Abstract
A photoelastic material will reveal its internal stresses when observed through polarizing filters. This eye-catching property has enlightened our understanding of granular materials for over half a century, whether in the service of art, education, or scientific research. In this review article in honor of Robert Behringer, we highlight both his pioneering use of the method in physics research, and its reach into the public sphere through museum exhibits and outreach programs. We aim to provide clear protocols for artists, exhibit-designers, educators, and scientists to use in their own endeavors. It is our hope that this will build awareness about the ubiquitous presence of granular matter in our lives, enlighten its puzzling behavior, and promote conversations about its importance in environmental and industrial contexts. To aid in this endeavor, this paper also serves as a front door to a detailed wiki containing open, community-curated guidance on putting these methods into practice (Abed-Zadeh et al. in Photoelastic methods wiki https://git-xen.lmgc.univ-montp2.fr/PhotoElasticity/Main/wikis/home, 2019).
Similar content being viewed by others
References
Frocht, M.M.: Photoelasticity: The Selected Scientific Papers of MM Frocht, vol. 2. Pergamon, New York (1969)
Cloud, G.: Photoelasticity, pp. 55–56. Cambridge University Press, Cambridge (1995)
Daniels, K.E., Kollmer, J.E., Puckett, J.G.: Photoelastic force measurements in granular materials. Rev. Sci. Instrum. 88(5), 051808 (2017)
Cox, M., Wang, D., Barés, J., Behringer, R.P.: Self-organized magnetic particles to tune the mechanical behavior of a granular system. Europhys. Lett. 115(6), 64003 (2016)
Wakabayashi, T.: Photo-elastic method for determination of stress in powdered mass. J. Phys. Soc. Jpn. 5(5), 383–385 (1950)
Dantu, P.: Proceedings of the 4th international conference on soil mechanics and foundations engineering (1957)
Drescher, A., De Jong De Josselin, G.: Photoelastic verification of a mechanical model for the flow of a granular material. J. Mech. Phys. Solids 20(5), 337–340 (1972)
Liu, C.H., Nagel, S.R., Schecter, D.A., Coppersmith, S.N., Majumdar, S., Narayan, O., Witten, T.A.: Force fluctuations in bead packs. Science 269(5223), 513–515 (1995)
Howell, D., Behringer, R.P., Veje, C.: Stress fluctuations in a 2d granular couette experiment: a continuous transition. Phys. Rev. Lett. 82(26), 5241 (1999)
Majmudar, T.S., Behringer, R.P.: Contact force measurements and stress-induced anisotropy in granular materials. Nature 435(7045), 1079 (2005)
Amon, A., Born, P., Daniels, K.E., Dijksman, J.A., Huang, K., Parker, D., Schröter, M., Stannarius, R., Wierschem, A.: Preface: focus on imaging methods in granular physics (2017)
Barés, J., Mora, S., Delenne, J.-Y., Fourcaud, T.: Experimental observations of root growth in a controlled photoelastic granular material. In: EPJ Web of Conferences, vol. 140. EDP Sciences, p. 14008 (2017)
Kollmer, J.E.: Photoelastic grain solver (pegs). https://github.com/jekollmer/PEGS (2018)
Lantsoght, O., Docquier, N.: Photoelastic grain solver with pyhton (pegspy). https://git.immc.ucl.ac.be/olantsoght/pegs_py (2018)
Barés, J., Wang, D., Wang, D., Bertrand, T., O’Hern, C.S., Behringer, R.P.: Local and global avalanches in a two-dimensional sheared granular medium. Phys. Rev. E 96(5), 052902 (2017)
Abed-Zadeh, A., Barés, J., Socolar, J., Behringer, R.P.: Seismicity in sheared granular matter. arXiv preprint arXiv:1810.12243 (2018)
Geng, J., Howell, D., Longhi, E., Behringer, R.P., Reydellet, G., Vanel, L., Clément, E., Luding, S.: Footprints in sand: the response of a granular material to local perturbations. Phys. Rev. Lett. 87(3), 035506 (2001)
