Skip to main content
SpringerLink
Log in

Stress field equations for a disk subjected to self-equilibrated arbitrary loads: revisited

  • Brief Communication
  • Published:
Granular Matter Aims and scope Submit manuscript

Abstract

Closed-form expressions for stress distribution in a disk subjected to self-equilibrated loads having arbitrary magnitudes and directions have been derived following the approach of Timoshenko. The stress field equations are simplified to a readily usable form by intelligently employing the solution to the problem of a concentrated load acting on a semi-infinite plate (Flamant’s solution) and the solution of Lame’s problem. The proposed equations eliminate a series of involved and avoidable steps to be followed in the existing methods for stress determination, which makes these new equations computationally more efficient. The isochromatic fringes plotted using the proposed equations for disks subjected to various numbers of loads revealed a subtle aspect that the fringe order at the free boundary of a disk is non-zero if the loads are acting in the non-radial direction whereas it is zero for radial loads. This heuristic information can further simplify the determination of contact forces from isochromatic fringes, which is the current focus of many of the researchers working in the field of granular materials.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

References

  1. Sergazinov, R., Kramar, M.: Machine learning approach to force reconstruction in photoelastic materials, pp. 1–20 (2020) [Online]. http://arxiv.org/abs/2010.01163

  2. Daniels, K.E., Kollmer, J.E., Puckett, J.G.: Photoelastic force measurements in granular materials. Rev. Sci. Instrum. 88(5), 051808 (2017). https://doi.org/10.1063/1.4983049

    Article  ADS  Google Scholar 

  3. Timoshenko, S., Goodier, J.N.: Theory of elasticity. McGraw Hill Education (1951)

    MATH  Google Scholar 

  4. Majmudar, T.S.: Experimental studies of two-dimensional granular systems using grain-scale contact force measurements. Graduate School of Duke University (2006)

  5. Puckett, J.G.: State variables in granular materials: an investigation of volume and stress fluctuations. North Carolina State University (2012).

  6. Surendra, K.V.N., Simha, K.R.Y.: Characterizing frictional contact loading via isochromatics. Exp. Mech. 54(6), 1011–1030 (2014). https://doi.org/10.1007/s11340-014-9865-3

    Article  Google Scholar 

  7. Martin, H.S.: Elasticity-Theory, Applications and Numerics. Elsevier (2005)

    Google Scholar 

  8. Daniels, K.E., Hayman, N.W.: Force chains in seismogenic faults visualized with photoelastic granular shear experiments. J. Geophys. Res. 113(B11), B11411 (2008). https://doi.org/10.1029/2008JB005781

    Article  ADS  Google Scholar 

  9. Ramesh, K.: Digital Photoelasticity Advanced Techniques and Applications. Springer, Berlin, Heidelberg (2000). https://doi.org/10.1115/1.1483353

    Book  Google Scholar 

  10. Ramesh, K.: Developments in Photoelasticity—A Renaissance. IOP Publishing (2021). https://doi.org/10.1088/978-0-7503-2472-4

  11. 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(2), 023009 (2019). https://doi.org/10.1088/1367-2630/ab05e7

    Article  ADS  Google Scholar 

  12. Abed Zadeh, A., et al.: Enlightening force chains: a review of photoelasticimetry in granular matter. Granul. Matter 21(4), 1–12 (2019). https://doi.org/10.1007/s10035-019-0942-2

    Article  Google Scholar 

  13. 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. Home · Wiki · PhotoElasticity_Main · GitLab

Download references

Funding

The authors did not receive support from any organization for the submitted work.

Author information

Authors and Affiliations

  1. Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, 600036, Tamil Nadu, India

    K. Ramesh & K. Shins

Authors
  1. K. Ramesh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Shins
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. Ramesh.

Ethics declarations

Conflict of interest

The authors have no conflicts of interest to declare that are relevant to the content of this article.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ramesh, K., Shins, K. Stress field equations for a disk subjected to self-equilibrated arbitrary loads: revisited. Granular Matter 24, 49 (2022). https://doi.org/10.1007/s10035-021-01205-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10035-021-01205-3

Keywords

Search

Navigation