Holographic method for stress distribution analysis in photoelastic materials

Sidney L. da Silva; Felipe M. Prado; Isis V. Brito; Diogo Soga; Lígia F. Gomes; Niklaus U. Wetter; Mikiya Muramatsu; Sidney L. da Silva; Felipe M. Prado; Isis V. Brito; Diogo Soga; Lígia F. Gomes; Niklaus U. Wetter; Mikiya Muramatsu

doi:10.3934/matersci.2024032

AIMS Materials Science

2024, Volume 11, Issue 4: 620-633. doi: 10.3934/matersci.2024032

Previous Article Next Article

Research article Special Issues

Holographic method for stress distribution analysis in photoelastic materials

1.
Optics and Applications Group, Fatec Itaquera, 08295005, São Paulo, SP, Brazil
2.
Energy and Nuclear Research Institute, IPEN-CNEN/SP, 05508-000, São Paulo, Brazil
3.
Institute of Physics, University of Sao Paulo, 05508-090, São Paulo, SP, Brazil

Received: 23 May 2024 Revised: 01 July 2024 Accepted: 11 July 2024 Published: 22 July 2024

An alternative method to obtain the internal stress distribution in photoelastic materials using digital holography (DH) is presented. Two orthogonally polarized holograms were used to obtain the phase maps and analyzed using the proposed approach. This method directly determines the stress distributions from the phase differences obtained in the reconstructed phase maps, unlike methods obtained by photoelasticity. Optical information, such as index of refraction, phase differences, etc., are not measured directly in traditional photoelasticity. However, this approach was validated with both the finite element method and the RGB (red, green, and blue) photoelasticity method that is traditionally used.
- polarized digital holography,
- photoelastic materials,
- stress and strain,
- polarization,
- RGB method,
- finite element method
Citation: Sidney L. da Silva, Felipe M. Prado, Isis V. Brito, Diogo Soga, Lígia F. Gomes, Niklaus U. Wetter, Mikiya Muramatsu. Holographic method for stress distribution analysis in photoelastic materials[J]. AIMS Materials Science, 2024, 11(4): 620-633. doi: 10.3934/matersci.2024032

Related Papers:

Abstract

An alternative method to obtain the internal stress distribution in photoelastic materials using digital holography (DH) is presented. Two orthogonally polarized holograms were used to obtain the phase maps and analyzed using the proposed approach. This method directly determines the stress distributions from the phase differences obtained in the reconstructed phase maps, unlike methods obtained by photoelasticity. Optical information, such as index of refraction, phase differences, etc., are not measured directly in traditional photoelasticity. However, this approach was validated with both the finite element method and the RGB (red, green, and blue) photoelasticity method that is traditionally used.

