  This study presents a novel approach for reconstructing all stress components
of the dynamic axisymmetric fields of a soft material using photoelastic
tomography (PT) and a high-speed polarization camera. This study focuses on
static and dynamic Hertzian contact as an example of transient stress field
reconstructions. For the static Hertzian contact (a solid sphere pressed
against a gel block), all stress components in the urethane gel, which has an
elastic modulus of 47.4 kPa, were reconstructed by PT using the measured
photoelastic parameters. The results were compared with theoretical solutions
and showed good agreement. For the dynamic Hertzian contact (a sphere impacting
gel), a high-speed polarization camera was used to reconstruct the transient
stress field within the gel. PT was used to quantitatively measure the shear
and axial stress waves and showed different propagation speeds on the
substrate. The technique allowed the simultaneous measurement of stress fields
ranging from $O(10^{-1})$ to $O(10^1)$ kPa during large deformations,
demonstrating its accuracy in capturing rapidly changing stress tensor
components in dynamic scenarios. The scaling laws of the calculated impact
force agreed with theoretical predictions, validating the accuracy of PT for
measuring dynamic axisymmetric stress fields in soft materials.