Zhang, J., Majmudar, T.S., Tordesillas, A., Behringer, R.P.: Statistical properties of a 2d granular material subjected to cyclic shear. Granul. Matter 12(2), 159–172 (2010)
Majmudar, T.S., Sperl, M., Luding, S., Behringer, R.P.: Jamming transition in granular systems. Phys. Rev. Lett. 98(5), 058001 (2007)
Bi, D., Zhang, J., Chakraborty, B., Behringer, R.P.: Jamming by shear. Nature 480, 355–358 (2011)
Ren, J., Dijksman, J.A., Behringer, R.P.: Reynolds pressure and relaxation in a sheared granular system. Phys. Rev. Lett. 110(1), 018302 (2013)
Zheng, H., Dijksman, J.A., Behringer, R.P.: Shear jamming in granular experiments without basal friction. EPL (Europhys. Lett.) 107(3), 34005 (2014)
Wang, D., Ren, J., Dijksman, J.A., Zheng, H., Behringer, R.P.: Microscopic origins of shear jamming for 2d frictional grains. Phys. Rev. Lett. 120, 208004 (2018)
Clark, A.H., Kondic, L., Behringer, R.P.: Particle scale dynamics in granular impact. Phys. Rev. Lett. 109(23), 238302 (2012)
Lim, M.X., Barés, J., Zheng, H., Behringer, R.P.: Force and mass dynamics in non-Newtonian suspensions. Phys. Rev. Lett. 119(18), 184501 (2017)
Zheng, H., Wang, D., Chen, D.Z., Wang, M., Behringer, R.P.: Intruder friction effects on granular impact dynamics. Phys. Rev. E 98, 032904 (2018)
Zuriguel, I., Mullin, T.: The role of particle shape on the stress distribution in a sandpile. Proc. R. Soc. A: Math. Phys. Eng. Sci. 464(2089), 99–116 (2008)
Lherminier, S., Planet, R., Simon, G., Vanel, L., Ramos, O.: Revealing the structure of a granular medium through ballistic sound propagation. Phys. Rev. Lett. 113(9), 098001 (2014)
Shukla, A.: Dynamic photoelastic studies of wave propagation in granular media. Opt. Lasers Eng. 14(3), 165–184 (1991)
Owens, E.T., Daniels, K.E.: Sound propagation and force chains in granular materials. Europhys. Lett. 94(5), 54005 (2011)
Huillard, G., Noblin, X., Rajchenbach, J.: Propagation of acoustic waves in a one-dimensional array of noncohesive cylinders. Phys. Rev. E 84, 016602 (2011)
Puckett, J.G., Daniels, K.E.: Equilibrating temperaturelike variables in jammed granular subsystems. Phys. Rev. Lett. 110(5), 058001 (2013)
Bililign, E.S., Kollmer, J.E., Daniels, K.E.: Protocol dependence and state variables in the force-moment ensemble. Phys. Rev. Lett. 122(3), 038001 (2019)
Kollmer, J., Daniels, K.: Betweenness centrality as predictor for forces in granular packings. Soft Matter (2018). https://doi.org/10.1039/C8SM01372A
Coulais, C., Seguin, A., Dauchot, O.: Shear modulus and dilatancy softening in granular packings above jamming. Phys. Rev. Lett. 113(19), 198001 (2014)
Iikawa, N., Bandi, M.M., Katsuragi, H.: Sensitivity of granular force chain orientation to disorder-induced metastable relaxation. Phys. Rev. Lett. 116(12), 128001 (2016)
Mahabadi, N., Jang, J.: The impact of fluid flow on force chains in granular media. Appl. Phys. Lett. 110(4), 041907 (2017)
Wendell, D.M., Luginbuhl, K., Guerrero, J., Hosoi, A.E.: Experimental investigation of plant root growth through granular substrates. Exp. Mech. 52(7), 945–949 (2012)
Kolb, E., Hartmann, C., Genet, P.: Radial force development during root growth measured by photoelasticity. Plant Soil 360, 19–35 (2012)
Daniels, K.E., Hayman, N.W.: Force chains in seismogenic faults visualized with photoelastic granular shear experiments. J. Geophys. Res. 113(B11), B11411 (2008)
Hayman, N.W., Ducloué, L., Foco, K.L., Daniels, K.E.: Granular controls on periodicity of stick-slip events: kinematics and force-chains in an experimental fault. Pure Appl. Geophys. 168(12), 2239–2257 (2011)
