Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-05-24T22:49:44.653Z Has data issue: false hasContentIssue false

9 - Photoelastic materials

Published online by Cambridge University Press:  05 July 2014

Brian Utter
Affiliation:
James Madison University
Jeffrey Olafsen
Affiliation:
Baylor University, Texas
Get access

Summary

Introduction

The behavior of dense granular materials, which consist of large collections of individual grains, is an example of a complex system. Despite the relative simplicity of the constituents, the large number of frictional contacts leads to indeterminacy, history dependance, and jamming. We still lack a general set of macroscopic equations to describe their flow. A continuum description of the relevant state variables is desirable, and early studies in soil mechanics focused on characterizing bulk stress/strain relationships and failure. However, it was determined through experiments using photoelastic materials [1–3] that forces transmitted through granular assemblies are carried through an inhomogeneous network of stress chains in which the majority of force is carried through chains of particles comprising a minority of grains (e.g. Figure 9.1(b)). The creation and failure of these chains are central to the fluctuations that can dominate in measurements of dense, granular systems [4].

To visualize internal stresses, these experiments used grains composed of photoelastic materials, which exhibit stress-induced birefringence. When placed between crossed polarizers, in a polariscope, the intensity of transmitted light varies with the local principal stress difference, allowing visualization of the internal stresses in the system. Regions of differential stress appear as a series of bright and dark fringes. The resulting pattern offers both an immediate insight into the spatial stress distribution and the opportunity to measure quantitative local force data in the sample.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] P., Dantu, “Etude statistique des forces intergranulaires dans un milieu pulverulent,Geoíechnique 18, 50–5 (1968).Google Scholar
[2] A., Drescher and G., De Josselin de Jong, “Photoelastic verification of a mechanical model for the flow of a granular material,Geoíechnique 18, 50–5 (1968).Google Scholar
[3] T., Travers, D., Bideau, A., Gervois, J. P., Troadec, and J. C., Messager, “Uniaxial compression effects on 2d mixtures of ‘hard’ and ‘soft’ cylindars,J. Phys. A: Math. Gen. 19, L1033-L1038 (1986).Google Scholar
[4] D. W., Howell, R. P., Behringer, and C. T., Veje, “Fluctuations in granular media,Chaos 9, 559–72 (1999).Google Scholar
[5] M. M., Frocht, Photoelasticity, vol. 1 (John Wiley and Sons, New York, 1941).Google Scholar
[6] J., Brujic, S. F., Edwards, D. V., Grinev, I., Hopkinson, D., Brujic, and H. A., Makse, “3d bulk measurements of the force distribution in a compressed emulsion system,Faraday Discuss. 123, 207–20 (2003).Google Scholar
[7] D., Howell, R. P., Behringer, and C., Veje, “Stress fluctuations in a 2d granular couette experiment: a continuous transition,Physical Review Letters 82, 524144 (1999).Google Scholar
[8] R. J., Sanford and J. W., Dally, “A general method for determining mixed-mode stress intensity factors from isochromatic fringe patterns,Engineering Fracture Mechanics 11, 621–33 (1979).Google Scholar
[9] A. J., Durelli and D., Wu, “Use of coefficients of influence to solve some inverse problems in plane elasticity,Transactions of the ASME 50, 288–96 (1983).Google Scholar
[10] A., Shukla and H., Nigam, “A numerical-experimental analysis of the contact stress problem,J. Strain Anal. 20, 241–5 (1985).Google Scholar
[11] S., Paikowsky and K. J., DiRocco, “Image analysis for interparticle contact modeling,” in Conference on Digital Image Processing: Techniques and Applications in Civil Engineering,ASCE Publication No. 236 (1993).Google Scholar
[12] T. S., Majmudar and R. P., Behringer, “Contact force measurements and stress-induced anisotropy in granular materials,Nature 435, 1079–82 (2005).Google Scholar
[13] T. S., Majmudar, M., Sperl, S., Luding, and R. P., Behringer, “Jamming transition in granular systems,Physical Review Letters 98, 058001 (2007).Google Scholar
[14] T. S., Majmudar, M., Sperl, S., Luding, and R. P., Behringer, “The jamming transition in granular systems – supplementary information,” available at www.aip.org/pubservs/epaps.html, document number E-PRLTAO-98-020705.
[15] T. Y., Chen, Selected Papers on Photoelasticity (SPIE Optical Engineering Press, Bellingham, WA, 1999).Google Scholar
[16] J.-C., Dupre, “Photoelastic analysis of a three-dimensional specimen by optical slicing and digital image processing,Experimental Mechanics 18, 393–7 (1968).Google Scholar
[17] H., Aben, L., Ainola, and J., Anton, “Integrated photoelasticity for nondestructive residual stress measurements in glass,Optics and Lasers in Engineering 33, 49–64 (2000).Google Scholar
[18] L., Ainola and H., Aben, “On the optical theory of photoelastic tomography,J. Opt. Soc. Am. A 21, 1093–101 (2004).Google Scholar
[19] C. T., Veje, D. W., Howell, and R. P., Behringer, “Kinematics of a two-dimensional granular couette experiment at the transition to shearing,Physical Review E 59, 739–45 (1999).Google Scholar
