Quasi-static rheology of foams. Part 1. Oscillating strain
A quasi-static simulation is used to study the mechanical response of a disordered bidimensional aqueous foam submitted to an oscillating shear strain. The application of shear progressively extends the elastic domain, i.e. the strain range within which no plastic process occurs. It is associated with the development of an irreversible normal stress difference, and a decrease in the shear modulus, which are both signatures of the appearance of anisotropy in the film network. Beyond this mechanical measurement, the evolutionof the structural properties of the foam is investigated. We focus in particular on the energy E0 defined as the minimum line-length energy under zero shear stress. For strainamplitude less than 0.5, this quantity is found to decay with the number of applied cycles as a result of the curing of topological defects. However, for higher strain amplitude, plastic events appear to increase the structural disorder and tend to gather near the shearing walls. This process is a precursor of the shear-banding transition observed in fully developed flows, which will be studied in the companion paper. Movies are available with the online version of the paper.