Methods to make photoelastic samples
Once you managed to get a photoelastic image of your loaded sample you can either be happy about such a nice picture or you may want to go a bit further and get something more quantitative. In this section we will present the different analysis you can carry out and what you could expect to measure. What you can get highly depends on the accuracy of your pictures, the sensitivity of sample and the behavior of its constitutive material. For different situations we tell you the best you can get and how you should proceed.
The applications given here are dedicated to photoelastic granular samples. However it can be generalized to any other geometries.
Detect and follow samples:
First of all, from the images using different colors you can get the sample position and exact geometry. In this section for the specific case of granular matter that can be generalized to any other sample, we present the image processing methods to get the exact grain position. We show how to track the sample position in dynamical case and how to obtain the material flow when image accuracy is not enough to make a proper sample detection.
Simple image intensity analysis:
Once you managed to get the sample positions, if you do not want detailed informations about the stress field or if you do not have pictures accurate enough, you can simply analyse the average image intensity. When properly calibrated this gives you an idea about the average stress underwent by the material. You assume that the brighter, the larger the stress and with a rough calibration you can get pressure estimation. In the case of granular matter, ridge filtering can also provide you the position and intensity of the force chains. More details about how to post-process images are given here.
Image gradient analysis:
If you want a better measure and if you have accurate enough pictures, a more sophisticated method consists in analysing the intensity of the squared image intensity gradient
G^2 which gives information about the photoelastic fringe density. It has been shown by Howell et al. that this is proportional to the inner pressure. Calibrating the method for your material, you can get a quite accurate information about the pressure in your sample. More details about this method are given here.
Inverse problem method:
An accurate measurement of the photoelastic signal of a loaded sample can provide much more than what presented before. Virtually (non-uniqueness of the solution), by inverting the mechanical problem, knowing the material behavior and geometry, is it possible to get the full stress field. For complex material and geometry this can be extremely complicated. But in the case of circular discs, assuming you are in the Hertz contact regime things are easier and you can get the external forces applied to the sample. This has been implement in granular matter by Majmudar and Behringer for example. More details about this method are given here.