Geller, D.A., Ecke, R.E., Dahmen, K.A., Backhaus, S.: Stick-slip behavior in a continuum-granular experiment. Phys. Rev. E 92(6), 060201 (2015)
Lherminier, S., Planet, R., Levy dit Vehel, V., Simon, G., Vanel, L., Maloy, K.J., Ramos, O.: Continuously sheared granular matter reproduces in detail seismicity laws. arXiv:1901.06735 (2019, January)
Abed-Zadeh, A., Barés, J., Brzinski, T., Daniels, K.E., Dijksman, J., Docqiuer, N., Everitt, H., Kollmer, J., Lantsoght, O., Wang, D., Workamp, M., Zhao, Y., Zheng, H.: Photoelastic methods wiki. https://git-xen.lmgc.univ-montp2.fr/PhotoElasticity/Main/wikis/home (2019)
Majmudar, T.S.: Experimental Studies of Two-Dimensional Granular Systems Using Grain-Scale Contact Force Measurements. PhD thesis, Duke University (2006)
Precision urethane pads. http://www.precisionurethane.com/polyurethane-pads.html
Clear flex™, castable urethane from smooth-on. https://www.smooth-on.com/product-line/clear-flex/
Vishay pads. http://www.vishaypg.com/micro-measurements/photo-stress-plus
Wang, D.: Response of Granular Materials to Shear: Origins of Shear Jamming, Particle Dynamics, and Effects of Particle Properties. PhD thesis, Duke University (2018)
Mold star™, castable silicone from smooth-on. https://www.smooth-on.com/product-line/mold-star/
So strong™, dye for urethane from smooth-on. https://www.smooth-on.com/product-line/strong/
Kilcast, D., Boyar, M.M., Hudson, J.B.: Gelatin photoelasticity: a new technique for measuring stress distributions in gels during penetration testing. J. Food Sci. 49(2), 654–655 (1984)
Workamp, M., Alaie, S., Dijksman, J.A.: What is fluidity? Designing an experimental system to probe stress and velocity fluctuations in flowing suspensions. In: EPJ Web of Conferences, vol. 140. EDP Sciences, p. 03020 (2017)
Tomlinson, R.A., Taylor, Z.A.: Photoelastic materials and methods for tissue biomechanics applications. Opt. Eng. 54(8), 081208 (2015)
Damink, L.H.O., Dijkstra, P.J., Van Luyn, M.J.A., Van Wachem, P.B., Nieuwenhuis, P., Feijen, J.: Glutaraldehyde as a crosslinking agent for collagen-based biomaterials. J. Mater. Sci. Mater. Med. 6(8), 460–472 (1995)
Workamp, M., Alaie, S., Dijksman, J.A.: Coaxial air flow device for the production of millimeter-sized spherical hydrogel particles. Rev. Sci. Instrum. 87(12), 125113 (2016)
Lherminier, S., Planet, R., Simon, G., Måløy, M., Vanel, L., Ramos, O.: A granular experiment approach to earthquakes. Rev. Cubana Fís 33(1), 55–58 (2016)
Veroclear™, printable transparent photoelastic material from smooth-on. https://www.stratasys.com/materials/search/veroclear
Wang, L., Ju, Y., Xie, H., Ma, G., Mao, L., He, K.: The mechanical and photoelastic properties of 3d printable stress-visualized materials. Sci. Rep. 7(1), 10918 (2017)
Polarization, a company which sells polarizers and quater-waves plates by the foot. http://www.polarization.com/polarshop/
Zhao, Y., Barés, J., Zheng, H., Behringer, R.P.: Tuning strain of granular matter by basal assisted couette shear. In: EPJ Web of Conferences, vol.140, p. 03049. EDP Sciences (2017)
Shattuck, M.D.: Experimental techniques. In: Franklin, S.V., Shattuck, M.D. (eds.) Handbook of Granular Materials. CRC Press, Boca Raton (2015)
Peng, T., Balijepalli, A., Gupta, S.K., LeBrun, T.: Algorithms for on-line monitoring of micro spheres in an optical tweezers-based assembly cell. J. Comput. Inf. Sci. Eng. 79, 330–338 (2007)
Crocker, J.C., Grier, D.G.: Methods of digital video microscopy for colloidal studies. J. Colloid Interface Sci. 179(1), 298–310 (1996)
Blair, D., Dufresne, E.: Matlab particle tracking code repository. http://site.physics.georgetown.edu/matlab/
