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Determination of loads between elements in granular media

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Abstract

A procedure is explained in this paper to determine the magnitude of several in-plane loads (normal and shear) applied to the outer boundaries of contacting particles used to model granular media. The approach is general, but in the test the particles have been modeled using disks. Maximum shear stresses at selected points in the field of the disks were determined photoelastically. The original equations of Hertz, as presented by Poritsky, permit the use of coefficients of influence for the computation. Examples of application and estimates of the precision obtained are also given.

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Abbreviations

a :

half the width of contact

F :

normal load:F=F′ h

F′ :

load by unit length perpendicular to contact

f :

photoelastic fringe value:\(\tau _{max{\mathbf{ }} = {\mathbf{ }}\frac{f}{h}{\mathbf{ }}n} \)

h :

thickness of the cylinder

k :

coefficient of influence, dimensionless

n :

photoelastic fringe order

p :

traction, normal to surface

R 1, R2 :

radii of the two cylinders in contact

T′ :

force by unit length, tangential to contact

t :

traction, tangential to surface

α:

angle of radius going through a point, and the axis

λ=T′/F′ :

ratio of normal and tangential forces

σ x :

normal stress in direction x

136-3 :

shear stress

References

  1. Durelli, A.J. andWu, D., “Use of Coefficients of Influence to Solve Some Inverse Problems in Plane Elasticity,”J. Appl. Mech.,50 (2),288–296 (June 1983).

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  2. Alberro, J., Distribucion Estadistica de las Fuerzas de Contacto en un Medio Granular, Informe Interno, Instituto de Ingenieria, UNAM, Mexico (1981).

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  3. Hertz, H. Gesammelte Werke,I,Leipzig (1895). Also Ueber die Beruehrung festes elastisches Koerper, Jr. fuer Mathematik,92,156 (1882).

  4. Poritsky, H., “Stresses and Deflections of Cylindrical Bodies in Contact,”J. Appl. Mech.,17,191–201 (June 1950).

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  5. Moench, E. andBush, M., Spannungsoptische Versuche zur Theorie der rollenden Reibung, Oestereichisches Ingenieur Archiv,XVIII (3–4),274–284 (1964).

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Authors and Affiliations

  1. Mechanical Engineering Department, University of Maryland, 20742, College Park, MD

    A. J. Durelli (Professor) & Y. H. Lin (Graduate Student)

  2. Chongqing Institute of Architecture and Engineering, Peoples Republic of China

    D. Wu (associated)

Authors
  1. A. J. Durelli
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  2. D. Wu
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  3. Y. H. Lin
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Durelli, A.J., Wu, D. & Lin, Y.H. Determination of loads between elements in granular media. Experimental Mechanics 26, 136–141 (1986). https://doi.org/10.1007/BF02320005

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  • DOI: https://doi.org/10.1007/BF02320005

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