[20] B., Utter and R., Behringer, “Self-diffusion in dense granular shear flows,Physical Review E 69, 031308 (2004).Google Scholar
[21] B., Utter and R., Behringer, “Self-diffusion in dense granular shear flows,European Physical Journal E 14, 373–80 (2004).Google Scholar
[22] A., Ajovalasit, S., Barone, and G., Petrucci, “Towards rgb photoelasticity – full-field automated photoelasticity in white-light,Experimental Mechanics 35, 193–200 (1995).Google Scholar
[23] A., Ajovalasit, S., Barone, and G., Petrucci, “A review of automated methods for the collection and analysis of photoelastic data,Journal of Strain Analysis 33, 75–91 (1998).Google Scholar
[24] V., Galiatsatos, “Refractive index, stress-optical coefficient, and optical configuration parameter,” in J. E., Mark (ed.), Physical Properties of Polymers, pp. 823–56 (Springer Science, New York, 2007).Google Scholar
[25] R. B., Heywood, Designing by Photoelasticity (Chapman and Hall, London, 1955).Google Scholar
[26] T. Y., Chen, “Digital determination of photoelastic birefringence using two wavelengths,Experimental Mechanics 37, 232–6 (1997).Google Scholar
[27] Vishay Intertechnology, Inc. (Malvern, PA).
[28] J. F., Geng, G., Reydellet, E., Clement, and R. P., Behringer, “Green's function measurements of force transmission in 2d granular materials,Physica D 182, 274–303 (2003).Google Scholar
[29] B., Utter and R. P., Behringer, unpublished.
[30] M. M., Frocht, Photoelasticity, vol. 2 (John Wiley and Sons, New York, 1948).Google Scholar
[31] N. W., Mueggenburg, H. M., Jaeger, and S. R., Nagel, “Stress transmission through three-dimensional ordered granular arrays,Physical Review E 66, 031304 (2002).Google Scholar
[32] E. I., Corwin, H. M., Jaeger, and S. R., Nagel, “Structural signature of jamming in granular media,Nature 435, 1075–8 (2005).Google Scholar
[33] J. F., Geng, E., Longhi, R. P., Behringer, and D., Howell, “Memory in two-dimensional heap experiments,Physical Review E 64, 060301 (2001).Google Scholar
[34] J. F., Geng, D., Howell, E., Longhi, R. P., Behringer, G., Reydellet, L., Vanel, E., Clement, and S., Luding, “Footprints in sand: The response of a granular material to local perturbations,Physical Review Letters 87, 035506 (2001).Google Scholar
[35] I., Zuriguel, T., Mullin, and R., Arevalo, “The role of particle shape on the stress distribution in a sandpile,Proc. R. Soc. London. Series A – Mathematical, Physical and Engineering Sciences 464, 99-116 (2008).Google Scholar
[36] I., Zuriguel, T., Mullin, and R., Arevalo, “Stress dip under a two-dimensional semipile of grains,Physical Review E 77, 061307 (2008).Google Scholar
[37] J., Zhang, T., Majmudar, and R. P., Behringer, “Force chains in a two-dimensional granular pure shear experiment,Chaos 18, 041107 (2008).Google Scholar
[38] M., Oda and H., Kazama, “Microstructure of shear bands and its relation to the mechanisms of dilatancy and failure of dense granular soils,Geotechnique 48, 465–81 (1998).Google Scholar
[39] M., Cates, J., Wittmer, J.-P., Bouchaud, and P., Claudin, “Jamming, force chains, and fragile matter,Physical Review Letters 81, 1841–4 (1998).Google Scholar
[40] M., Toiya, J., Stambaugh, and W., Losert, “Transient and oscillatory granular shear flow,Physical Review Letters 93, 088001 (2004).Google Scholar
[41] R., Hartley and R., Behringer, “Logarithmic rate dependence of force networks in sheared granular materials,Nature 421, 928–31 (2003).Google Scholar
[42] R., Wan, P., Guo, and M., Al-Mamun, “Behaviour of granular materials in relation to their fabric dependencies,Soils and Foundations 45, 77–86 (2005).Google Scholar
[43] R. J., Sanford and J. W., Dally, “Dynamic photoelastic studies of wave-propagation in antigranulocytes media,Optics and Lasers in Engineering 14, 165–84 (1979).Google Scholar
[44] R. J., Sanford and J. W., Dally, “Experimental investigation of fabric-stress relations in antigranulocytes materials,Mechanics of Materials 11, 87-106 (1991).Google Scholar
[45] D., Amon, E., Hoppmann, and B., Utter, unpublished.
[46] K. E., Daniels and N. W., Hayman, “Force chains in seismogenic faults visualized with photoelastic granular shear experiments,Journal of Geophysical Research 113, B11411 (2008).Google Scholar
[47] D., Lesniewska and D. M., Wood, “Observations of stresses and strains in a granular material,Journal of Engineering Mechanics –ASCE 135, 1038–54 (2009).Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Photoelastic materials
  • Edited by Jeffrey Olafsen, Baylor University, Texas
  • Book: Experimental and Computational Techniques in Soft Condensed Matter Physics
  • Online publication: 05 July 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9780511760549.009
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Photoelastic materials
  • Edited by Jeffrey Olafsen, Baylor University, Texas
  • Book: Experimental and Computational Techniques in Soft Condensed Matter Physics
  • Online publication: 05 July 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9780511760549.009
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Photoelastic materials
  • Edited by Jeffrey Olafsen, Baylor University, Texas
  • Book: Experimental and Computational Techniques in Soft Condensed Matter Physics
  • Online publication: 05 July 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9780511760549.009
Available formats
×