Integrated photoelasticity in a soft material: phase retardation, azimuthal angle, and stress-optic coefficient

Abstract

Integrated photoelasticity is investigated for a soft material subjected to a three-dimensional stress state with large deformation. Our measurement target is designed based on the axisymmetric stress field (Hertzian contact problem). In the experiment, a solid sphere is pressed against a gelatin gel (Young’s modulus is about 4.2 kPa) with varying applied forces from zero to the maximum force that deforms the gel up to approximately 4.5 mm. For soft materials, two-dimensional photoelasticity, as conventionally practiced, is difficult to be used. This is because two-dimensional slices of highly deformable materials, such as the gelatin used in this study, do not allow stable experiments. This requires a three-dimensional body with sufficient thickness for stability, where integrated photoelasticity is demanded. The stressed gel’s photoelastic parameters (phase retardation and azimuthal angle) are measured using a polarization camera. The measured phase retardation and azimuthal angle are compared with the analytical prediction based on Hertzian contact problem. Remarkably, experimental and analytical results of the photoelastic parameters show a reasonable agreement not only in the phase retardation but also in the azimuthal angle that is related to the direction of secondary principal stresses. Never before validated in previous studies, which is crucial for reconstructing three-dimensional stress fields in soft materials. In addition, the stress-optic coefficient of the gelatin gel used is measured to be 3.12×10−8 1/Pa. Such findings proved that integrated photoelasticity benefits measure the three-dimensional stress field in soft materials, which is essential in biomedical engineering and cell printing applications.