Dimers convergence behavior

The multiple counting of lobe interactions for compressed dimer-shaped particles gives rise to anomalous behavior for the structural and mechanical properties, which do not approach those for disks in the 1 limit. We now describe a micromechanical model based on the area of overlap between compressed dimershaped particles that result in structural and vibrational properties that converge smoothly to those in the —> 1 limit at all values of the compression A( ). 

Figure 3.18e shows the effective force law (force versus displacement) between two parallel dimers with aspect ratio = 1.3 undergoing compression for the micromechanical model in which (1) lobe interactions are multiply counted or (2) the interaction potential is given by Equation 3.15. The two force laws are the same as long as overlaps between lobes have not merged, or < 0.021 for the configuration in Figure 3.18a. Beyond Sm, the two force laws differ. The force law based on the total area of overlap converges to linear behavior f 5 more quickly than the one that multiply counts lobe interactions, for example, it is not sensitive to the formation of the fourth lobe contact at 8/a = 84/a = 0.075. In future studies, these results can be compared to finite element analyses of linear elastic particles with complex shapes.

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