Applied Plasticity pp 538-649 | Cite as
Dynamic Plasticity
Abstract
In this chapter we shall be concerned with the class of problems in which the plastic deformation is so rapid that the inertia effects cannot be disregarded. Problems of dynamic plasticity arise in the high-velocity forming of metals, penetration of high-speed projectiles into fixed targets, enlargement of cavities by underground explosion, and the design of crash barriers related to collisions, to name only a few. The rate of loading and the size of the components are usually such that the deformation process can be described in terms of the propagation of elastic/plastic waves. However, simplified theories which disregard the wave propagation phenomenon are generally capable of providing useful information for practical purposes. In the case of structural members subjected to impact loading, the mode of plastic deformation can be most conveniently represented by the existence of discrete yield hinges that rapidly move away from the point of loading. The concept of moving yield hinges is a useful device for the dynamic analysis of structures.
Keywords
Wave Front Circular Plate Plastic Hinge Strain Rate Effect Central DeflectionPreview
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References
- Abrahamson, G.R. and Goodier, J.N. (1966), Dynamic Flexural Buckling of Thin Rods Within an Axial Plastic Compressive Wave, J. Appl. Mech, 33, 241.CrossRefGoogle Scholar
- Abramowicz, W. and Jones, N. (1984), Dynamic Axial Crushing of Circular Tubes, Int. J. Impact Engng., 2, 263.CrossRefGoogle Scholar
- Aizawa, T., Murata, M. and Suzuki, H. (1990), Electromagnetic Tube Bulging by the Direct Electrode Contact Method and the Solenoidal Coil Method, Proc. 3rd Int. Conf. Technol. Plasticity, Kyoto, Japan, p. 1593.Google Scholar
- Al-Hassani, S.T.S. and Johnson, W. (1969), The Dynamics of the Fragmentation Process for Spherical Bombs, Int. J. Mech. Sci., 11, 811.CrossRefGoogle Scholar
- Alter, B.E.K. and Curtis, C.W. (1956), The Effect of Strain Rate on the Propagation of a Plastic Strain Pulse Along a Lead Bar, J. Appl. Mech., 27, 1079.Google Scholar
- Appleby, E.J. (1964), The Dynamic Viscoplastic Expansion of a Cylindrical Tube, J. Appl. Mech., 31, 654.MathSciNetCrossRefGoogle Scholar
- Apsden, R.J. and Campbell, J.D. (1966), The Effect of Loading Rate on the Elastic-Plastic Flexure of Steel Beams, Proc. Roy. Soc. London Ser. A, 290, 266.CrossRefGoogle Scholar
- Backman, M.E. and Goldsmith, W. (1978), The Mechanics of Penetration of Projectiles into Targets, Int. J. Engng. Sci., 16, 1.CrossRefGoogle Scholar
- Baker, W.E. (1960), The Elastic-Plastic Response of Thin Spherical Shells to Internal Blast Loading, J. Appl. Mech., 27, 139.MathSciNetCrossRefMATHGoogle Scholar
- Balendra, R. and Travis, F.W. (1970), Static and Dynamic Blanking of Varying Hardness, Int. J. Mach. Tool. Des. Res., 10, 249.CrossRefGoogle Scholar
- Banerjee, A.K. and Malvern, L.E. (1975), Computation of Incremental Torsional Plastic Waves with Rate-Dependent Models, Int. J. Solids Struct., 11, 347.CrossRefGoogle Scholar
- Bell, J.F. (1960), The Propagation of Large Amplitude Waves in Annealed Aluminum, J. Appl. Phys., 31, 277.CrossRefGoogle Scholar
- Bell, J.F. (1968), The Physics of Large Deformation of Crystalline Solids, Springer Tracts in Natural Philosophy, Vol. 14, Springer-Verlag, Berlin.CrossRefGoogle Scholar
- Bell, J.F. (1973), The Experimental Foundations of Solid Mechanics, Handbuch der Physik, Vol. VI, Springer-Verlag, Berlin.Google Scholar
- Bell, J.F. and Stein, A. (1962), The Incremental Loading Wave in the Pre-stressed Plastic Field, J. Mecan., 1, 395.Google Scholar
- Bianchi, G. (1964), Some Experimental and Theoretical Studies on the Propagation of Longitudinal Plastic Waves in a Strain-Rate Dependent Material, in IUTAM Symp. Stress Waves in Anelastic Solids (eds., H. Kolsky and W. Prager), Springer-Verlag, Berlin, p. 101.CrossRefGoogle Scholar
- Bishop, J.F.W., Hill, R., and Mott, N.F. (1945), The Theory of Indentation and Hardness Tests, Proc. Roy. Phys. Soc, 57, 147.CrossRefGoogle Scholar
- Bleich, H.H. and Salvadori, N.G. (1953), Impulsive Motion of Elastic-Plastic Beams, Proc. ASCE, 79, 287.Google Scholar
