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29 March 2024
 
  » arxiv » cond-mat/0301017

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A texture tensor to quantify deformations: the example of two-dimensional flowing foams
Marius Asipauskas ; Miguel Aubouy ; James A. Glazier ; François Graner ; Yi Jiang ;
Date 2 Dec 2002
Subject Soft Condensed Matter; Materials Science | cond-mat.soft cond-mat.mtrl-sci
AbstractIn a continuum description of materials, the stress tensor field $ar{% ar{sigma}}$ quantifies the internal forces the neighbouring regions exert on a region of the material. The classical theory of elastic solids assumes that $ar{ar{sigma}}$ determines the strain, while hydrodynamics assumes that $ar{ar{sigma}}$ 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, {em 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.
Source arXiv, cond-mat/0301017
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