Impact mechanics and high-energy absorbing materials: Review

Journal of Aerospace Engineering

Volumn 21, Issue 4, 2008, Pages 235-248

  Qiao, Pizhong ^a   Yang, Mijia ^b   Bobaru, Florin ^c  

^a Washington State University   (United States)

^b UNIVERSITY OF TEXAS AT SAN ANTONIO   (United States)

^c UNIVERSITY OF NEBRASKA LINCOLN   (United States)

Author keywords

Blasting; Composite materials; Damage; Dynamics; Energy absorption; Finite difference method; Finite element method; Honeycomb structures; Impact; Nonlinear methods; Sandwich structures; Shock waves; Strain rate

Indexed keywords

BLASTING; COMPOSITE MATERIALS; CONSTITUTIVE MODELLING; DAMAGE; DYNAMICS; ENERGY-ABSORBING MATERIALS; EXPERIMENTAL EVALUATIONS; FINITE DIFFERENCE METHOD; FINITE DIFFERENCING; FINITE ELEMENTS; FUTURE RESEARCH; HIGH ENERGIES; HONEYCOMB STRUCTURES; IMPACT; IMPACT DAMAGES; IMPACT MECHANICS; IMPACT PROBLEMS; MAGNETO-RHEOLOGICAL FLUIDS; MESH-FREE METHODS; METAL FOAMS; MODELING AND SIMULATION; NEW DESIGN; NON-LOCAL MODELS; NONLINEAR METHODS; NUMERICAL SIMULATIONS; PERIDYNAMICS; PLASTIC WAVE PROPAGATION; POROUS SHAPE-MEMORY ALLOYS; RIGID-BODY DYNAMICS; SANDWICH COMPOSITES; SANDWICH STRUCTURES; SHOCK WAVES; TRUSS STRUCTURES;

AEROSPACE ENGINEERING; ALLOYS; CARBON FIBER REINFORCED PLASTICS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; ENERGY ABSORPTION; ENGINEERING RESEARCH; FINITE ELEMENT METHOD; FOAMS; HIGH ENERGY PHYSICS; MECHANICS; MESH GENERATION; METALLIC COMPOUNDS; METALLIC MATRIX COMPOSITES; METALS; POLYMER MATRIX COMPOSITES; SPEED; STRAIN RATE; TECHNOLOGY;

HYBRID MATERIALS;

EID: 52949091895     PISSN: 08931321     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)0893-1321(2008)21:4(235)     Document Type: Article

References (151)

