Applied Mathematics and Plasma Physics

Marius Asipauskas, Miguel Aubouy, James A. Glazier, Francois Graner and Yi Jiang, "A texture tensor to quantify deformations:
the example of two-dimensional flowing foams ", *Granular Matter*, vol. 5, pp. 71-76, 2003

In a continuum description of materials, the stress tensor
field $\overline{\overline{\sigma }}$ quantifies the internal forces the
neighbouring regions exert on a region of the material. The classical
theory of elastic solids
assumes that $\overline{\overline{\sigma }}$ determines the strain, while
hydrodynamics assumes that $\overline{\overline{\sigma }}$ 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 on microscopic
details (``A texture tensor to quantify deformations''
M.Au., Y.J., J.A.G.,
F.G, companion paper, * Granular Matter *, same issue).
Here, 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.

@article{asipauskas-2003-a-texture,

author = {Marius Asipauskas and Miguel Aubouy and James A. Glazier and Francois Graner and Yi Jiang},

title = {A texture tensor to quantify deformations:
the example of two-dimensional flowing foams },

year = {2003},

urlpdf = {http://math.lanl.gov/~yi/Papers/GranularMatterExp.pdf},

journal = {Granular Matter},

volume = {5},

pages = {71-76}

}