Particle scale force sensor based on intensity gradient method in granular photoelastic experiments
Particle scale force sensor based on intensity gradient method in granular photoelastic experiments
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DOI：
10.1088/1367-2630/ab05e7
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发表时间：
2019-02
影响因子：
3.3
通讯作者：
Yiqiu Zhao;Hu Zheng;Dong Wang;Meimei Wang;R. Behringer
中科院分区：
文献类型：
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作者：
Yiqiu Zhao;Hu Zheng;Dong Wang;Meimei Wang;R. Behringer
强度梯度法（G2法），即计算光强梯度平方，是一种广泛应用的提取准二维光弹性颗粒材料应力信息的无损伤实验方法。以前的工作表明，校准的G2是一个准确的测量全球应力。然而，它是否可以在颗粒尺度上使用，除了直径加载的特殊情况仍然不清楚。我们在这里测试的适用性和局限性的G2作为粒子尺度应力指标，并指定其依赖于相关的实验参数的粒子，光条件，和成像系统。本文首先基于线弹性理论和光弹性理论给出了G2值与应力关系的显式计算公式，然后通过数值计算和实验验证了公式的正确性。我们发现，当力不大时，对于圆盘颗粒，G2与接触力的大小之和∑ i <$F <$i <$成正比。我们还观察到，对于足够大的分辨率，在相同的∑ i值下，G2不随接触的数量以及接触力的方向而变化。然而，我们发现G2和∑ i <$F <$i <$之间的这种关系对于任何粒子形状都不是普适的。作为一个例子，我们表明，一个正方形颗粒可以有显着不同的G2值下相同的接触力与不同的接触类型（点-边接触和边-边接触）。
The intensity gradient method (G2 method), namely computing the light intensity gradient-squared, is a widely used non-invasive experimental method to extract stress information from quasi-two-dimensional photoelastic granular materials. Previous works show that calibrated G2 is an accurate measure of global stress. However, whether it can be used at the particle scale aside from the special case of diametric loading remains unclear. We test here the applicability and limitations of G2 as particle scale stress indicator and specify its dependence on relevant experimental parameters of the particles, light conditions, and imaging system. We first propose an explicit formula to calculate the relationship between the G2 value and stress based on the linear elasticity and photoelasticity theories, and then validate our formula by numerical and experimental tests. We find that G2 is proportional to ∑ i ∣ F ⃗ i ∣ , the sum of magnitudes of the contact forces, for disc particles when forces are not large. We also observe that, for large enough resolution, G2 does not change with the number of contacts as well as the direction of the contact forces under same ∑ i ∣ F ⃗ i ∣ value. However, we find that this relation between G2 and ∑ i ∣ F ⃗ i ∣ is not universal for any particle shape. As an example, we show that a square particle can have dramatically different values of G2 under the same contact forces with different contact types (point-edge contact and edge–edge contact).