- Bodner, S.R. and Symonds, P.S. (1962), Experimental and Theoretical Investigation of the Plastic Deformation of Cantilever Beams Subjected to Impulsive Loading, J. Appl. Mech.,29, 719.CrossRefGoogle Scholar
- Boyd, D.E. (1966), Dynamic Deformation of Circular Membranes, J. Engng. Mech. Div., Trans. ASCE, 92, 1.Google Scholar
- Calder, C.A. and Goldsmith, W. (1971), Plastic Deformaion and Perforation of Thin Plates Resulting from Projectile Impact, Int. J. Solids Struct., 7, 863.CrossRefGoogle Scholar
- Campbell, J.D. (1954), The Yield of Mild Steel Under Impact Loading, J. Mech. Phys. Solids, 3, 54.CrossRefGoogle Scholar
- Campbell, J.D. (1972), Dynamic Plasticity of Metals, Springer-Verlag, New York.MATHGoogle Scholar
- Campbell, J.D. (1973), Dynamic Plasticity: Macroscopic and Microscopic Aspects, Mater. Sci. Engng., 12, 3.CrossRefGoogle Scholar
- Chadwick, P. (1959), The Quasi-Static Expansion of a Spherical Cavity in Metals and Ideal Soils, Quart. J. Mech. Appl. Math., 12, 52.MathSciNetCrossRefMATHGoogle Scholar
- Chadwick, P., Cox, A.D., and Hopkins, H.G. (1964), Mechanics of Deep Underground Explosions, Phil. Trans. Roy. Soc, 256, 235.MathSciNetCrossRefGoogle Scholar
- Chakrabarty, J. (1998), Theory of Plasticity, 2nd Edition, McGraw-Hill, Singapore.Google Scholar
- Chon, C.T. and Symonds, PS. (1977), Large Dynamic Plastic Deflection of Plates by Mode Method, J. Engng. Mech. Div., Trans. ASCE, 103, 169.Google Scholar
- Chou, P.C. (1961), Perforation of Plates by High Speed Projectiles, in Developments in Mechanics (eds., J.E. Lay and L.E. Malvern), North-Holland, Amsterdam, p. 286.Google Scholar
- Clifton, R.J. (1966), An Analysis of Combined Longitudinal and Torsional Plastic Waves in a Thin-Walled Tube, Proc. 5th U.S. Nat. Congr. Appl. Mech., p. 456.Google Scholar
- Clifton, R.J. (1973), Plastic Waves: Theory and Experiment, in Mechanics Today (ed., Nemal-Nasser), Pergamon Press, New York, p. 102.Google Scholar
- Clifton, R.J. and Bodner, S.R. (1966), An Analysis of Longitudinal Elastic-Plastic Pulse Propagation, J. Appl. Mech., 33, 248.CrossRefGoogle Scholar
- Cline, C.B. and Jahsman, W.E. (1967), Response of a Rigid-Plastic Ring to Impulsive Loading, J. Appl. Mech., 34, 329.CrossRefGoogle Scholar
- Conroy, M.F. (1952), Plastic-Rigid Analysis of Long Beams Under Transverse Impact Loading, J. Appl. Mech., 19, 465.Google Scholar
- Conroy, M.F. (1956), Plastic Deformation of Semi-Infinite Beams Subject to Transverse Impact Loading, J. Appl. Mech., 23, 239.MATHGoogle Scholar
- Conroy, M.F. (1969), Rigid-Plastic Analysis of a Simply Supported Circular Plate due to Dynamic Circular Loading, J. Franklin Inst., 288, 121.CrossRefGoogle Scholar
- Cotter, B.A. and Symonds, P.S. (1955), Plastic Deformation of a Beam Under Impulsive Loading, Proc. ASCE, 81, 675.Google Scholar
- Cox, A.D. and Morland, L.W. (1959), Dynamic Plastic Deformations of Simply Supported Square Plates, J. Mech. Phys. Solids, 7, 229.MathSciNetCrossRefMATHGoogle Scholar
- Craggs, J.W (1954), Wave Motion in Plastic-Elastic Strings, J. Mech. Phys. Solids, 2, 286.MathSciNetCrossRefGoogle Scholar
- Craggs, J.W. (1957), The Propagation of Infinitesimal Plane Waves in Elastic-Plastic Materials, J. Mech. Phys. Solids,5, 115.MathSciNetCrossRefGoogle Scholar
- Craggs, J.W (1961), Plastic Waves, in Progress in Solid Mechanics (eds., I.N. Sneddon and R. Hill), Vol. 2, Chap. 4, North-Holland, Amsterdam.Google Scholar
- Cristescu, N. (1960), Some Observations on the Propagation of Plastic Waves in Plates, in Plasticity (eds., E.H. Lee and P.S. Symonds), Pergamon Press, New York, p. 501.Google Scholar
- Cristescu, N. (1963), On the Propagation of Elastic-Plastic Waves in Metallic Rods, Bull. Acad. Polon. Sci., 11, 129.Google Scholar
- Cristescu, N. (1964), Some Problems on the Mechanics of Extensible Strings, in Stress Waves in Anelastic Solids (eds., H. Kolsky and W. Prager), Springer-Verlag, Berlin, p. 118.CrossRefGoogle Scholar
- Cristescu, N. (1965), Loading/Unloading Criteria for Rate Sensitive Materials, Arch. Mech. Stos., 17, 291.Google Scholar
- Cristescu, N. (1967), Dynamic Plasticity, North-Holland, Amsterdam.MATHGoogle Scholar
- Cristescu, N. (1970), The Unloading in Symmetric Longitudinal Impact of Two Elastic-Plastic Bars, Int. J. Mech. Sci., 12, 723.CrossRefGoogle Scholar
