Plotting of Isoclinic Phasemap from Finite Element Results and its Use in Digital Photoelasticity

Abstract

Digital photoelasticity is an experimental method for determining stresses in 2D and 3D models. In digital photoelasticity one gets a wrapped isoclinic phasemap. The main issue with wrapped isoclinic phasemaps is that the isoclinic values obtained do not uniformly represent the principal stress direction of one of the principal stresses consistently over the entire domain. These zones are labelled as inconsistent zones. Such zones need to be identified and corrected to get unwrapped values of continuous isoclinic phase values. In this paper, a method is developed to plot the simulated wrapped and unwrapped isoclinic phasemap from 2D Finite Element (FE) results so that one can use this as a convenient tool for identification and correction of inconsistent zones in isoclinic phasemaps obtained experimentally for complex problems. The method is explained by using the problem of a circular disc under diametral compression. The application of this method for handling complex problems is demonstrated by solving the cantilever bending of a binocular specimen.

Adaptive Quality Guided Phase Unwrapping Algorithm for Whole‐Field Digital Photoelastic Parameter Estimation of Complex Models

“… Unwrapped isoclinic and isochromatic phasemaps obtained for the problem of a cantilever beam with central cavity under bending obtained using the 10‐step phase‐shifting algorithm: (A) model line diagram with appropriate boundary conditions and loading; (B) dark‐field monochromatic image along with the isotropic points marked; (C) wrapped isoclinic phasemap obtained using the first four optical arrangements in Table 1 (along with inconsistent zones and seed point marked); (D) unwrapped isoclinic phasemap obtained using AQGPU; (E) unwrapped isoclinic phasemap plotted using finite element method [27]; (F) isochromatic phasemap obtained using using θ calculated from last six optical arrangements in Table 1 (ambiguous zones are marked); (G) isochromatic phasemap obtained using unwrapped isoclinic value in ; (H) isochromatic phasemap plotted using finite element method [28]; (I) Matlab plot of unwrapped isochromatic phasemap obtained using phase derivative variance quality guided algorithm …”

“…The unwrapping algorithm has performed well in handling all the isotropic points and the inconsistent zones while unwrapping. Figure 7E shows the unwrapped isoclinic phasemap plotted using the finite element method [27]. There is almost a one‐to‐one correspondence between Figures 7D and E except at a few places near the model boundary.…”