In a continuum description of materials, the stress tensor field $\bar{%\bar{\sigma}}$ quantifies the internal forces the neighbouring regions exert ona region of the material. The classical theory of elastic solids assumes that$\bar{\bar{\sigma}}$ determines the strain, while hydrodynamics assumes that$\bar{\bar{\sigma}}$ determines the strain rate. To extend both successfultheories to more general materials, which display both elastic and fluidproperties, we recently introduced a descriptor generalizing the classicalstrain to include plastic deformations: the ``statistical strain'', based onaverages 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 steadilyflowing through a constriction, a problem beyond reach of both theories, andprove that the foam has the elastic properties of a (linear and isotropic)continuous medium.
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机译：在材料的连续描述中，应力张量场$ \ bar {％\ bar {\ sigma}} $量化了相邻区域施加在材料区域上的内力。弹性固体的经典理论假设$ \ bar {\ bar {\ sigma}} $决定应变，而流体力学假设$ \ bar {\ bar {\ sigma}} $决定应变率。为了将两种成功的理论扩展到同时显示弹性和流体特性的更一般的材料，我们最近引入了一个描述符，该描述符基于微观细节的平均值将``经典应变''概括为包括塑性变形：``统计应变''（``量化纹理的张量M.Au.，YJ，JAG，FG，伴侣纸，{\ em Granular Matter}，同一期）。在此，我们将这种统计分析应用于平稳地流过收缩处的二维泡沫，这是一个超越两种理论的广泛应用，并证明泡沫材料具有（线性和各向同性）连续介质的弹性。
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