- Cristescu, N. (1972), A Procedure for Determining the Constitutive Equations for Materials Exhibiting Both Time-Dependent and Time-Independent Plasticity, Int. J. Solids Struct., 8, 511.CrossRefGoogle Scholar
- Cristescu, N. (1974), Rate-Type Constitutive Equations in Dynamic Plasticity, in Problems of Plasticity (ed., A. Sawczuk), Noordhoff International, Groningen, p. 287.CrossRefGoogle Scholar
- Cristescu, N. and Bell, J.F. (1970), On Unloading in the Symmetrical Impact of Two Aluminium Bars, in Inelastic Behaviour of Solids (eds., M.F. Kannienen et al.), McGraw-Hill, New York, p. 397.Google Scholar
- Cristescu, N. and Suliciu, I. (1982), Viscoplasticity, Martinus Nijhoff, The Hague.MATHGoogle Scholar
- Davies, R.M. and Hunter, S.C. (1963), The Dynamic Compression Testing of Solids by the Method of the Split Hopkinson Pressure Bar, J. Mech. Phys. Solids, 11, 155.CrossRefGoogle Scholar
- Dean, T.H. (1970), Influence of Billet Inertia and Die Friction in Forging Processes, Proc. 11th Int. M.T.D.R. Conf, Pergamon Press, Oxford.Google Scholar
- De Juhasz, K.J. (1949), Graphical Analysis of Impact of Bars Stressed above the Elastic Range, J. Franklin Inst., 248, 15 and 113.Google Scholar
- Dillons, O.W. (1968), Experimental Data on Small Plastic Deformation Waves in Annealed Aluminium, Int. J. Solids Struct., 4, 197.CrossRefGoogle Scholar
- Donnel, L.H. (1930), Longitudinal Wave Transmission and Impact, Trans. ASME, 52, 153.Google Scholar
- Dowling, A.R., Harding, J., and Campbell, J.D. (1970), The Dynamic Punching of Metals, J. Inst. Metals, 98 , 215.Google Scholar
- Duwez, P.E. and Clark, D.S. (1947), An Experimental Study of the Propagation of Plastic Deformation Under Conditions of Longitudinal Impact, Proc. ASTM, 47, 502.Google Scholar
- Duwez, P.E., Clark, D.S., and Bohenblust, H.F. (1950), The Behaviour of Long Beams Under Impact Loading, J. Appl. Mech., 7, 27.Google Scholar
- Eason, G. and Shield, R.T. (1956), Dynamic Loading of Rigid-Plastic Cylindrical Shells, J. Appl. Mech., 4, 53.MathSciNetCrossRefMATHGoogle Scholar
- Efron, L. and Malvern, L.E. (1969), Electromagnetic Velocity Transducer Studies of Plastic Waves in Aluminum Bars, Experimental Mech., 9, 255.CrossRefGoogle Scholar
- Ezra, A.A. (1958), The Plastic Response of a Simply Supported Beam Under Impact Loading, Proc. 3rd U.S. Nat. Congr. Appl. Mech., p. 513.Google Scholar
- Florence, A.L. (1965), Annular Plate Under a Transverse Line Impulse, AIAA J., 3, 1726.CrossRefGoogle Scholar
- Florence, A.L. (1966), Clamped Circular Rigid-Plastic Plates Under Blast Loading, J. Appl. Mech., 33, 256.CrossRefGoogle Scholar
- Florence, A.L. (1977), Response of Circular Plates to Central Pulse Loading, Int. J. Solids Struct., 13, 1091.CrossRefMATHGoogle Scholar
- Forrestal, M.J., Barr, N.S., and Luk, V.K. (1991), Penetrating of Strain-Hardening Targets with Rigid Spherical Nose Rods, J. Appl. Mech., 58, 7.CrossRefGoogle Scholar
- Forrestal, M.J. and Luk, V.K. (1988), Dynamic Spherical Cavity Expansion in a Compressible Elastic-Plastic Solid, J. Appl. Mech., 55, 275.CrossRefGoogle Scholar
- Forrestal, M.J., Okajima, K., and Luk, V.K. (1988), Penetration of 6061-T651 Aluminum Targets with Rigid Long Rods, J. Appl. Mech., 55, 755.CrossRefGoogle Scholar
- Freiberger, W. (1952), A Problem of Dynamic Plasticity. The Enlargement of a Circular Hole in a Flat Sheet, Proc. Cambridge Philos. Soc, 48, 135.MathSciNetCrossRefMATHGoogle Scholar
- Galiev, S.U. and Nechitailo, N.V (1985), The Dynamics of Shape Changes, in Thin Plates and Shells of Revolution, Acad. Sci. Ukrainian SSR, Kiev.Google Scholar
- Gilman, J.J. (1960), Physical Nature of Plastic Row and Fracture, in Plasticity (eds., E.H. Lee and P.S. Symonds) Pergamon Press, Oxford, UK, p. 44.Google Scholar
- Goel, R.P. and Malvern, L.E. (1970), Biaxial Plastic Simple Waves with Combined Isotropic and Kinematic Work-Hardening, J. Appl. Mech., 37, 1100.CrossRefGoogle Scholar
- Goldsmith, W (1960), Impact, Edward Arnold, London.MATHGoogle Scholar
- Goldsmith, W and Finnegan, S.A. (1971), Penetration and Perforation Processes in Metal Targets at and above Ballistic Velocities, Int. J. Mech. Sei., 13, 843.CrossRefGoogle Scholar
