Chandan Shakya and Joshua A. DijksmanVan der Waals-Zeeman Institute, Institute of Physics,University of Amsterdam, Amsterdam, The NetherlandsPhysical Chemistry and Soft Matter, Wageningen University, Wageningen, Netherlands Jasper van der GuchtPhysical Chemistry and Soft Matter, Wageningen University, Wageningen, Netherlands.(Dated: March 26, 2024)Granular materials are ubiquitous in nature and industry; their mechanical behavior has been of academic and engineering interest for centuries. One of the reasons for their rather complex mechanical behavior is that stresses exerted on a granular material propagate only through contacts between the grains. These contacts can change as the packing evolves. This makes any deformation and mechanical response from a granular packing a function of the nature of contacts between the grains and the material response of the material the grains are made of. We present a study in which we isolate the role of the grain material in the contact forces acting between two particles sliding past each other. We use hydrogel particles and find that a viscoelastic material model, in which the shear modulus decays with time, coupled with a simple Coulomb friction model captures the experimental results. The results suggest that the particle material evolution itself may play a role in the collective behavior of granular materials.
Velocity dependence of the contact force Figure 4a) compares the horizontal force response of spherical hydrogels in response to sliding at dierent constant velocity levels. The rst feature that is apparent from this gure is that the amplitude of the troughs for the dierent sliding velocities do not coincide. On closer inspection, we notice that the amplitude of these troughs is greater for larger velocities. The same is also true for the peaks, but this feature is less pronounced in the plot as the relaxation is contact duration dependent, and at the peaks, the contact is younger. Thus, a clear velocity-dependent response can be observed. When we recall equation 4 which essentially models the eective shear modulus as a decaying function with time, this experimental model makes sense. Experiments done at lower sliding velocities take a longer time and therefore work with a lower eective shear modulus; thus their force response to the same strain or overlap is lower.
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Another feature of interest can be seen at the very end of the contact. The force response just before the two particles detach is highlighted in the inset in gure 4a). Here we see that even though all of these tests were performed on the same set of particles, the points of detachment at dierent velocities do not coincide. The particle seems to detach earlier when the particles move slower relative to each other. This too is consistent with the model explained in equation 4. In gure 4 b) we plot the the geometric contact length (lg) and the deformed contact length (lc) obtained at the dierent sliding speeds (v) at which the experiments were performed. Here, we clearly see that the variation in lg at dierent speeds is much lower than the variation of lc. Furthermore, we see that lc seems to grow at larger sliding speeds and approaches lg. This trend is consistent when the experiment is performed in either direction as can also be seen in the gure 4.
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Recreating experimental features with the analytical model Figure 5 describes how the forces from the model described in section III are vectorially resolved so that they can be compared to the data observed in the experiment. The two dimensional analytical model consists of measuring the eective overlap of two circles moving past each other. The upper circle is moving from left to right at a velocity v and the lower circle is xed. Figure 5a) shows the geometric quantities involved in calculating the total forces in the horizontal and vertical directions at contact. At contact, the distance between the particle centers are R1 + R2. max is the the maximum overlap between the particles. Thus the vertical distance between max. is the angle bethe particle centers is R1 + R2 tween the horizontal plane and the line joining the two particle centers and can be calculated using the triangle shown in gure 5a). is the horizontal distance between the particle centers which can also be calcu
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After this moment (at t = 0), the overlap () is zero. After this vt. The vertical dismoment, t grows from 0 and = 0 max tance between the particle centers remains R1+R2 and a new distance between particle centers can be calvt). These quanculated as tities are also used to calculate a new . Similarly, = (R1 + R2) vt).), for (R1 + R2 any instant of time t, when the horizontal displacement = vt.
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