1. Ahmadian, M., Appleton, R., and Norris, J. (2002). " An analytical study of fire out of battery using magnetorheological dampers.." Shock Vib., 9 (3), 129-142.
2. Ahmadian, M., and Poynor, J. C. (2001). " An evaluation of magneto-rheological dampers for controlling gun recoil dynamics.." Shock Vib., 8 (3-4), 141-146.
3. Ambur, D. R., Jaunky, N., Lawson, R. E., and Keight, N. F., Jr. (2001). " Numerical simulations for high-energy impact of thin plates.." Int. J. Impact Eng., 25 (7), 683-702.
4. Andrews, E. W., and Kim, K.-S. (1998). " Threshold conditions for dynamic fragmentation of ceramic particles.." Mech. Mater., 29 (3-4), 161-180.
5. Balk, A. M., Cherkaev, A. V., and Slepyan, L. I. (2001). " Dynamics of chains with non-monotone stress-strain relations. I. Model and numerical experiments.." J. Mech. Phys. Solids, 49 (1), 131-148.
6. Banerjee, B., Guilkey, J. E., Harman, T. B., Schmidt, J. A., and McMurty, P. A. (2005). " Simulation of impact and fragmentation with material point method.." Proc., 11th Int. Conf. on Fracture, International Congress on Fracture (ICF), Turin, Italy.
7. Barenblatt, G. I. (1962). " The mathematical theory of equilibrium of cracks in brittle fracture.." Adv. Appl. Mech., 7 (1), 55-129.
8. Bazant, Z. P. (1991). " Why continuum damage is nonlocal: Micromechanics arguments.." J. Eng. Mech., 117 (5), 1070-1087.
9. Bazant, Z. P., and Jirasek, M. (2002). " Nonlocal integral formulations of plasticity and damage: Survey of progress.." J. Eng. Mech., 128 (11), 1119-1149.
10. Bazant, Z. P., and Lin, F.-B. (1988). " Nonlocal yield-limit degradation.." Int. J. Numer. Methods Eng., 26 (8), 1805-1823.
11. Belytschko, T., Liu, W. K., and Moran, B. (2000). Nonlinear finite-elements for continua and structures, Wiley, New York.
12. Belytschko, T., Lu, Y. Y., and Gu, L. (1994). " Element-free Galerkin methods.." Int. J. Numer. Methods Eng., 37 (2), 229-256.
13. Belytschko, T., Lu, Y. Y., Gu, L., and Tabbara, M. (1995). " Element-free Galerkin methods for static and dynamic fracture.." Int. J. Solids Struct., 32 (17-18), 2547-2570.
14. Belytschko, T., and Tabbara, M. (1996). " Dynamic fracture using element-free Galerkin methods.." Int. J. Numer. Methods Eng., 39 (6), 923-938.
15. Binienda, W. K. (2004). " High energy impact of composite structures-Ballistic experiments and explicit finite-element analysis.." Rep., submitted to NASA Glenn Research Center, The Univ. of Akron, Akron, Ohio.
16. Bobaru, F. (2007). " Influence of van der Waals forces on increasing the strength and toughness in dynamic fracture of nanofiber networks: A peridynamic approach.." Modell. Simul. Mater. Sci. Eng., 15 (5), 397-417.
17. Bobaru, F., Yang, M., Alves, L. F., Silling, S. A., Askari, E., and Xu, J. (2008). " Convergence, adaptive refinement, and scaling in 1D peridynamics.." Int. J. Numer. Methods Eng., in press.
18. Bordonaro, C. M. (1995). " Rate dependent mechanical behavior of high strength plastics: Experiment and modeling.." Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, NY.
19. Brach, R. M. (1991). Mechanical impact dynamics: Rigid body collisions, Wiley, New York.
20. Camacho, G. T., and Ortiz, M. (1997). " Adaptive Lagrangian modelling of ballistic penetration of metallic targets.." Comput. Meth. Appl. Math., 142 (3-4), 269-301.
21. Caprino, G., and Teti, R. (1994). " Impact and post impact behavior of foam core sandwich structures.." Compos. Struct., 29 (1), 47-55.
22. Chang, W. J., and Pan, J. (1997). " Effects of yield surface shape and round-off vertex on crack-tip fields for pressure-sensitive materials.." Int. J. Solids Struct., 34 (25), 3291-3320.
