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TECHNICAL PAPERS

Analyical Solutions for Failure Evolution With a Nonlinear Local Damage Model

[+] Author and Article Information
X. Xin

Department of Civil and Environmental Engineering, University of Missouri, Columbia, MO 65211e-mail: xxin@model1.civil.missouri.edu

C. Chicone

Department of Mathematics, University of Missouri, Columbia, MO 65211

Z. Chen

Department of Civil and Environmental Engineering, University of Missouri, Columbia, MO 65211 Mem. ASME

J. Appl. Mech 68(6), 835-843 (Nov 10, 2000) (9 pages) doi:10.1115/1.1406956 History: Received November 09, 1999; Revised November 10, 2000
Copyright © 2001 by ASME
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References

Sandler, I. S., 1984, “Strain Softening for Static and Dynamic Problems,” Constitutive Equations: Macro and Computational Aspects, K. J. William, ed., ASME, New York, pp. 217–231.
Valanis,  K. C., 1985, “On the Uniqueness of Solutions of the Initial Value Problems in Softening Materials,” ASME J. Appl. Mech., 52, pp. 649–653.
Bazant,  Z. P., and Belytschko,  T. B., 1985, “Wave Propagation in a Strain-Softening Bar: Exact Solution,” J. Eng. Mech., 111, pp. 381–389.
Chen, Z., 1993, “A Partitioned-Solution Method With Moving Boundaries for Nonlocal Plasticity,” Modern Approaches to Plasticity, D. Kolymbas, ed., Elservier, New York, pp. 449–468.
Chen,  Z., and Sulsky,  D., 1995, “A Partitioned-Modeling Approach With Moving Jump Conditions for Localization,” Int. J. Solids Struct., 32, pp. 1893–1905.
Chen,  Z., and Xin,  X., 1999, “An Analytical and Numerical Study of Failure Waves,” Int. J. Solids Struct., 36, pp. 3977–3991.
Xin,  X., and Chen,  Z., 2000, “An Analytical Solution With Local Elastoplastic Models for the Evolution of Dynamic Softening,” Int. J. Solids Struct., 37, pp. 5855–5872.
Xin,  X., and Chen,  Z., 2000, “An Analytical and Numerical Study to Simulate the Evolution of Dynamic Failure With Local Elastodamage Models,” International Journal of Damage Mechanics, 9, pp. 305–328.
Armero, F., 1997, “On the Characterization of Localized Solutions in Inelastic Solids: An Analysis of Wave Propagation in a Softening Bar,” UCB/SEMM-97/18, University of California, Berkeley, CA.
Feng, R., and Chen, Z., 1999, “Propagation of Heterogeneous Microdamage in Shocked Glasses,” Applied Mechanics in the Americas, Vol. 7, P. Goncalves, I. Jasiuk, D. Pamplona, C. Steele, H. Weber, and L. Bevilacqua, eds., American Academy of Mechanics, Northwestern University, Evanston, IL, pp. 691–694.
Kanel, G. I., Rasorenov, S. V., and Fortov, V. E., 1991, “The Failure Waves and Spallations in Homogeneous Brittle Materials,” Shock Compression of Condensed Matter, S. C. Schmidt, R. D. Dick, J. W. Forbes, and D. G. Tasker, eds., Elsevier, New York, pp. 451–454.
Kanel,  G. I., Rasorenov,  S. V., Utkin,  A. V., He,  H., Jing,  F., and Jin,  X., 1998, “Influence of the Load Conditions on the Failure Wave in Glasses,” High Press. Res., 16, pp. 27–44.
John, F., 1982, Partial Differential Equations, Springer-Verlag, New York.
McOwen, R. C., 1996, Partial Differential Equations: Methods And Applications, Prentice-Hall, Englewood Cliffs, NJ.
Bluman, G. W., and Kumei, S., 1989, Symmetries and Differential Equations, Springer-Verlag, New York.
Olver, P. J., 1993, Applications of Lie Group to Differential Equations. Springer-Verlag, New York.

Figures

Grahic Jump Location
A nonlinear local elastodamage model
Grahic Jump Location
After the limit state is reached, the whole solution domain is partitioned by a moving boundary (∂ΩI) into two domains: an elliptic domain (ΩI) and hyperbolic domain (ΩIIIII)
Grahic Jump Location
Evolution of localization along the bar
Grahic Jump Location
Normalized stress profiles corresponding to Fig. 3
Grahic Jump Location
Damage evolution corresponding to Fig. 3
Grahic Jump Location
Strain profiles for different b at t=1.25tL
Grahic Jump Location
Stress profiles for different b at t=1.25tL
Grahic Jump Location
Damage profiles for different b at t=1.25tL
Grahic Jump Location
Strain profiles for different vb at t=1.25tL
Grahic Jump Location
Stress profiles for different vb at t=1.25tL
Grahic Jump Location
Damage profiles for different vb at t=1.25tL
Grahic Jump Location
Strain history at x/L=0.05 and 0.1 after localization occurs
Grahic Jump Location
After the limit state is reached, the whole solution domain for a static bar is partitioned by a moving boundary (∂Ω) into two elliptic domains: ΩI and ΩII
Grahic Jump Location
Evolution of localization along the bar
Grahic Jump Location
Normalized stress profiles corresponding to Fig. 14
Grahic Jump Location
Damage evolution corresponding to Fig. 14
Grahic Jump Location
Strain profiles for different vb at t=1.25tL
Grahic Jump Location
Stress profiles for different vb at t=1.25tL
Grahic Jump Location
Damage profiles for different vb at t=1.25tL

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