- Goodier, J.N. (1968), Dynamic Buckling of Rectangular Plates in Sustained Plastic Compressive Row, in Engineering Plasticity (eds., J. Heyman J. and F.A. Leckie), Cambridge University Press, Cambridge, UK, p. 183.Google Scholar
- Gu, W., Tang, W., and Liu, T. (1996), Dynamic Pulse Buckling of Cylindrical Shells Subjected to External Impulsive Loading, J. Pressure Vessel Technol, 118, 33.CrossRefGoogle Scholar
- Haddow, J.B. (1965), On the Compression of a Thin Disc, Int. J. Mech. Sci., 7, 657.CrossRefGoogle Scholar
- Hashmi, M.S.J. (1980), Strain Rate Sensitivity of Mild Steel at Room Temperature and Strain Rate of up to 105 s_1, Analysis, 15, 201.Google Scholar
- Hawkyard, J.B. (1969), A Theory for the Mushrooming of Rat-Ended Projectiles Impinging on a Flat Rigid Anvil Using Energy Considerations, Int. J. Mech. Sci., 11, 313.CrossRefGoogle Scholar
- Hill, R. (1962), Acceleration Waves in Solids, J. Mech. Phys. Solids, 10, 1.MathSciNetCrossRefMATHGoogle Scholar
- Hill, R. (1980), Cavitation and the Influence of Headshape in Attack of Thick Targets by Nondeforming Projectiles, J. Mech. Phys. Solids, 28, 249.CrossRefMATHGoogle Scholar
- Hodge, R. G. (1955), Impact Pressure Loading of Rigid-Plastic Cylindrical Shells, J. Mech. Phys. Solids, 3, 176.MathSciNetCrossRefGoogle Scholar
- Hodge, PG. (1956), The Influence of Blast Characteristics on the Final Deformation of Circular Cylindrical Shells, J. Appl. Mech., 23, 617.MATHGoogle Scholar
- Hodge, PG. (1959), The Effect of End Conditions on the Dynamic Loading of Plastic Shells, J. Mech. Phys. Solids, 7, 258.MathSciNetCrossRefMATHGoogle Scholar
- Hopkins, H.G. (1960), Dynamic Expansion of Spherical Cavities, in Metals, Progress in Solid Mechanics (eds., I.N. Sneddon and R. Hill), Vol.1, Chap. 3, North Holland Publishing Company, Amsterdam.Google Scholar
- Hopkins, H.G. (1968), The Method of Characteristics and its Application to the Theory of Stress Waves in Solids, in Engineering Plasticity (eds., J. Heyman and F.A. Leckie), Cambridge University Press, Cambridge, UK, p. 277.Google Scholar
- Hopkins, H.G. and Prager, W. (1954), On the Dynamics of Plastic Circular Plates, Z Angew. Math. Mech., 5, 317.MathSciNetCrossRefMATHGoogle Scholar
- Hudson, G.E. (1951), A Theory of Dynamic Plastic Deformation of a Thin Diaphragm, J. Appl. Phys., 22, 1.MathSciNetCrossRefMATHGoogle Scholar
- Humphreys, J.S. (1965), Plastic Deformation of Impulsively Loaded Straight Clamped Beams, J. Appl. Mech., 32, 7.CrossRefGoogle Scholar
- Hunter, S.C. (1957), The Propagation of Spherically Symmetric Disturbances in Ideally Plastic Materials, Proc. Conf. Prop. Mat. at High Rates of Strain, Instn. Mech. Engrs. (London), p. 147.Google Scholar
- Hunter, S.C. and Crozier, R.J.M. (1968), Similarity Solution for the Rapid Uniform Expansion of a Spherical Cavity in a Compressible Elastic-Plastic Solid, Quart. J. Mech. Appl. Math., 21, 467.CrossRefMATHGoogle Scholar
- Jahsman, W.E. (1974), Reflection and Refraction of Weak Elastic-Plastic Waves, J. Appl. Mech., 41, 117.CrossRefMATHGoogle Scholar
- Jansen, D.M. ,Datta, S.K., and Jahsman, W.E. (1972), Propagation of Weak Waves in Elastic-Plastic Solids, J. Mech. Phys. Solids, 20, 1.MathSciNetCrossRefGoogle Scholar
- Johnson, W (1972), Impact Strength of Materials, Edward Arnold, London.MATHGoogle Scholar
- Johnson, W, Kormi, K., and Travis, F.W. (1965), The Explosive Drawing of Square and Rat-Bottomed Circular Cups and Double Pulsation Phenomenon, Proc. 5th Int. M.T.D.R. Conf Pergamon Press, Oxford, p. 293.Google Scholar
- Johnson, W and Travis, F.W. (1966), High Speed Blanking of Copper, Proc. Inst. Mech. Engrs. 180, Paper No. 16.Google Scholar
- Johnson, W., Sengupta, A.K., and Ghosh, S.K. (1982), Plasticine Modelled High Velocity Impact and Ricochet of Long Rods, Int. J. Mech. Sci., 24, 437.CrossRefGoogle Scholar
- Jones, N. (1967), Influence of Strain-Hardening and Rate-Sensitivity on the Permanent Deformation of Impulsively Loaded Rigid Plastic Beams, Int. J. Mech. Sci., 9 , 111.CrossRefGoogle Scholar
- Jones, N. (1968a), Impulsive Loading of a Simply Supported Circular Rigid-Plastic Plate, J. Appl. Mech., 35, 59.CrossRefGoogle Scholar
