A texture tensor to quantify deformations: the example of two-dimensional flowing foams

In a continuum description of materials, the stress tenser field (σ) over bar quantifies the internal forces the neighbouring regions exert on a region of the material. The classical theory of elastic solids assumes that (σ) over bar determines the strain, while hydrodynamics assumes that (σ) over bar determines the strain rate. To extend both successful theories to more general materials, which display both elastic and fluid properties, we recently introduced a descriptor generalizing the classical strain to include plastic deformations: the statistical strain, based on averages of microscopic details (A texture tenser to quantify deformations M.Au., Y.J., J.A.G., F.G, companion paper, Granular Matter, this issue). Here, we apply such a statistical analysis to a two-dimensional foam steadily flowing through a constriction, a problem beyond reach of both traditional theories, and prove that the foam has the elastic properties of a (linear and isotropic) continuous medium.