Orthogonal Photoelastic Imaging for Three-Dimensional Stress Estimation in a Transparent Cubical Block

TL;DR

The paper tackles the limitation of 2D photoelasticity for resolving multi-component surface traction by introducing a cubic, low-stiffness, prestress-free epoxy block that produces three independent isochromatic fringe fields from three orthogonal views. Fringe orders are extracted with a peak–valley intensity method, enabling sub-fringe resolution and quantitative stress mapping when paired with calibrated material properties and the stress-optic constant $f_\sigma$. Through careful fabrication, calibration of $E$, ${\nu}$, and $f_\sigma$, and a three-view experimental setup, the authors demonstrate high-quality fringe patterns, cross-view consistency at low loading, and tens of microseconds response. This work lays the groundwork for full 3D force reconstruction in dynamic environments and offers a path to biomechanical and diagnostic applications where rapid, multi-component traction sensing is critical.

Abstract

Conventional photoelastic methods are largely limited to two-dimensional stress visualization, leaving a gap in techniques that can capture three-dimensional force interactions with high sensitivity at low stress levels, a capability that is critical for biomechanics and dynamic force analysis. This study develops and demonstrates a cubic photoelastic model that enables accurate fringe-order estimation from three orthogonal views, providing a foundation for reconstructing full three-dimensional stress states. A transparent, low-elasticity epoxy cube, free of prestress, was fabricated and examined using combined transmission and reflection photoelastic imaging. Three mutually orthogonal isochromatic fringe fields were recorded simultaneously under a single applied load. Image analysis employed a peak-valley intensity method to extract sub-fringe orders and to resolve low-stress cases with minimal noise. The cubic block produced high-quality fringe patterns in all directions, enabling separation of tangential and normal stress components. Independent orthogonal views confirmed directional sensitivity and yielded consistent fringe-order estimates under low loading, with response times on the order of tens of microseconds. These results establish a practical approach for three-dimensional photoelastic stress measurement from orthogonal views and create a pathway toward full vector force reconstruction with strong potential for biomedical applications and studies of dynamic loading.

Figures (15)

• Figure 1: (a) Schematic of bright circular polariscope: polarizer and analyzer are parallel to each other, both quarter wave plates cross to each other, and the angle between polarizer and quarter wave plate is $\pi$/4. (b) Schematic of reflected polariscope: arrangement of polarizers and quarter wave plates is similar to bright circular polariscope but due to reflection from the top of the surface the angle changes and the bright field becomes a dark field. L - white diffuse light, P - polarizer, Q - quarter wave plate, M - photoelastic model, A - analyzer.
• Figure 2: (a) Image of photoelastic cubic block with size 0.05 m made by resin/hardener solution with all required properties including, free of internal-stress, good transmittance, smooth sides, sharp edges, and no bubbles. (b) Hardener mass and resin mass plotted for cubic block of size 0.01 m, 0.02 m, 0.03 m, 0.04 m and 0.05 m (open circle), and the solid line is quadratic fit of hardener mass and resin mass.
• Figure 3: Photoelastic cubic of size 0.04m block visualize through bright circular polariscope without loading and showing free of internal stress with approximately constant intensity entire the block.
• Figure 4: (a) Schematic of the experimental setup for calibration of the modulus of elasticity and Poisson ratio. (b) Experimental setup used to measure the response time of the photoelastic block. Acoustic transducer attaches with indenter used to give a high-frequency pulse on the photoelastic block and the optical signal are visualize through high-speed camera. Photoelastic block kept on plate and plate is placed on two translation stages to maintain level and proper contact between indenter and photoelastic block. (c) Golf ball impact on the photoelastic block, used to measure response time.
• Figure 5: Calibration curves for (a) elastic modulus: stress $\sigma$ (N/m$^2$) versus compressional or longitudinal strain $\epsilon_{||}$ (dimensionless) and (b) Poisson ratio: Lateral strain $\epsilon_{\perp}$ (dimensionless) vs compressional or longitudinal strain $\epsilon_{||}$ (dimensionless).