23. Chen, Y., Lee, J., and Eskandarian, A. (2004). " Atomistic viewpoint of the applicability of micro-continuum theories.." Int. J. Solids Struct., 41 (8), 2085-2097.
24. Cheng, J., and Binienda, W. K. (2006). " Simulation of soft projectiles impacting composite targets using an arbitrary Lagrangian-Eulerian Formulation.." J. Aircr., 43 (6), 1726-1731.
25. Cheng, J., and Binienda, W. K. (2008). " Simplified braiding through integration points model for triaxially braided composites.." J. Aerosp. Eng., 21 (3), 119-131.
26. Cheng, M., McCauley, J., and Hemker, K. (2003). " Shock-induced localized amorphization in Boron Carbide.." Science, 299 (7), 1563-1566.
27. Cherkaev, A., and Slepyan, L. (1995). " Waiting element structures and stability under extension.." Int. J. Damage Mech., 4 (1), 58-82.
28. Conrad, M. M., and Sayir, M. B. (1998). " Optical methods in impact and vibrations.." 〈 www.ifm.mavt.ethz.ch/research/contents.html 〉 or 〈 http://www.zfm.ethz.ch/e/abo/adr/index.htm 〉.
29. Cox, B., and Yang, Q. D. (2006). " In quest of virtual test for structural composites.." Science, 314 (5802), 1102-1107.
30. Dancila, D. S., and Armanios, E. A. (2002). " Energy-dissipating composite members with progressive failure: Concept development and analytical modeling.." AIAA J., 40 (10), 2096-2104.
31. Daniel, I. M., Hsiao, H. M., and Cordes, R. D. (1995). " Dynamic response of carbon/epoxy composites.." High strain rate effects on polymer, metal and ceramic matrix composites and other advanced materials, AD-Vol. 48, Y. D. S. Rajapakse, and, J. R. Vinson, eds., American Society of Mechanical Engineers (ASME), Washington, D.C., 167-177.
32. Davalos, J. F., Qiao, P., Xu, X. F., Robinson, J., and Barth, K. E. (2001). " Modeling and characterization of fiber-reinforced plastic honeycomb sandwich panels for highway bridge applications.." Compos. Struct., 52 (3-4), 441-452.
33. Davies, G. A. O., Hitchings, D., and Wang, J. (1995). " Prediction of thresholds of glass fiber reinforced laminates.." Compos. Struct., 31 (1), 185-193.
34. Dobyns, A. L., and Porter, T. R. (1981). " A study of the structural integrity of graphite composite structure subjected to a low velocity impact.." Polym. Eng. Sci., 21 (8), 493-498.
35. Dugdale, D. S. (1960). " Yielding of steel sheets containing slits.." J. Mech. Phys. Solids, 8 (1), 100-108.
36. El Wahed, A. K., Sproston, J. L., and Schleyer, G. K. (2002). " Electrorheological and magnetorheological fluids in blast resistant design applications.." Mater. Des., 23 (4), 391-404.
37. Eringen, A. C. (1981). " On nonlocal plasticity.." Int. J. Eng. Sci., 19 (12), 1461-1474.
38. Erofeyev, V. I. (2003). Wave processes in solids with microstructure, World Scientific, Singapore.
39. Evans, A. G., Hutchinson, J. W., Fleck, N. A., Ashby, M. F., and Wadley, H. N. G. (2001). " The topological design of multifunctional cellular metals.." Prog. Mater. Sci., 46 (3-4), 309-327.
40. Fahrenthold, E. P., and Horban, B. A. (2001). " An improved hybrid particle-element method for hypervelocity impact simulation.." Int. J. Impact Eng., 26 (1-10), 169-178.
41. Fleck, N. A., and Deshpande, V. S. (2004). " The resistance of clamped sandwich beams to shock loading.." J. Appl. Mech., 71 (3), 386-401.
42. Gao, H., and Huang, Y. (2001). " Taylor-based nonlocal theory of plasticity.." Int. J. Solids Struct., 38 (42-43), 2615-2637.
43. Gilat, A., Goldberg, R. K., Roberts, and G. (2005). " Strain rate sensitivity of epoxy resin in tensile and shear loading.." NASA Tech. Memo., 2005-213595, NASA Glenn, Cleveland, Ohio.
