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TECHNICAL PAPERS

Crushing of an Elastic-Plastic Ring Between Rigid Plates With and Without Unloading

[+] Author and Article Information
T. J. McDevitt

Naval Surface Warfare Center, Dahlgren Division, Dahlgren, VA 22448-5100

J. G. Simmonds

Department of Civil Engineering, University of Virginia, P.O. Box 400742 Charlottesville, VA 22904–4742

J. Appl. Mech 70(6), 799-808 (Jan 05, 2004) (10 pages) doi:10.1115/1.1630814 History: Received July 20, 2001; Revised April 22, 2003; Online January 05, 2004
Copyright © 2003 by ASME
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References

DeRuntz,  J. A., and Hodge,  P. G., 1963, “Crushing of a Tube Between Plates,” ASME J. Appl. Mech., 30, pp. 391–395.
Redwood,  R. G., 1964, “Crushing of a Tube Between Rigid Plates,” ASME J. Appl. Mech., 31, pp. 357–358.
Reid,  S. R., and Reddy,  T. Y., 1978, “Effect of Strain Hardening on the Lateral Compression of Tubes Between Rigid Plates,” Int. J. Solids Struct., 14, pp. 213–225.
Reddy,  T. Y., and Reid,  S. R., 1980, “Phenomena Associated With the Crushing of Metal Tubes Between Rigid Plates,” Int. J. Solids Struct., 16, pp. 545–562.
Liu,  J. H., Stonge,  W. J., and Yu,  T. X., 1989, “Large Deflections of an Elastoplastic Strain-Hardening Cantilever,” ASME J. Appl. Mech., 56, pp. 737–743.
Lubliner, J., 1990, Plasticity Theory, Macmillan, New York.
Frish-Fay, R., 1962, Flexible Bars, Butterworths and Co., London.
Avalle,  M., and Goglio,  L., 1997, “Static Lateral Compression of Aluminum Tubes: Strain Gauge Measurements and Discussion of Theoretical Models,” J. Strain Anal., 32, pp. 335–343.
Libai, A., and Simmonds, J. G., 1998, The Nonlinear Theory of Elastic Shells, 2nd Ed., Cambridge University Press, New York.
Avalle,  M., and Goglio,  L., 1999, “Lateral Compression of Thin-Walled Tubes: Strain Measurements by Image Analysis,” Exp. Mech., 39, pp. 231–235.
Leu,  D.-K., 1999, “Finite-Element Simulation of the Lateral Compression of Aluminum Tube Between Rigid Plates,” Int. J. Mech. Sci., 41, pp. 621–638.
Wang,  C. Y., 1987, “Crushing of an Elastic-Perfectly Plastic Ring or Tube Between Two Planes,” ASME J. Appl. Mech., 54, pp. 159–164.
Burton, R. H., and Craig, J. M., 1963, “An Investigation into the Energy Absorbing Properties of Metal Tubes Loaded in the Transverse Direction,” B. Sc. (Engr.) Rept. University of Bristol, Bristol, UK.
Dyrbye, C., and Hansen, P. L., 1954, “Studies on the Load Carrying Capacities of Steel Structures,” Research Laboratory of Building Technique, Technical University of Denmark, Bulletin No. 3.

Figures

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Two crushing sequences for an initially straight beam bent elastically into a ring (scenario I0) with μ=0.5. The parts of the rings shown in solid black are elastic; dashed (loading) and solid gray (unloading) parts are plastic. In (a), λ=10−6; in (b), λ=0.1.
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Dimensionless moment-curvature relation for an elastic-plastic ring
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Dimensionless load-deflection curves for an initially straight beam bent elastically and inextensionally into a ring (scenario I0) for various values of dimensionless material (λ) and geometric-material (μ) parameters. Solid curves include unloading effects; dashed curves do not.
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Dimensionless load-deflection curves of an initially stress-free ring (scenario II0). Solid curves include unloading effects; dashed curves do not.
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Dimensionless load-deflection curves of an initially straight beam bent elastically-plastically into a ring (scenario III0) with λ=0.1. Note that unloading effects (dashed curves) become increasingly important as μ increases.
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Comparison of rescaled dimensionless predicted load-deflection curves for scenario II0 with λ=0.01 and μ=10,20 with experimental data from Reddy and Reid 4
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Comparison of predicted load-deflection curve for Scenario II0 with λ=0.02 and μ=11 with experimental data from Avalle and Goglio 8

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