... | ... | @@ -41,7 +41,7 @@ For diametric loaded disc, $`G^2`$ is proportional to the disc boundary pressure |
|
|
The slope $`k`$ of the linear dependence between the $`G^2`$ and the sum of contact force magnitude $`\sum_i|F_i|`$ depends on many parameters: (1) The background light intensity $`I_0`$. (2) The stress-optic coefficient $`f_{\sigma}`$. (3) The radius of the disc $`R`$. (4) The resolution $`N`$ defined as the number of pixels per meter. Theoretical derivations, supported by numerical and experimental tests, show $`k\propto I_0^2/(f_{\sigma}R^2N)`$. A first intuition from this result is, in polydisperse system, the relation between $`G^2`$ and contact forces for particles with different sizes must be calibrated separately. [4]
|
|
|
|
|
|
|
|
|
### 3.4. Particle shape influence
|
|
|
### 3.4. Contact type influence
|
|
|
|
|
|
The discussion so far only considered disc particles. An unproved empirical expectation is for particles with only point contacts the linear dependence between $`G^2`$ and contact forces on particle scale should still hold. However, when contact with finite area occurs, the $`G^2`$ value no longer uniquely determined by the contact forces. An example is shown in the figure below, where a square shape particle is under point-point diametric load (left) or surface-surface diametric load (right). The magnitude of the contact forces are same for both cases. But the photoelastic patterns are very different, resulting in different $`G^2`$ value.
|
|
|
|
... | ... | |