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### Cite Details

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

### Abstract

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.

### BibTeX Entry

@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}
}