Willert, C.E., Gharib, M.: Digital particle image velocimetry. Exp. Fluids 10(4), 181–193 (1991)
Landau, L.D., Lifshitz, E.M.: Theory of elasticity, vol. 7. Course Theor. Phys. 3, 109 (1986)
Abed-Zadeh, A., Barés, J., Behringer, R.P.: Crackling to periodic dynamics in granular media. Phys. Rev. E 99(4), 040901 (2019b)
Zhao, Y., Zheng, H., Wang, D., Wang, M., Behringer, R.P.: Particle scale force sensor based on intensity gradient method in granular photoelastic experiments. New J. Phys. 21, 023009 (2019). https://doi.org/10.1088/1367-2630/ab05e7
Majmudar, T.S.: Experimental studies of two-dimensional granular systems using grain-scale contact force measurements (Doctoral Dissertation). Duke University (2006)
Farhadi, S., Behringer, R.P: Dynamics of sheared ellipses and circular disks: effects of particle shape. Phys. Rev. Lett. 112(14), 148301 (2014)
Farhadi, S., Zhu, A.Z, Behringer, R.P: Stress relaxation for granular materials near jamming under cyclic compression. Phys. Rev. Lett. 115(18), 188001 (2015)
Iikawa, N., Bandi, M.M., Katsuragi, H.: Structural evolution of a granular pack under manual tapping. J. Phys. Soc. Jpn. 84(9), 094401 (2015). https://doi.org/10.7566/JPSJ.84.094401
Lantsoght, O.: Couplage entre dynamique multicorps et méthode des éléments discrets: modélisation et expérimentation. phdthesis, Université Catholique de Louvain (2019)
Timoshenko, S., Goodier, J.N.: Theory of Elasticity, 3rd edn. McGraw-Hill, New York (1970)
Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)
Yu, P., Frank-Richter, S., Börngen, A., Sperl, M.: Monitoring three-dimensional packings in microgravity. Granul. Matter 16(2), 165–173 (2014)
Mahon, R.J., Murphy, J.A., Lanigan, W.: Digital holography at millimetre wavelengths. Opt. Commun. 260(2), 469–473 (2006)
Heimbeck, M.S., Kim, M.K., Gregory, D.A., Everitt, H.O.: Terahertz digital holography using angular spectrum and dual wavelength reconstruction methods. Opt. Express 19(10), 9192–9200 (2011)
Everitt, H.O., Tyler, T., Caraway, B.D., Bingham, C.M., Llopis, A., Heimbeck, M.S., Padilla, W.J., Smith, D.R., Jokerst, N.M.: Strain sensing with metamaterial composites. Adv. Opt. Mater. 7, 1801397 (2019)
Thomas, A.L., Vriend, N.M.: Photoelastic study of dense granular free-surface flows. preprint (2019)
Acknowledgements
We would like to thank Rémy Mozul for his technical support with the wiki [44]. Several conversations and collaborations have led to sharing the techniques described in this paper. We are grateful to Bernie Jelinek and Richard Nappi for sharing their technical knowledge about photoelastic material cutting. The outlook section contains insights gained from Chris M. Bingham, Willie J. Padilla, Anthony Llopis and Nan M. Jokerst (recent work on terahertz photoelasticity), and from Nathalie Vriend and Amalia Thomas (fast-imaging photoelasticity). Finally, we thank the late Robert Behringer for his kindness, his depth of knowledge gained from developing photoelastic techniques for two decades, and his stimulating attitude towards every new generation of scientists passing through his laboratory. This review article is a product of his excellent mentorship.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This article is part of the Topical Collection: In Memoriam of Robert P. Behringer.
Rights and permissions
About this article
Cite this article
Abed Zadeh, A., Barés, J., Brzinski, T.A. et al. Enlightening force chains: a review of photoelasticimetry in granular matter. Granular Matter 21, 83 (2019). https://doi.org/10.1007/s10035-019-0942-2
Received:
Published:
DOI: https://doi.org/10.1007/s10035-019-0942-2