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TECHNICAL PAPERS

A Normal Force-Displacement Model for Contacting Spheres Accounting for Plastic Deformation: Force-Driven Formulation

[+] Author and Article Information
L. Vu-Quoc

e-mail: vu-quoc@ufl.edu

X. Zhang, L. Lesburg

Aerospace Engineering, Mechanics and Engineering Science, University of Florida, Gainesville, FL 32611

J. Appl. Mech 67(2), 363-371 (Sep 30, 1999) (9 pages) doi:10.1115/1.1305334 History: Received October 06, 1998; Revised September 30, 1999
Copyright © 2000 by ASME
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References

Cundall,  P., and Strack,  O., 1979, “A Discrete Numerical Model for Granular Assemblies,” Géotech., 29, No. 1, pp. 47–65.
Vu-Quoc, L., Zhang, X., and Walton, O. R., 2000, “A 3-D Discrete Element Method for Dry Granular Flows of Ellipsoidal Particles,” Comput. Methods Appl. Mech. Eng., invited paper for the special issue on Dynamics of Contact/Impact Problems, to appear.
Hertz,  H., 1882, “Über die Berührung fester elastischer Körper (On the Contact of Elastic Solids),” J. Reine Angew. Math., 92, pp. 156–171.
Johnson, K. L., 1985, Contact Mechanics, 2nd Ed., Cambridge University Press, New York.
Mindlin,  R. D., and Deresiewicz,  H., 1953, “Elastic Spheres in Contact Under Varying Oblique Forces,” ASME J. Appl. Mech., 20, pp. 327–344.
Shih,  C. W., Schlein,  W. S., and Li,  J. C. M., 1992, “Photoelastic and Finite Element Analysis of Different Size Spheres in Contact,” J. Mater. Res., 7, No. 4, pp. 1011–1017.
Vu-Quoc, L., and Lesburg, L., 2000, “Contact Force-Displacement Relations for Spherical Particles Accounting for Plastic Deformation,” Int. J. Solids Struct., submitted for publication.
Dobry,  R., Petrakis,  E., and Seridi,  A., 1991, “General Model for Contact Law Between Two Rough Spheres,” J. Eng. Mech., 117, No. 6, pp. 1365–1381.
Walton,  O. R., and Braun,  R. L., 1986, “Viscosity, Granular-Temperature, and Stress Calculations for Shearing Assemblies of Inelastic, Frictional Disks,” J. Rheol., 30, No. 5, pp. 949–980.
Goldsmith, W., 1960, Impact: The Theory and Physical Behavior of Colliding Solids, Edward Arnold, London.
Kangur,  K. F., and Kleis,  I. R., 1988, “Experimental and Theoretical Determination of the Coefficient of Velocity Restitution Upon Impact,” Mech. Solids, 23, No. 5, pp. 182–185.
Thornton,  C., 1997, “Coefficient of Restitution for Collinear Collisions of Elastic Perfectly Plastic Spheres,” ASME J. Appl. Mech., 64, pp. 383–386.
Brilliantov,  N. V., Spahn,  F., Hertzsch,  J., and Poschel,  T., 1996, “Model for Collisions on Granular Gases,” Phys. Rev. E, 53, No. 5, pp. 5382–5392.
Vu-Quoc, L., Lesburg, L., and Zhang, X., 1999, “A Tangential Force-Displacement Model for Contacting Spheres Accounting for Plastic Deformation: Force-Driven Formulation,” J. Mech. Phys. Solids, submitted for publication.
Davies,  R. M., 1949, “The Determination of Static and Dynamic Yield Stresses Using a Steel Ball,” Proc. R. Soc. London, Ser. A, 197, pp. 416–432.
Vu-Quoc,  L., and Zhang,  X., 1999, “An Elasto-Plastic Contact Force-Displacement Model in the Normal Direction: Displacement-Driven Version,” Proc. R. Soc. London, Ser. A, 455, No. 1991, pp. 4013–4044.
Zhang, X., and Vu-Quoc, L., 2000, “A Method to Extract the Mechanical Properties of Particles in Collision Based on a New Elasto-Plastic Normal Force-Displacement Model,” Int. J. Plast., submitted for publication.
LoCurto,  G. J., Zhang,  X., Zakirov,  V., Bucklin,  R. A., Vu-Quoc,  L., Hanes,  D. M., and Walton,  O. R., 1997, “Soybean Impacts: Experiments and Dynamic Simulations,” Trans. Am. Soc. Agr. Eng. (ASAE), 40, No. 3, pp. 789–794.
Vemuri,  B. C., Chen,  L., Vu-Quoc,  L., Zhang,  X., and Walton,  O. R., 1998, “Efficient and Accurate Collision Detection for Granular Flow Simulation,” Graph. Models Image Process., 60, No. 6, pp. 403–422.
Vu-Quoc,  L., and Zhang,  X., 1999, “An Accurate and Efficient Tangential Force-Displacment Model for Elastic-Frictional Contact in Particle-Flow Simulations,” Mech. Mater., 31, pp. 235–269.
Zhang,  X., and Vu-Quoc,  L., 2000, “Simulation of Chute Flow of Soybeans Using an Improved Tangential Force-Displacement Model,” Mech. Mater., 32, No. 2, pp. 115–129.

Figures

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Two spheres in contact, subjected to normal load P
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Normal force P versus normal displacement α: comparison between FEA results and Hertz theory for the loading path with Pmax=1500 N
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Distribution of normal stress on the contact surface at maximum normal force Pmax=1500 N: comparison between FEA results and Hertz theory
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Contact area radius a versus normal force P: comparison between FEA results and Hertz theory
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Variation of J2 and J2 along the z-axis for ν=0.3
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Contact radius aep versus normal force P for elasto-plastic contact, with comparison to Hertz theory (elastic)
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Plastic contact radius ap versus normal contact force P. Symbols (+, ○): FEA results. Solid line: model for loading. Dashed line: model for unloading.
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Normal stress distribution on the contact surface
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Normal displacement α versus the radius of total contact area (aep for elasto-plastic contact, aH for elastic contact)
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Plastic deformation increases the radius of relative contact curvature
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Loading paths of normal force
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Normal force P versus normal displacement α by different models for the loading path AFG in Fig. 11
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Contact areas radii aep,ae,ap versus normal force P by the proposed elasto-plastic NFD model for the loading path: AFG in Fig. 11
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Normal force P versus normal displacement α by different models for the loading path ADE in Fig. 11
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Normal force P versus normal displacement α by different models for the loading path ABC in Fig. 11

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