44. Gingold, R. A., and Monaghan, J. J. (1977). " Smoothed particle hydrodynamics-Theory and application to non-spherical stars.." Mon. Not. R. Astron. Soc., 181 (2), 375-389.
45. Goldberg, R. K., Roberts, G. D., and Gilat, A. (2005). " Implementation of an associative flow rule including hydrostatic stress effects into the high strain rate deformation analysis of polymer matrix composites.." J. Aerosp. Eng., 18 (1), 18-27.
46. Goldberg, R. K., Roberts, G. D., Littell, J. D., and Binienda, W. K. (2008). " Approximation of nonlinear unloading effects in the strain rate dependent deformation analysis of polymer matrix materials utilizing a state variable approach.." J. Aerosp. Eng., 21 (3), 119-131.
47. Goldsmith, W. (1960). Impact, Arnold, London.
48. Goldsmith, W., and Sackman, J. L. (1992). " An experimental study of energy absorption in impact on sandwich plates.." Int. J. Impact Eng., 12 (2), 241-262.
49. Guruprasad, S., and Mukherjee, A. (2000). " Layered sacrificial claddings under blast loading, I: Analytical studies.." Int. J. Impact Eng., 24, 957-973.
50. Ha, K., and Dancila, D. S. (2003). " Energy-dissipating snap-resistant tether.." AIAA 41st Aerospace Sciences Meeting and Exhibit.
51. Hallquist, J. O. (1993). LS-DYNA3D theoretical manual, Livermore Software Technology Corporation, Livermore, Calif., 135-180.
52. Hallquist, J. O., Goudreau, G. L., and Bension, D. J. (1985). " Sliding interfaces with contact-impact in large-scale Lagrangian computations.." Comput. Methods Appl. Mech. Eng., 51 (1-3), 107-137.
53. Hamza, K., and Saitou, K. (2005). " Design optimization of vehicle structures for crashworthiness using equivalent mechanism approximations.." J. Mech. Des., 127 (3), 485-492.
54. Hexcel Corporation. (1964). " Design data for the preliminary selection of honeycomb energy absorption systems.." Rep. No. TSB 122, Stamford, Conn.
55. Hexcel Corporation. (1968). " Mechanical properties of hexcel honeycomb materials.." Rep. No. TSB 120, Stamford, Conn.
56. Hogg, P. J. (2006). " Composites in armor.." Science, 314 (5802), 1100-1101.
57. Jamjian, M., Sackman, J. L., and Goldsmith, W. (1994). " Responses of an infinite plate on a honeycomb foundation to a rigid cylindrical impactor.." Int. J. Impact Eng., 15 (3), 183-200.
58. Johnson, G. R., and Stryk, R. A. (2003). " Conversion of 3D distorted elements into meshless particles during dynamic deformation.." Int. J. Impact Eng., 28 (9), 947-966.
59. Johnson, G. R., Stryk, R. A., Beissel, S. R., and Holmquist, T. J. (2001). " Conversion of finite-elements into meshless particles for penetration computations involving ceramic targets.." Proc., 12th APS Topical Conf. on Shock Compression of Condensed Matter, American Physical Society, College Park, Md., 1287-1290.
60. Johnson, K. L. (1985). Contact mechanics, Cambridge University Press, Cambridge, UK.
61. Jolly, M. R. (2000). " Properties and applications of magnetorheological fluids.." Mater. Res. Soc. Symp. Proc., MRS, Warrendale, Pa., 604, 167-176.
62. Jones, S. E., Maudlin, A. E., and Foster, J. C. (1997). " An engineering analysis of plastic wave propagation in the Taylor test.." Int. J. Impact Eng., 19 (2), 95-106.
63. Kang, Y. S., Kikuchi, K., and Kawasaki, A. (2001). " Fabrication and characterization of functionally graded NiAl2O3Ni compliant pad.." Proc. ISSPS, Singapore.
64. Kolsky, H. (1963). Stresses waves in solids, Dover, New York.
65. Kunin, I. A. (1982). Elastic media with microstructure, Vols. I and II, Springer, Berlin.
