Research Papers

Low-Velocity Impact Response of Structures With Local Plastic Deformation: Characterization and Scaling

[+] Author and Article Information
Andreas P. Christoforou

e-mail: andreas.christoforou@ku.edu.kw

Majed Majeed

Department of Mechanical Engineering,
Kuwait University,
P.O. Box 5969,
Safat 13060, Kuwait

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 9, 2012; final manuscript received March 17, 2012; published online June 14, 2012. Assoc. Editor: José L. Escalona.

J. Comput. Nonlinear Dynam 8(1), 011012 (Jun 14, 2012) (10 pages) Paper No: CND-12-1004; doi: 10.1115/1.4006532 History: Received January 09, 2012; Revised March 17, 2012

This paper presents a methodology for the characterization and scaling of the response of structures having different shapes, sizes, and boundary conditions that are under impact by spherical objects. The objectives are to demonstrate the accuracy of a new bilinear contact law that accounts for permanent indentation in the contact zone, and to show the efficacy of a characterization diagram in the analysis and design of structures subject to impact. The characterization diagram shows the normalized functional relationship between the maximum impact force and three nondimensional parameters that cover the complete dynamic spectrum for low-velocity impact. The validity of using the bilinear elastoplastic contact law is demonstrated by both finite element (FE) and Rayleigh-Ritz discretization procedures for simply-supported plates. The efficacy of the characterization diagram, which was developed using simple structural models, is demonstrated by the FE simulations of more complicated and realistic structures and boundary conditions (clamped, stiffened plates, and cylindrical panels). All of the necessary parameters needed for the characterization are ‘measured’ using the FE models simulating real-world experiments. Impact parameters are varied to cover the complete dynamic spectrum with excellent results.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Goldsmith, W., 1960, Impact, Edward Arnold, London.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, New York.
Cantwell, W. J. and Morton, J., 1991, “The Impact Resistance of Composite Materials—A Review,” Composites, 22, pp. 347–361. [CrossRef]
Abrate, S., 1998, Impact on Composite Structures, Cambridge University Press, New York.
Stronge, W. J., 2000, Impact Mechanics, Cambridge University Press, New York.
Gilardi, G. and Sharf, I., 2002, “Literature Survey of Contact Dynamics Modeling,” Mech. Mach. Theory, 37, pp. 1213–1239. [CrossRef]
Seifried, R., Schiehlen, W., and Eberhard, P., 2010, “The Role of the Coefficient of Restitution on Impact Problems in Multi-Body Dynamics,” Proc. Inst. Mech. Eng. Part K: J. Multi-Body Dyn., 224, pp. 279–289.
Tan, T. M. and Sun, C. T., 1985, “Use of Statistcal Indentation Laws in the Impact Analysis of Laminated Composite Plates,” ASME J. Appl. Mech., 52, pp. 6–12. [CrossRef]
Yigit, A. S. and Christoforou, A.P., 1994, “On the Impact of a Spherical Indenter and an Elastic-Plastic Transversely Isotropic Half-Space,” Composites Eng., 4(11), pp. 1143–1152. [CrossRef]
Zhang, X. and Vu-Quoc, L., 2002, “Modeling the Dependence of the Coefficient of Restitution on the Impact Velocity in Elasto-Plastic Collisions,” Int. J. Impact Eng., 27, pp. 317–341. [CrossRef]
Wu, C., Li, L., and Thornton, C., 2003, “Rebound Behavior of Spheres for Plastic Impacts,” Int. J. Impact Eng., 28, pp. 929–946. [CrossRef]
Jackson, R. L., Green, I., and Marghitu, D. B., 2010, “Predicting the Coefficient of Restitution of Impacting Elastic-Perfectly Plastic Spheres,” Nonlinear Dyn., 60, pp. 217–229. [CrossRef]
Hunt, K. H. and Crossley, F. R. E., 1975, “Coefficient of Restitution Interpreted as Damping in Vibroimpact,” ASME J. Appl. Mech., 42, pp. 440–445. [CrossRef]
Khulief, Y. A. and Shabana, A. A, 1987, “A Continuous Force Model for the Impact Analysis of Flexible Multibody Systems,” Mech. Mach. Theory, 22, pp. 213–224. [CrossRef]
Lankarani, H. M. and Nikravesh, P. E., 1994, “Continuous Contact Force Models for Impact Analysis in Multi-Body Systems,” Nonlinear Dyn., 5, pp. 193–207.
Yigit, A. S., Christoforou, A. P., and Majeed, A. M., 2011, “A Nonlinear Visco-Elastoplastic Impact Model and the Coefficient of Restitution,” Nonlinear Dyn., 66, pp. 509–521. [CrossRef]
Christoforou, A. P. and Yigit, A. S., 1998, “Characterization of Impact in Composite Plates,” Compos. Struct., 43, pp. 15–24. [CrossRef]
Christoforou, A. P. and Yigit, A. S., 1998, “Effect of Flexibility on Low-Velocity Impact Response,” J. Sound Vibr., 217(3), pp. 563–578. [CrossRef]
Choi, I. H. and Lim, C. H., 2004, “Low-Velocity Impact Analysis of Composite Laminates Using Linearized Contact Law,” Compos. Struct., 66, pp. 125–132. [CrossRef]
Apetre, N. A., Sankara, B. V., and Ambur, D. R, 2006, “Low-Velocity Impact Response of Sandwich Beams With Functionally Graded Core,” Int. J. Solids Struct., 43, pp. 2479–2496. [CrossRef]
Pashah, S., Massenzio, M., and Jacquelin, E., 2008, “Prediction of Structural Response for Low Velocity Impact,” Int. J. of Impact Eng., 35, pp. 119–132. [CrossRef]
Doyle, J. F., 1987, “Experimentally Determining the Contact Force During the Transverse Impact of an Orthotropic Plate,” J. Sound Vibr., 118(3), pp. 441–448. [CrossRef]
Bucinell, R. B., Nuismer, R. J., and Koury, J. L., 1991, “Response of Composite Plates to Quasi-Static Impact Events,” Composite Materials: Fatigue and Fracture(Third Volume), ASTM Spec. Tech. Publ., 1110, pp. 528–549.
Swanson, S. R., 1992, “Limits of Quasi-Static Solutions in Impact of Composite Structures,” Composites Eng., 2, pp. 261–267. [CrossRef]
Olsson, R., 1992, “Impact Response of Orthotropic Composite Plates Predicted from a One-Parameter Differential Equation,” AIAA J., 30, pp. 1587–1596. [CrossRef]
Yigit, A. S. and Christoforou, A. P., 2007, “Limits of Asymptotic Solutions in Low-Velocity Impact of Composite Plates,” Compos. Struct., 81(4), pp. 568–574. [CrossRef]
Christoforou, A. P. and Yigit, A. S., 2009, “Scaling of Low-Velocity Impact Response in Composite Structures,” Compos. Struct., 91, pp. 358–365. [CrossRef]
Christoforou, A. P., Yigit, A. S., Cantwell, W. J., and Yang, F., 2010, “Impact Response Characterization in Composite Plates – Experimental Validation,” Appl. Compos. Mater., 17(5), pp. 463–472. [CrossRef]
Meirovitch, L., 1980, Computational Methods in Structural Dynamics, Sijthoff & Noordhoff, Alphen aan den Rijn, The Netherlands.
Majeed, A. M., Yigit, A. S., and Christoforou, A. P., 2011, “Modeling and Analysis of Elastoplastic Impacts on Supported Composites,” Key Eng. Mater., 471–472, pp. 367–372. [CrossRef]
Timoshenko, S. P. and Woinowsky-Krieger, S., 1959, Theory of Plates and Shells, 2nd ed., McGraw-Hill, Singapore.