- Jones, N. (1968b), Finite Deflections of a Simply Supported Rigid Plastic Annular Plate Loaded Dynamically, Int. J. Solids Struct., 4, 593.CrossRefGoogle Scholar
- Jones, N. (1970), The Influence of Large Deflections on the Behaviour of Rigid/Plastic Cylindrical Shells Loaded Impulsively, J. Appl. Mech., 37, 416.CrossRefGoogle Scholar
- Jones, N. (1971), A Theoretical Study of the Dynamic Plastic Behaviour of Beams and Plates with Finite Deflections, Int. J. Solids Struct., 7, 1007.CrossRefMATHGoogle Scholar
- Jones, N. (1989), Structural Impact, Cambridge University Press, Cambridge, UK.Google Scholar
- Jones, N. and Ahn, CS. (1974), Dynamic Elastic and Plastic Buckling of Complete Spherical Shells, Int. J. Solids Struct., 10, 1357.CrossRefMATHGoogle Scholar
- Jones, N. and Okawa, D.M. (1976), Dynamic Plastic Buckling of Rings and Cylindrical Shells, Nuclear Engng. Design, 37, 125.CrossRefGoogle Scholar
- Jones, N, Uran, T., and Tekin, S.A. (1970), The Dynamic Plastic Behaviour of Fully Clamped Rectangular Plates, Int. J. Solids Struct., 6, 1499.CrossRefGoogle Scholar
- Kalisky, S. (1970), Approximate Solutions for Dynamically Loaded Inelastic Structures and Continua, Int. J. Nonlinear Mech., 5, 143.CrossRefGoogle Scholar
- Kalisky, S. (1989), Plasticity Theory and Engineering Applications, Elsevier, Amsterdam.Google Scholar
- Karunes, B. and Onat, E.T. (1960), On the Effect of Shear on Plastic Deformation of Beams Under Transverse Impact Loading, J. Appl. Mech., 27, 10.Google Scholar
- Keil, A.H. (1960), Problems of Plasticity in Naval Structures, Explosive and Impact Loading, in Plasticity (eds., E.H. Lee and P.S. Symonds), Pergamon Press, Oxford, UK, p. 22.Google Scholar
- Kelly, J.M. and Wilshaw, T.R. (1968), A Theoretical and Experimental Study of Projectile Impact on Clamped Circular Plates, Proc. Roy. Soc. London Ser. A, 306, 435.CrossRefGoogle Scholar
- Klepaczko, J. (1968), Strain Rate History Effects for Polycrystalline Aluminium and Theory of Intersection, J. Mech. Phys. Solids, 16, 255.CrossRefGoogle Scholar
- Kolsky, H. (1949), An Investigation of the Mechanical Properties of Materials at Very High Rates of Loading, Proc. Phys. Soc, B62, 676.Google Scholar
- Kolsky, H. (1953), Stress Waves in Solids, Clarendon Press, Oxford, UK.MATHGoogle Scholar
- Kolsky, H. and Douch, L.S. (1962), Experimental Studies in Plastic Wave Propagation, J. Mech. Phys. Solids, 10, 195.CrossRefGoogle Scholar
- Krajcinovic, D. (1972), Dynamic Analysis of Clamped Plastic Circular Plates, Int. J. Mech. Sci., 14, 225.CrossRefMATHGoogle Scholar
- Kukudjanov, V.N. (1967), Propagation of Elastic-Plastic Waves in Rods Taking into Account the Rate Influence (in Russian), Computing Centr. Acad. Sci., USSR, Moscow.Google Scholar
- Kumar, A. and Reddy, V.V.K. (1986), Dynamic Plastic Response of Circular Plates with Transverse Shear, J. Appl. Mech., 53, 952.CrossRefGoogle Scholar
- Kuzin, P.A. and Shapiro, G.S. (1966), On Dynamic Behaviour of Plastic Structures, Proc. 11th Int. Congr. Appl. Mech. (Munich, 1964), Springer-Verlag, New York, p. 629.Google Scholar
- Lebedev, N.F. (1954), Prikl. Mat. Mekh., 18, 167.MATHGoogle Scholar
- Lee, E.H. (1953), A Boundary Value Problem in the Theory of Plastic Wave Propagation, Quart. Appl Math., 10, 335.MathSciNetMATHGoogle Scholar
- Lee, E.H. (1960), The Theory of Wave Propagation in Anelastic Materials, in Stress Wave Propagation in Materials (ed. N. Davids), Interscience, New York, p. 199.Google Scholar
- Lee, E.H. and Symonds, P.S. (1952), Large Plastic Deformation of Beams Under Transverse Impact Loading. J. Appl. Mech., 19, 308.Google Scholar
- Lee, E.H. and Tupper, S.J. (1954), Analysis of Plastic Deformation in a Steel Cylinder Striking a Rigid Target, J. Appl. Mech., 21, 63.Google Scholar
- Lee, L.H.N. (1977), Quasi-Bifurcation in Dynamics of Elastic-Plastic Continua, J. Appl. Mech., 44, 413.CrossRefMATHGoogle Scholar
- Lee, L.H.N. (1981), Dynamic Buckling of an Inelastic Column, Int. J. Solids Struct., 17, 271.CrossRefMATHGoogle Scholar
- Lee, L.S.S. and Martin, J.B. (1970), Approximate Solutions of Impulsively Loaded Structures of a Rate Sensitive Material, Z Angew. Math. Phys, 21, 1011.CrossRefMATHGoogle Scholar
- Lensky, VS. (1949), Prikl Mat. Mekh., 13, 165.Google Scholar
