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TECHNICAL PAPERS

Coupled Plastic Wave Propagation and Column Buckling

[+] Author and Article Information
Denzil G. Vaughn, James M. Canning, John W. Hutchinson

Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138

J. Appl. Mech 72(1), 139-146 (Feb 01, 2005) (8 pages) doi:10.1115/1.1825437 History: Received April 21, 2004; Revised May 03, 2004; Online February 01, 2005
Copyright © 2005 by ASME
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References

Xue,  Z., and Hutchinson,  J. W., 2004, “Preliminary assessment of sandwich plates subject to blast loads,” Int. J. Mech. Sci., 45, pp. 687–705.
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Abrahamson,  G. R., and Goodier,  J. N., 1966, “Dynamic flexural buckling of rods within an axial plastic compression wave,” J. Appl. Mech., 33, pp. 241–247.
Karagiozova,  D., and Jones,  N., 1996, “Dynamic elastic-plastic buckling phenomena in a rod due to axial impact,” Int. J. Impact Eng., 18, pp. 919–947.
Calladine,  C. R., and English,  R. W., 1984, “Strain rate and inertia effects in the collapse of two types of energy-absorbing structures,” Int. J. Mech. Sci., 26, pp. 689–701.
Anwen,  W., and Wenying,  T., 2003, “Characteristic-value analysis for plastic dynamic buckling of columns under elastoplastic compression waves,” Int. J. Non-Linear Mech., 38, pp. 615–628.
Lepik,  Ulo, 2001, “Dynamic buckling of elastic-plastic beams including effects of axial stress waves,” Int. J. Impact Eng., 25, pp. 537–552.
Kenny,  S., Pegg,  N., and Taheri,  F., 2002, “Finite element investigations on the dynamic plastic buckling of a slender beam subject to axial impact,” Int. J. Impact Eng., 27, pp. 179–195.
von Karman,  T., and Duwez,  P., 1950, “The propagation of plastic deformation in solids,” J. Appl. Phys., 21, pp. 987–994.
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Figures

Grahic Jump Location
Plastic compression wave propagating along a rod for both the small strain approximation and the finite strain solution. (a) Strain εU in the region of uniform deformation behind the propagating front. (b) Nominal compressive stress at the left end of the rod and in the adjacent region of uniform strain. The normalizations for the small strain approximation are valid for all yield strains; the results for the finite strain solution are computed with εY=0.003.
Grahic Jump Location
Undeformed and deformed meshes for a straight rod subject to velocities V=140 ms−1 and V=200 ms−1[V/(c0εY)=13.3 and 19] at its left end and fixed at its right end. The deformed rods have been deformed to an overall strain of 20%. No material rate dependence.
Grahic Jump Location
Nominal stress exerted by a rod on the plates at its two ends, where the left plate impacts the rod at V=140 ms−1[V/(c0εY)=13.3] and the right plate is fixed.
Grahic Jump Location
Undeformed and deformed meshes of column with initial imperfection for quasistatic, V=20 m/s, and V=200 m/s[V/(c0εY)=1.9] and high [V/(c0εY)=19]. No material rate dependence.
Grahic Jump Location
Plastic energy dissipation as a function of V/(c0εY) [and V/(Lε̇0)], with and without strain-rate dependence at an overall strain ε̄=0.1 for the material specified by (9) and c0εY/(Lε̇0)=0.0175.
Grahic Jump Location
Quasistatic nominal stress-end shortening behavior with and without strain hardening. The material is specified by (9) with Et=0 and m=0 for the elastic-perfectly plastic case and Et=2.4 GPa and m=0 for the hardening material. The stockiness ratio is R/L=0.077 and the imperfection amplitude is ζ=1/4.
Grahic Jump Location
Nominal stress acting by the column on the left plate as a function of the normalized imposed velocity V at three levels of overall strain for both an elastic-perfectly plastic material [(9) with Et=0 and m=0] and a material with high strain hardening [(9) with Et=2.4 GPa,m=0]. The imperfection amplitude is ζ=1/4.
Grahic Jump Location
Nominal stress acting by the column on the left plate as a function of the normalized imposed velocity V for a strain hardening material (9) with (m=0.154) and without (m=0) strain-rate dependence at an overall strain of 10%. The imperfection amplitude is ζ=1/4 and c0εY/(Lε̇0)=0.0175.
Grahic Jump Location
(a) Effect of the stockiness, R/L, on the nominal stress acting by the column on the left plate as a function of the normalized imposed velocity V for a strain hardening material with no strain-rate dependence [(9) with Et=2.4 GPa,m=0]. The imperfection amplitude is ζ=1/4. (b) Effect of the yield strain, εYY/E, on the nominal stress acting by the column on the left plate as a function of the normalized imposed velocity V for a strain hardening material with no strain-rate dependence [(9) with Et=2.4 GPa,m=0]. The imperfection amplitude is ζ=1/4.
Grahic Jump Location
Normal component of reaction force exerted by an inclined column member of a tetragonal truss core on left plate as a function of normalized imposed velocity V at three levels of overall strain and the result derived from an axially loaded column with three levels of initial imperfection. The insert on the right shows the dynamically loaded column (with V/c0εY=15) while the insert on the left shows the quasistatically deformed column.

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