66. Lee, D. Y., Choi, Y. T., and Wereley, M. N. (2002). " Performance analysis of ER/MR impact damper systems using Herschel-Bulkley model.." J. Intell. Mater. Syst. Struct., 13 (7-8), 525-531.
67. Lee, M., and Yoo, Y. H. (2001). " Analysis of ceramic/metal armour system.." Int. J. Impact Eng., 25 (9), 819-829.
68. Lee, Y. S., Wetzel, E. D., and Wagner, N. J. (2003). " The ballistic impact characteristics of Kevlar woven fabrics impregnated with a colloidal shear thickening fluid.." J. Mater. Sci., 38 (13), 2825-2833.
69. Li, F. Z., and Pan, J. (1990). " Plane-stress crack-tip fields for pressure-sensitive dilatant materials.." J. Appl. Mech., 57 (1), 40-49.
70. Libersky, L. D., and Petschek, A. G. (1991). " Smoothed particle hydrodynamics with strength of materials.." Proc., Next Free-Lagrange Conf., W. P. Crowley, M. J. Fritts, H. E. Trease, eds., Springer, Berlin, 248-257.
71. Lim, T. S., Lee, C. S., and Lee, D. G. (2004). " Failure modes of foam core sandwich beams under static and impact loads.." J. Compos. Mater., 38 (18), 1639-1662.
72. Littell, J. D., Ruggeri, C. R., Goldberg, R. K., Roberts, G. D., Arnold, W. A., and Binienda, W. K. (2008). " Measurement of epoxy resin tension, compression, shear stress-strain curves over a wide range of strain rates and temperatures.." J. Aerosp. Eng., 21 (3), 162-173.
73. Liu, W. K., Li, S. F., and Belytschko, T. (1997). " Moving least square reproducing kernel method. 1: Methodology and convergence.." Comput. Methods Appl. Mech. Eng., 143 (1-2), 113-154.
74. Lopez-Puente, J., Arias, A., Zaera, R., and Navarro, C. (2005). " The effect of the thickness of the adhesive layer on the ballistic limit of ceramic/metal armours. An experimental and numerical study.." Int. J. Impact Eng., 32, 321-336.
75. Lucy, L. B. (1977). " Numerical approach to testing of fission hypothesis.." Astron. J., 82 (12), 1013-1024.
76. Magee, C. L., and Thornton, P. H. (1978). " Design consideration in energy absorption by structural collapse.." SAE Rep. No. 78-434, Society of Automotive Engineers, Warrendale, Pa.
77. Matemilola, S. A., and Strong, W. J. (1995). " Impact induced dynamic deformation and stresses in CFRP composite laminates.." Composites Eng., 5 (2), 211-222.
78. McFarland, R. K. (1963). " Hexagonal cell structures under postbuckling axial load.." AIAA J., 1 (6), 1380-1385.
79. Meyers, M. A. (1994). Dynamic behavior of materials, Wiley, New York.
80. Miyoshi, T., (1999). " Enhancement of energy absorption in closed-cell aluminum by the modification of cellular structures.." J. Phys.: Condens. Matter, 41 (10), 1055-1060.
81. Molinari, A., and Ravichandran, G. (2004). " Fundamental structure of steady plastic shock waves in metals.." J. Appl. Phys., 95 (4), 1718-1732.
82. Mota, A., Klug, W. S., Ortiz, M., and Pandolfi, A. (2003). " Finite-element simulation of firearm injury to the human cranium.." Comput. Mech., 31 (1-2), 115-121.
83. Needleman, A. (1987). " A continuum model for void nucleation by inclusion debonding.." J. Appl. Mech., 54 (3), 525-531.
84. Nemat-Nasser, S., Kang, W. J., McGee, J. D., Guo, W.-G., and Isaacs, J. B. (2007). " Experimental investigation of energy-absorption characteristics of components of sandwich structures.." Int. J. Impact Eng., 34 (6), 1119-1146.
85. Nesterenko, V. F. (2001). Dynamics of heterogeneous materials, Springer, New York.
86. Ortiz, M., and Pandolfi, A. (1999). " Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis.." Int. J. Numer. Methods Eng., 44 (9), 1267-1282.