- Lin, H.C. and Wu, H.C. (1976), Strain Rate Effect in Endochronic Theory of Viscoplasticity, J. Appl. Mech., 43, 92.Google Scholar
- Lin, H.C. and Wu, H.C. (1983), On the Rate Dependent Endochronic Theory of Viscoplasticity and its Application to Plastic Wave Propagation, Int. J. Solids Struct., 19, 587.CrossRefMATHGoogle Scholar
- Lindholm, U.S. (1964), Some Experiments with the Split Hopkinson Pressure Bar, J. Mech. Phys. Solids, 12, 317.CrossRefGoogle Scholar
- Lippmann, H. (1966), On the Dynamics of Forging, Proc. 7th Int. Conf. MTDR, Pergamon Press, Oxford, UK.Google Scholar
- Liu, D. and Stronge, W.J. (1996), Deformation of Simply Supported Circular Plate by Central Pressure Pulse, Int. J. Solids Struct., 33, 283.CrossRefMATHGoogle Scholar
- Lubiner, J. (1965), The Strain Rate Effect in Plastic Wave Propagation, J. Mecan., 4, 111.Google Scholar
- Ludwik, P. (1909), Elemente der Technologischen Mechanik, Springer-Verlag, Berlin.MATHGoogle Scholar
- Luk, V.K. and Arnos, D.E. (1991), Dynamic Cylindrical Cavity Expansion of Compressible Strain-Hardening Material, J. Appl. Mech., 58, 334.CrossRefGoogle Scholar
- Luk, V.K., Forrestal, M.J., and Amos, D.E. (1991), Dynamic Spherical Cavity Expansion of Strain-Hardening Material, J. Appl. Mech., 58, 1.CrossRefGoogle Scholar
- Malvern, L.E. (1951), The Propagation of Longitudinal Waves of Plastic Deformation in a Bar of Material Exhibiting Strain-Rate Effect, J. Appl. Mech., 18, 203.MathSciNetGoogle Scholar
- Malvern, L.E. (1965), Experimental Studies of Strain Rate Effects and Plastic Wave Propagation in Annealed Aluminum, in Behavior of Materials Under Dynamic Loading, ASME,p. 81.Google Scholar
- Malyshev, V.M. (1961), J. Prikl Mekh. Tech. Fiz.,2, 104.Google Scholar
- Mandel, J. (1962), Ondes Plastiques dans Milieu Indéfini a Trois Dimensions, in Extrait du Seminaire de Plasticite, Publ. Sci. Techn. Min. Air. NT 116, Paris, p. 151.Google Scholar
- Mandel, J. (1972), Plasticite Classique et Viscoplasticite, Springer-Verlag, Wien.MATHGoogle Scholar
- Manjoine, M.J. (1944), The Influence of Rate of Strain and Temperature on Yield Stresses of Mild Steel, J. Appl. Mech., 11, 211.Google Scholar
- Martin, J.B. and Lee, L.S.S. (1968), Approximate Solutions for Impulsively Loaded Elastic-Plastic Beams, J. Appl. Mech., 35, 803.CrossRefMATHGoogle Scholar
- Martin, J.B. and Symonds, P.S. (1966), Mode Approximations for Impulsively Loaded Rigid-Plastic Structures, J. Engng. Mech. Div., Proc. ASCE, 92, 43.Google Scholar
- Mentel, T.J. (1958), The Plastic Deformation due to Impact of a Cantilever Beam with an Attached Tip Mass, J. Appl. Mech., 25, 515.MATHGoogle Scholar
- Morland, L.W. (1959), The Propagation of Plane Irrotational Waves Through an Elasto-plastic Medium, Philos. Trans. Roy. Soc. London Ser A, 251, 341.MathSciNetCrossRefMATHGoogle Scholar
- Munday, G. and Newitt, D.M. (1963), The Deformation of Transversely Loaded Discs Under Dynamic Loads, Philos. Trans. Roy. Soc. London Ser. A, 256, 1.CrossRefMATHGoogle Scholar
- Nicholas, T. (1971), Strain Rate History Effects in Several Metals in Torsion, Experimental Mech., 11, 153.CrossRefGoogle Scholar
- Nicholas, T. (1982), Elastic-Plastic Stress Waves, in Impact Dynamics (eds., A. Zukas et al.), Wiley, New York, pp. 95–153.Google Scholar
- Nonaka, T. (1977), Shear and Bending Response of a Rigid Plastic Beam in Blast Type Loading, Ingenieur-Archiv, 46, 35.CrossRefGoogle Scholar
- Nurick, G.N., Pearce, H.T., and Martin, J.B. (1987), Prediction of Transverse Deflection and In-Plane Strain in Impulsively Loaded Thin Plates, Int. J. Mech. Sci., 29, 435.CrossRefMATHGoogle Scholar
- Owens, R.H. and Symonds, P.S. (1955), Plastic Deformation of a Free Ring Under Concentrated Dynamic Loading, J. Appl. Mech., 22, 523.MATHGoogle Scholar
- Parkes, E.W. (1955), The Permanent Deformation of a Cantilever Struck Transversely at its Tip, Proc. Roy. Soc. London, Ser. A, 228, 462.CrossRefGoogle Scholar
- Parkes, E.W. (1958), The Permanent Deformation of an Encastre Beam Struck Transversely at any Point in its Span, Proc. Inst. Civil Engrs., 10, 277.CrossRefGoogle Scholar
- Perrone, N. (1965), On a Simplified Method of Solving Impulsively Loaded Structures of Rate-Sensitive Materials, J. Appl Mech., 32, 489.MathSciNetCrossRefGoogle Scholar