Grahic Jump Location
Fig. 1

Structures used in simulations

Grahic Jump Location
Fig. 2

Characterization diagram showing various impact situations on different structures

Grahic Jump Location
Fig. 4

Quasi-static impact on a simply-supported plate: λ = 0.2, and ζ = 7.6

Grahic Jump Location
Fig. 5

Force-indentation curves from quasi-static impact on a simply-supported plate

Grahic Jump Location
Fig. 6

Transition region (dynamic) impact on a simply-supported plate: λ = 0.2, and ζ = 0.76

Grahic Jump Location
Fig. 7

Force-indentation curves from dynamic impact on a simply-supported plate

Grahic Jump Location
Fig. 8

Quasi-static impact on simply-supported and scaled clamped plates: λ = 0.2, and ζ = 7.6

Grahic Jump Location
Fig. 9

Transition impact on simply-supported and scaled clamped plates: λ = 0.2, and ζ = 0.76

Grahic Jump Location
Fig. 10

Quasi-static impact on a stiffened plate: λ = 0.5, and ζ = 8.64

Grahic Jump Location
Fig. 11

Transition impact on a stiffened plate: λ = 0.5, and ζ = 0.86

Grahic Jump Location
Fig. 12

Small mass impact on a flexible cylindrical panel: λ = 0.05, and ζ = 0.42



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In