87. Pandolfi, A., Krysl, P., and Ortiz, M. (1999). " Finite-element simulation of ring expansion and fragmentation, The capturing of length and time scales through cohesive models of fracture.." Int. J. Fract., 95 (1-4), 279-297.
88. Park, Y. K., and Fahrenthold, E. P. (2005). " A kernel free particle-finite-element method for hypervelocity impact simulation.." Int. J. Numer. Methods Eng., 63 (5), 737-759.
89. Parks, M. L., Lehoucq, R. B., Plimpton, S. J., and Silling, S. A. (2008). " Implementing peridynamics within a molecular dynamics code.." Comput. Phys. Commun., in press (available online June 26, 2008).
90. Pedersen, C. B. W. (2002). " Topology optimization of energy absorbing frames.." WCCM V, 5th World Congress on Computational Mechanics, H. A. Mang, F. G. Rammerstorfer, and, J. Eberhardsteiner, eds., Vienna, Austria.
91. Pedersen, C. B. W. (2003). " Topology optimization of 2D-frame structures with path-dependent response.." Int. J. Numer. Methods Eng., 57 (10), 1471-1501.
92. Polizzotto, C., Borino, G., and Fuschi, P. (1998). " A thermodynamic consistent formulation of nonlocal and gradient plasticity.." Mech. Res. Commun., 25 (1), 75-82.
93. Pouget, J. (1992). " Stability of nonlinear structures in a lattice model for phase transformations in alloys.." Phys. Rev. B, 46 (17), 10554-10562.
94. Pouget, J. (1993). " Lattice dynamics and stability of modulated-strain structures for elastic phase transitions in alloys.." Phys. Rev. B, 48 (2), 864-875.
95. Qiao, P., and Bibienda, W. K. (2008). " Impact mechanics of composite materials for aerospace application.." J. Aerosp. Eng., 21 (3), 117-118.
96. Qiao, P., and Wang, J. L. (2005). " Mechanics of composite sinusoidal honeycomb cores.." J. Aerosp. Eng., 18 (1), 42-50.
97. Qiao, P., and Yang, M. J. (2007). " Impact analysis of fiber reinforced polymer honeycomb composite sandwich beams.." Composites, Part B, 38 (5-6), 739-750.
98. Qiao, P., Yang, M. J., and Mosallam, A. S. (2004). " Impact analysis of I-Lam sandwich system for over-height collision protection of highway bridges.." Eng. Struct., 26 (7), 1003-1012.
99. Rathbun, H. J., (2006). " Performance of metallic honeycomb-core sandwich beams under shock loading.." Int. J. Solids Struct., 43 (6), 1746-1763.
100. Reid, S. R., and Zhou, G. (2000). Impact behavior of fiber reinforced composite materials and structures, CRC Press, Boca Raton, Fla.
101. Repetto, E. A., Radovitzky, R., and Ortiz, M. (2000). " Finite-element simulation of dynamic fracture and fragmentation of glass rods.." Comput. Methods Appl. Mech. Eng., 183 (1-2), 3-14.
102. Rogula, D. (1982). Nonlocal theory of material media, Springer, Berlin.
103. Sarva, S., Nemat-Nasser, S., McGee, J., and Isaacs, J. (2007). " The effect of thin membrane restraint on the ballistic performance of armor grade ceramic tiles.." Int. J. Impact Eng., 34 (2), 277-302.
104. Shim, V. W., Tan, V. B. C., and Tay, T. E. (1995). " Modeling deformation and damage characteristics of woven fabric under small projectile impact.." Int. J. Impact Eng., 16 (14), 585-605.
105. Shipsha, A. Hallstrom, S., and Zenkert, D. (2003). " Failure mechanisms and modeling of impact damage in sandwich beams-A 2D approach. I: Experimental investigation.." J. Sandwich Struct. Mater., 5 (1), 7-32.
106. Shivarama, R., and Fahrenthold, E. P. (2004). " An ellipsoidal particle-finite-element method for hypervelocity impact simulation.." Int. J. Numer. Methods Eng., 59 (5), 737-753.
107. Silling, S. A. (2000). " Reformulation of elasticity theory for discontinuities and long-range forces.." J. Mech. Phys. Solids, 48 (1), 175-209.
