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A texture tensor to quantify deformations: the example of two-dimensional flowing foams

机译：纹理张量以量化变形：二维流动泡沫的示例

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In a continuum description of materials, the stress tensor field a quantifies the internal forces the neighbouring regions exert on a region of the material. The classical theory of elastic solids assumes that a determines the strain, while hydrodynamics assumes that a 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 of microscopic details ("A texture tensor to quantify deformations" M.Au., Y.J., J.A.G., F.G, companion paper, Granular Matter, this issue). Here, we apply such a statistical analysis to a two-dimensional foam steadily flowing through a constriction, a problem beyond reach of both traditional theories, and prove that the foam has the elastic properties of a (linear and isotropic) continuous medium.
机译：在材料的连续描述中，应力张量场a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a决定应变，而流体力学假设a决定应变率。为了将成功的理论扩展到同时显示弹性和流体特性的更通用的材料，我们最近引入了一个描述符，将经典应变概括为包括塑性变形：“统计应变”，基于微观细节的平均值（“纹理张量”量化变形”，M.Au.，YJ，JAG，FG，伴侣纸，颗粒状物质，本期）。在这里，我们将这种统计分析应用于稳定地流过缩颈的二维泡沫，这是两个传统理论都无法解决的问题，并证明了泡沫具有（线性和各向同性）连续介质的弹性。

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