- Perrone, N. (1967), Impulsively Loaded Strain Rate Sensitive Plates, J. Appl. Mech., 34, 380.CrossRefGoogle Scholar
- Perrone, N. (1970), Impulsively Loaded Strain-Hardened Rate Sensitive Rings and Tubes, Int. J. Solids Struct., 6, 119.CrossRefGoogle Scholar
- Perrone, N. and Bhadra, P. (1984), Simplified Large Deflection Mode Solutions for Impulsively Loaded Viscoplastic Circular Membranes, J. Appl. Mech., 51, 505.CrossRefGoogle Scholar
- Perzyna, P. (1958), Dynamic Load Carrying Capacity of a Circular Plate, Arch. Mech. Stos., 10, 635.MathSciNetMATHGoogle Scholar
- Perzyna, P. (1963), The Constitutive Equations for Rate Sensitive Plastic Solids, Quart. Appl. Math., 20, 321.MathSciNetMATHGoogle Scholar
- Perzyna, P. (1966), Fundamental Problems in Viscoplasticity, Adv. in Appl. Mech., 9, 243.Google Scholar
- Rakhmatulin, H.A. (1945), On the Propagation of Waves of Unloading (in Russian), Prikl. Mat. Mekh., 9, 91.MathSciNetMATHGoogle Scholar
- Rakhmatulin, H.A. and Shapiro, G.S. (1948), Prikl Mat. Mekh., 12, 369.MATHGoogle Scholar
- Raphanel, J.L. and Symonds, P.S. (1984), The Estimation of Large Deflections of a Portal Frame Under Asymmetric Pulse Loading, J. Appl Mech., 51, 494.CrossRefGoogle Scholar
- Rawlings, B. (1964), Mode Changes in Frames Deforming Under Impulsive Loads, J. Mech. Engng. Sci., 6, 327.CrossRefGoogle Scholar
- Recht, R.F. and Ipson, T.W. (1963), Ballistic Performance Dynamics, J. Appl. Mech., 30, 384.CrossRefGoogle Scholar
- Reid, S.R. and Gui, X.G. (1987), On the Elastic-Plastic Deformation of Cantilever Beams Subjected to Tip Impact, Int. J. Impact Engng., 6, 109.CrossRefGoogle Scholar
- Reid, S.R., Wang, B., and Yu, T.X. (1995),Yield Mechanism for a Bent Cantilever Beam Subjected to a Suddenly Applied Constant Out-of-Plane Tip Force, Int. J. Impact Engng., 16, 89.Google Scholar
- Rinehart, J.S. and Pearson, J. (1965), Behavior of Metals Under Impulsive Loads, Dover, New York.Google Scholar
- Ripperger, E.A. (1960), Experimental Studies of Plastic Wave Propagation in Bar, in Plasticity (eds., E.H. Lee and P.S. Symonds), Pergamon Press, New York, p. 475.Google Scholar
- Rosenberg, Z. and Dekel, E. (1994), The Relation Between the Penetration Capability of Long Rods and Their Length to Diameter Ratios, Int. J. Impact Engng., 15, 125.CrossRefGoogle Scholar
- Sankaranaryanan, R. (1963), On the Dynamics of Plastic Spherical Shells, J. Appl. Mech., 30, 87.CrossRefGoogle Scholar
- Sankaranarayanan, R. (1966), On the Impact Pressure Loading of a Plastic Spherical Cap., J. Appl Mech., 33, 704.CrossRefGoogle Scholar
- Seiler, J.A., Cotter, B.A., and Symonds, P.S. (1956), Implsive Loading of Elastic-Plastic Beams, J. Appi. Mech., 23, 516.Google Scholar
- Seiler, J. A. and Symonds, P.S. (1954), Plastic Deformation of Beams Under Distributed Dynamic Loads, J. Appl. Phys., 25, 556.CrossRefMATHGoogle Scholar
- Shapiro, G.S. (1959), On a Rigid-Plastic Annular Plate Under Impulsive Load (translation from Russian), J. Appl. Math. Mech., 23, 234.MathSciNetCrossRefMATHGoogle Scholar
- Sokolovsky, W.W. (1948), The Propagation of Elastic Viscoplastic Waves in Bars (in Russian), Prikl. Math. Mekh., 12, 261.Google Scholar
- Steinberg, D. and Lund, O. (1989), A Constitutive Model for Strain Rates from 10–4 to 106 s-1, J. Appl. Phys., 65, 1528.CrossRefGoogle Scholar
- Sternglass, E.J. and Stuart, D.A. (1953), An Experimental Study of Propagation of Transient Longitudinal Deformation in Elastic-Plastic Media, J. Appl. Mech., 20, 427.Google Scholar
- Stronge, W.J., Shu, D., and Shim, V.P.W. (1990), Dynamics Modes of Plastic Deformation for Suddenly Loaded Curved Beams, Int. J. Impact Engng., 9, 1.CrossRefGoogle Scholar
- Stronge, W.J. and Yu, T.X. (1993), Dynamic Models for Structural Plasticity, Springer-Verlag, London.CrossRefGoogle Scholar
- Symonds, P.S. (1953), Dynamic Load Characteristics in Plastic Bending of Beams, J. Appl. Mech., 20, 475.MATHGoogle Scholar
- Symonds, P.S. (1954), Large Plastic Deformation of Beams Under Blast Type Loading, Proc. 2nd U.S. Nat. Congr. Appl. Mech., Ann Arbor, p. 506.Google Scholar
- Symonds, P.S. (1980), Finite Elastic and Plastic Deformations of Pulse Loaded Structures by an Extended Mode Technique, Int. J. Mech. Sci., 22, 597.CrossRefMATHGoogle Scholar