References

[1]	Kale S, Ramesh K (2013) Advancing front scanning approach for three-fringe photoelasticity. Opt Laser Eng 51: 592–599. https://doi.org/10.1016/j.optlaseng.2012.12.013 doi: 10.1016/j.optlaseng.2012.12.013
[2]	Moura BA (2014) Isaac Newton and the double refraction of light. Rev Bras Ensino Fis 36: 01–15. https://doi.org/10.1590/S1806-11172014000400021 doi: 10.1590/S1806-11172014000400021
[3]	Lohne JA (1977) Nova experimenta crystalli islandici disdiaclastici. Centaurus 21: 106–148. http://dx.doi.org/10.1111/j.1600-0498.1977.tb00350.x doi: 10.1111/j.1600-0498.1977.tb00350.x
[4]	Magie FW, Weber LR (1965) A source book in physics. Am J Phys 33: 247. https://doi.org/10.1119/1.1971416 doi: 10.1119/1.1971416
[5]	Brewster D (1815) On the laws which regulate the polarisation of light by reflection from transparent bodies. Philos Trans R Soc 105: 125–159. https://doi.org/10.1098/rstl.1815.0010 doi: 10.1098/rstl.1815.0010
[6]	Dally WJ (1980) An introduction to dynamic photoelasticity. Exp Mech 20: 409–416. https://doi.org/10.1007/BF02320881 doi: 10.1007/BF02320881
[7]	Ramesh K, Kasimayan T, Simon NB (2011) Digital photoelasticity—A comprehensive review. J Strain Anal Eng 46: 245–266. https://doi.org/10.1177/0309324711401501 doi: 10.1177/0309324711401501
[8]	Ajovalasit A, Petrucci G, Scafidi M (2015) Review of RGB photoelasticity. Opt Laser Eng 68: 58–73. https://doi.org/10.1016/j.optlaseng.2014.12.008 doi: 10.1016/j.optlaseng.2014.12.008
[9]	Coker GE, Filon LNG (1932) A treatise on photo-elasticity, In: South VR, The Mathematical Gazette, Cambridge: Cambridge University Press, 16: 277–279. https://doi.org/10.2307/3605934
[10]	Frocht MM, Guernsey R (1953) A special investigation to develop a general method for three-dimensional photoelastic stress analysis. NTRS 2: 963–979. https://ntrs.nasa.gov/citations/19930092176
[11]	Fö ppl L, Mö nch E (2013) Praktische Spannungsoptik, 1 Eds., Heidelberg: Springer Berlin. https://doi.org/10.1007/978-3-642-52730-2
[12]	Smith WC (1991) Applications of the photoelastic method to some problems in solid mechanics. Opt Laser Eng 14: 147–149. https://doi.org/10.1016/0143-8166(91)90045-U doi: 10.1016/0143-8166(91)90045-U
[13]	Lee J, Yoon L, Kim YL, et al. (2016) Effect of implant number and distribution on load transfer in implant-supported partial fixed dental prostheses for the anterior maxilla: A photoelastic stress analysis study. J Prosthet Dent 115: 161–169. https://doi.org/10.1016/j.prosdent.2015.08.021 doi: 10.1016/j.prosdent.2015.08.021
[14]	Goiato CM, Ribeiro PP, Pellizer PE, et al. (2009) Photoelastic analysis of stress distribution in different retention systems for facial prosthesis. J Craniofac Surg 20: 757–761. https://doi.org/10.1097/scs.0b013e3181a28a96 doi: 10.1097/scs.0b013e3181a28a96
[15]	Strang G, Fix GJ (1973) An analysis of the finite element method. Z Angew Math Mech 55: 696–697. https://doi.org/10.1002/zamm.19750551121 doi: 10.1002/zamm.19750551121
[16]	Chen YT, Huang P, Chuang S (2014) Modeling dental composite shrinkage by digital image correlation and finite element methods. Opt Laser Eng 61: 23–30. https://doi.org/10.1016/j.optlaseng.2014.04.006 doi: 10.1016/j.optlaseng.2014.04.006
[17]	Silva SL (2016) Quantitative study of stresses in photoelastic samples using digital holography. Institute of Physics at the University of Sã o Paulo (IFUSP), Sã o Paulo. Available from: http://www.teses.usp.br/teses/disponiveis/43/43134/tde-22102016-154751/.
[18]	Schnars U, Falldorf C, Watson J, et al. (2015) Digital Holography and Wavefront Sensing, 2 Eds., Hagen: Springer Berlin Heidelberg, 226. https://doi.org/10.1007/978-3-662-44693-5
[19]	Kronrod MA, Merzlyakov NS, Yaroslavskii LP (1972) Digital holography experiments. Avtometrija 6: 30–40. Available from: http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=PASCAL7313011243.
[20]	Oliveira NG, Rodrigues CDM, Nunes SLC, et al. (2012) Digital Fourier Transform holography was applied to investigate mechanical deformation in polymers. Opt Laser Eng 50: 1798–1803. https://doi.org/10.1016/j.optlaseng.2012.06.016 doi: 10.1016/j.optlaseng.2012.06.016
[21]	Silva SL, Prado MF, Toffoli JD, et al. (2023) Characterization of the photoelastic dispersion coefficient using polarized digital holography. J Opt Soc Am A 40: C108. https://doi.org/10.1364/JOSAA.482543 doi: 10.1364/JOSAA.482543
[22]	Silva SL, Prado MF, Toffoli JD, et al. (2020) Measuring photoelastic dispersion coefficients in material samples with digital holography. In Proceedings of the Practical Holography XXXIV: Displays, Materials, and Applications. https://doi.org/10.1117/12.2544874
[23]	Fourney EM (1968) Application of holography to photoelasticity. Exp Mech 8: 33–38. https://doi.org/10.1007/BF02326248 doi: 10.1007/BF02326248
[24]	Colomb T, Dahlgren P, Beghuin D, et al. (2002) Polarization imaging by use of digital holography. Appl Optics 41: 27–37. https://doi.org/10.1364/AO.41.000027 doi: 10.1364/AO.41.000027
[25]	Yokota M, Terui Y, Yamaguchi I (2007) Polarization analysis with digital holography by use of polarization modulation for single reference beam. Opt Eng 46: 055801. https://doi.org/10.1117/1.2740601 doi: 10.1117/1.2740601
[26]	Zienkiewicz OC (2005) The Finite Element Method, 6 Eds., London: McGraw-Hill, 1872. Available from: https://books.google.com.br/books?id = iqfue5Kv2tkC & lpg = PP1 & hl = pt-BR & pg = PP1#v = onepage & q & f = false.
[27]	Vuolo JH (1996) Fundamentals of Error Theory, 2Eds., Sã o Paulo: Blucher, 264. Available from: https://books.google.com.br/books?id = q-uyDwAAQBAJ & lpg = PP1 & hl = pt-BR & pg = PP1#v = [onepage & q & f = false.
[28]	Kuske A (1974) Photoelastic Stress Analysis, London: Wiley-Interscience, 519p. Available from: https://lccn.loc.gov/73002788.
[29]	Carcolé E, Campos J, Bosch S (1994) Diffraction theory of Fresnel lenses encoded in low-resolution devices. Appl Optics 33: 162–174. https://doi.org/10.1364/AO.33.000162 doi: 10.1364/AO.33.000162
[30]	Jacquot M, Sandoz P, Tribillon G (2001) High resolution digital holography. Opt Commun 190: 87–94. https://doi.org/10.1016/S0030-4018(01)01046-X doi: 10.1016/S0030-4018(01)01046-X
[31]	Mann C, Yu L, Lo CM, et al. High-resolution quantitative phase-contrast microscopy by digital holography. Opt Express 13: 8693–8698. https://doi.org/10.1364/OPEX.13.008693
[32]	Schnars U, Jüptner WPO (2002) Digital recording and numerical reconstruction of holograms. Meas Sci Technol 13: R85. https://doi.org/10.1088/0957-0233/13/9/201 doi: 10.1088/0957-0233/13/9/201
[33]	James DFV, Agarwal GS (1996) The generalized Fresnel transform and its application to optics. Opt Commun 126: 207–212. https://doi.org/10.1016/0030-4018(95)00708-3 doi: 10.1016/0030-4018(95)00708-3
[34]	Volkov VV, Zhu U (2003) Deterministic phase unwrapping in the presence of noise. Opt Lett 28: 2156–2158. https://doi.org/10.1364/OL.28.002156 doi: 10.1364/OL.28.002156

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)