108. Silling, S. A., and Askari, E. (2005). " A meshfree method based on the peridynamic model of solid mechanics.." Comput. Struct., 83 (17-18), 1526-1535.
109. Silling, S. A., and Bobaru, F. (2005). " Peridynamic modeling of membranes and fibers.." Int. J. Non-Lin. Mech., 40 (2-3), 395-409.
110. Silling, S. A., Epton, M., Weckner, O., Xu, J., and Askai, E. (2007). " Peridynamic states and constitutive modeling.." J. Elast., 88 (2), 151-184.
111. Silling, S. A., Zimmermann, M., and Abeyaratne, R. (2003). " Deformation of a peridynamic Bar.." J. Elast., 73 (1-3), 173-190.
112. Slepyan, L. I., and Ayzenberg-Stepanenko, M. V. (2004). " Localized transition waves in bistable-bond lattices.." J. Mech. Phys. Solids, 52 (7), 1447-1479.
113. Soto, C. A. (2004). " Structural topology optimization for crashworthiness.." Int. J. Crashworthiness, 9 (3), 277-283.
114. Sulsky, D., Chen, Z., and Schreyer, H. L. (1994). " A particle method for history dependent materials.." Comput. Methods Appl. Mech. Eng., 118 (1-2), 179-196.
115. Sulsky, D., Zhou, S., and Schreyer, H. L. (1995). " Application of a particle-in-cell method to solid mechanics.." Comput. Phys. Commun., 87 (1-2), 236-252.
116. Svedberg, T. (1996). " A thermodynamically consistent theory of gradient-regularized plasticity coupled to damage.." Licentiate thesis, Chalmers Univ. of Technology, Chalmers, Sweden.
117. Swegle, J. W., Hicks, D. L., and Attaway, S. W. (1995). " Smoothed particle hydrodynamics stability analysis.." J. Comput. Phys., 116 (1), 123-134.
118. Taylor, W. J., and Vinson, J. R. (1990). " Modeling ballistic impact into flexible materials.." AIAA J., 28 (12), 2098-2103.
119. Thomsen, O. T. (1995). " Theoretical and experimental investigation of local bending effects in sandwich plates.." Compos. Struct., 30 (1), 85-101.
120. Tsai, C. Z., Wu, E., and Luo, B. H. (1998). " Forward and inverse analysis for impact on sandwich panels.." AIAA J., 36 (11), 2130-2136.
121. Turk, M. H., and Hoo-Fatt, M. S. (1999). " Localized damage response of composite sandwich plates.." Composites, Part B, 30 (2), 157-165.
122. Vaziri, A., and Hutchinson, J. W. (2007). " Metal sandwich plates subject to intense air shocks.." Int. J. Solids Struct., 44 (6), 2021-2035.
123. Vaziri, A., Xue, Z., and Hutchinson, J. W. (2006). " Metal sandwich plates with polymeric foam-filled cores.." J. Mech. Mater. Struct., 1 (1), 95-128.
124. Wang, F. J., Wang, L. P., Cheng, J. G., and Yao, Z. H. (2007). " Contact algorithm in explicit transient analysis using finite-element method.." Finite Elem. Anal. Design, 43 (6-7), 580-587.
125. Weckner, O., and Abeyaratne, R. (2005). " The effect of long range forces on the dynamics of a bar.." J. Mech. Phys. Solids, 53 (3), 705-728.
126. Weckner, O., and Emmrich, E. (2005). " Numerical simulation of the dynamics of a nonlocal inhomogeneous, infinite bar.." J. Comput. Appl. Mech., 6 (2), 311-319.
127. Wierzbicki, T. (1983). " Crushing analysis of metal honeycombs.." Int. J. Impact Eng., 1 (1), 157-174.
128. Wierzbicki, T., Alvarez, A., and Hoo Fatt, M. S. (1995). " Impact energy absorption of sandwich plates with crushable core.." AMD-205, Proc., 1995 Joint ASME Applied Mechanics & Materials Summer Meeting, American Society of Mechanical Engineers (ASME), Washington, D.C.
129. Wriggers, P., Vu Van, T., and Stein, E. (1990). " Finite-element formulation of large deformation impact-contact problems with friction.." Comput. Struct., 37 (3), 319-331.
