  Integrated photoelasticity is investigated for a soft material subjected to a
three-dimensional stress state. In the experiment, a solid sphere is pressed
against a gelatin gel (Young's modulus is about 4.2 kPa) that deforms up to 4.5
mm depending on the loading forces. The resulting photoelastic parameters
(phase retardation, azimuthal angle, and stress-optic coefficient) in the gel
are measured using a polarization camera. The measured retardation and azimuth
are compared with the analytical prediction based on Hertzian contact theory.
Remarkably, experimental and analytical results of the photoelastic parameters
show a reasonable agreement not only in the retardation but also in the azimuth
that is related to the direction of principal stresses and but rarely validated
in previous studies, is essential for reconstructing three-dimensional stress
fields in soft materials. The stress-optic coefficient of the gelatin gel used
is 3.12$\times10^{-8}$ 1/Pa. Such findings proved that integrated
photoelasticity is useful for measuring the three-dimensional stress field in
soft materials, which is of importance in biomedical engineering and cell
printing applications.
