity, elasticity and flow of a foam

The plastic flow of a foam results from bubble rearrangements. We study their occurrence in experiments where a foam is forced to flow in 2D: around an obstacle; through a narrow hole; or sheared between rotating disks. We describe their orientation and frequency using a topological matrix defined in the companion paper (Graner et al., preprint), which links them with continuous plasticity at large scale. We then suggest a phenomenological equation to predict the plastic strain rate: its orientation is determined from the foam's local elastic strain; and its rate is determined from the foam's local elongation rate. We obtain a good agreement with statistical measurements. This enables us to describe the foam as a continuous medium with fluid, elastic and plastic properties. We derive its constitutive equation, then test several of its terms and predictions.