Mathematical Modeling and Analysis
Mathematical Modeling and Analysis
In a continuum description of materials, the stress tensor field quantifies the internal forces the neighboring regions exert on a region of the material. The classical theory of elastic solids assumes that stress determines the strain, while hydrodynamics assumes that stress determines the strain rate. To extend both successful theories to more general materials, which display both elastic and fluid properties, we introduce a descriptor generalizing the classical strain to include plastic deformations: the "statistical strain", based on averages on microscopic details. We apply such a statistical analysis to a two-dimensional foam steadily flowing through a constriction, a problem beyond reach of both theories, and prove that the foam has the elastic properties of a linear and isotropic continuous medium.