130. Xie, W. (2005). " Peridynamic flux-corrected transport algorithm for shock wave studies.." Master thesis, The Univ. of Nebraska-Lincoln, Lincoln, Neb.
131. Xu, J., Askari, A., Weckner, O., and Silling, S. A. (2008) " Peridynamic analysis of impact damage in composite laminates.. " J. Aerosp. Eng., 21 (3), 174-186.
132. Xu, X. F., Qaio, P., and Davalos, J. F. (2001). " Transverse sheara stiffness of composite honeycomb core with general configuration.." J. Eng. Mech., 127 (11), 1144-1151.
133. Xue, Z., and Hutchinson, J. W. (2004). " A comparative study of impulse-resistant metal sandwich plates.." Int. J. Impact Eng., 30, 1283-1305.
134. Yang, G. Q., Spencer, B. F. Jr., Jung, H.-J., and Carlson, J. D. (2004). " Dynamic modeling of large-scale magnetorheological damper systems for civil engineering applications.." J. Eng. Mech., 130 (9), 1107-1114.
135. Yang, M. J. (2006). " Impact mechanics of elastic and elastic-plastic sandwich structures.." Ph.D. dissertation, The Univ. of Akron, Akron, Ohio.
136. Yang, M. J., and Qiao, P. (2005a). " Higher-order impact modeling of sandwich beams with flexible core.." Int. J. Solids Struct., 42 (20), 5460-5490.
137. Yang, M. J., and Qiao, P. (2005b). " Nonlinear impact analysis of fully-backed composite sandwich structures.." Compos. Sci. Technol., 65 (3-4), 551-562.
138. Yang, M. J., and Qiao, P. (2007). " Impact and damage prediction of sandwich beams with flexible core considering arbitrary boundary effects.." J. Sand. Struct. Mater., 9 (5), 411-444.
139. Yang, M. J., and Qiao, P. (2008a). " Quasistatic crushing behavior of aluminum honeycomb materials.." J. Sandwich Struc. Mater., 10 (2), 133-160.
140. Yang, M. J., and Qiao, P. (2008b). " Quasistatic indentation behavior of honeycomb sandwich materials and its application in impact simulations.." J. Aerosp. Eng., 21 (4), 266-234.
141. Zhang, Y. G., and Ballmann, J. (1996). " An explicit finite-difference procedure for contact-impact analysis of crack edges.." Arch. Appl. Mech., 66 (7), 493-502.
142. Zhao, Y., Taya, M., and Izui, H. (2006). " Study on energy absorbing composite structure made of concentric NiTi spring and porous NiTi.." Int. J. Solids Struct., 43 (9), 2497-2512.
143. Zhao, Y., Taya, M., Kang, Y. S., and Kawasaki, A. (2005). " Compression behavior of porous NiTi shape memory alloy.." Acta Mater., 53 (2), 337-343.
144. Zheng, X., and Binienda, W. K. (2008). " Rate dependent shell element composite material model implementation in LS-DYNA.." J. Aerosp. Eng., 21 (3), 140-151.
145. Zhong, Z. H. (1993). Finite-element procedures for contact-impact problems, Oxford University Press, Oxford, U.K..
146. Zhou, F. H., Molinari, J.-F., and Armes, K. T. (2005). " A cohesive model based fragmentation analysis: Effects of strain rate and initial defects distribution.." Int. J. Solids Struct., 42 (18-19), 5181-5207.
147. Zhu, L. F., Chattopadhyay, A., and Goldberg, R. K. (2006). " A 3D micromechanics model for strain rate dependent inelastic polymer matrix composites.." 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conf., Newport, R.I.
148. Zhu, L. F., Chattopadhyay, A., and Goldberg, R. K. (2008). " Failure model for rate dependent polymer matrix composite laminates under high velocity impact.." J. Aerosp. Eng., 21 (3), 132-139.
149. Zukas, J. A. (2004). Introduction to hydrocodes, Elsevier, New York.
150. Zukas, J. A., Nicholas, T., Swift, H. F., Greszczuk, L. B., and Curran, D. R. (1992). Impact dynamics, Krieger, Malabar, Fla.
151. Zukas, J. A., and Scheffler, D. R. (2001). " Impact effects in multilayered plates.." Int. J. Solids Struct., 38, 3321-3328.