- Symonds, P.S. and Fleming, W.T. (1984), Parkes Revisited: On Rigid-Plastic and Elastic-Plastic Dynamic Structural Analysis, Int. J. Impact Engng., 2, 1.CrossRefGoogle Scholar
- Symonds, P.S. and Leth, C.F. (1954), Impact of Finite Beams of Ductile Metal, J. Mech. Phys. Solids, 2, 92.MathSciNetCrossRefGoogle Scholar
- Symonds, P.S. and Mentel, T.J. (1958), Inpulsive Loading of Plastic Beams with Axial Restraint, J. Mech. Phys. Solids, 6, 183.MathSciNetCrossRefGoogle Scholar
- Symonds, P.S. and Wierzbicki, T. (1979), Membrane Mode Solutions for Impulsively Loaded Circular Plates, J. Appl. Mech., 46, 58.CrossRefMATHGoogle Scholar
- Tate, A. (1969), Further Results on Long Rod Penetration, J. Mech. Phys. Solids, 17, 141.MathSciNetCrossRefGoogle Scholar
- Taylor, G.I. (1942), The Plastic Wave in a Wire Extended by an Impact Load, British Official Report, RC 329.Google Scholar
- Taylor, G.I. (1948), The Use of Flat-Ended Projectiles for Determining Dynamic Yield Stress, I, Proc. Roy. Soc. London Ser. A, 194, 289.CrossRefGoogle Scholar
- Thomas, H.K. (1961), Large Plastic Flow and Fracture in Solids, Thames Hudson, London.Google Scholar
- Thomson, W.T. (1955), An Approximate Theory of Armour Penetration, J. Appl Phys., 26, 80.CrossRefGoogle Scholar
- Ting, T.C.T. (1964), The Plastic Deformation of a Cantilever Beam with Strain Rate Sensitivity Under Inpulsive Loading, J. Appl. Mech., 11, 38.MathSciNetCrossRefGoogle Scholar
- Ting, T.C.T. (1972), The Initiation of Combined Stress Waves in a Thin-Walled Tube due to Impact Loading. Int. J. Solids Struct., 8, 269.CrossRefMATHGoogle Scholar
- Ting, T.C.T. (1977), Plastic Wave Speeds in Isotropically Work-Hardening Material, J. Appl. Mech., 44, 68.CrossRefMATHGoogle Scholar
- Travis, F.W and Johnson, W. (1962), Experiments in the Dynamic Deformation of Clamped Circular Sheets of Various Metals Subject to an Underwater Explosive Charge, Sheet Metal Indust., 39, 456.Google Scholar
- Vaughan, H. and Florence, A.L. (1970), Plastic Row Buckling of Cylindrical Shells Due to Impulsive Loading, J. Appl. Mech., 37, 171.CrossRefGoogle Scholar
- von Karman, Th. (1942), On the Propagation of Plastic Deformation in Solids, NDRC Report No.A-29.Google Scholar
- von Karman, Th. and Duwez, P.E. (1950), The Propagation of Plastic Deformation in Solids, J. Appl. Phys., 21, 987.MathSciNetCrossRefMATHGoogle Scholar
- Wang, A.J. (1955), The Permanent Deflection of a Plastic Plate Under Blast Loading, J. Appl. Mech., 22, 375.MATHGoogle Scholar
- Wang, A.J. and Hopkins, H.G. (1954), On the Plastic Deformation of Built-in Circular Plates Under Impulsive Loading, J. Mech. Phys. Solids, 3, 22.MathSciNetCrossRefGoogle Scholar
- Whiffen, A.C. (1948), The Use of Flat-Ended Projectiles for Determining Dynamic Yield Stress, II, Proc. Roy. Soc. London Sen A, 194, 300.CrossRefGoogle Scholar
- White, M.P. and Griffis, Le Van (1947), The Permanent Strain in a Uniform Bar due to Longitudinal Impact, J. Appl. Mech., Trans. ASME, 69, 33.Google Scholar
- Wierzbicki, T. and Jones, N. (1989), Structural Failure (eds.), Wiley, New Delhi.Google Scholar
- Wu, H.C. and Lin, H.C. (1974), Combined Plastic Wave in a Thin-Walled Tube, Int. J. Solids Struct., 10, 903.CrossRefMATHGoogle Scholar
- Wu, H.C. and Yip, M.C. (1980), Strain Rate and Strain History Effects on the Dynamic Behaviour of Metallic Materials, Int. J. Solids Struct., 16, 515.MathSciNetCrossRefMATHGoogle Scholar
- Youngdahl, CK. (1971), Influence of Pulse Shape on the Final Plastic Deformation of Circular Plates, Int. J. Solids Struct., 1, 1127.CrossRefGoogle Scholar
- Youngdahl, C.K. (1972), Dynamic Plastic Deformation of Cylindrical Shells, J. Appl. Mech., 39, 746.CrossRefGoogle Scholar
- Youngdahl, C.K. (1987), Effect of Pulse Shape and Distribution on the Plastic Deformation of a Circular Plate, Int. J. Solids Struct., 23, 1179.CrossRefMATHGoogle Scholar
- Yu, T.X. and Chen, EL. (1992), The Large Deflection Dynamic Plastic Response of Rectangular Plates, Int. J. Impact Engng., 12, 603.CrossRefGoogle Scholar
- Yu, T.X. and Jones, N. (1989), Numerical Simulation of a Clamped Beam Under Impact Loading, Computers and Structures, 32, 281.CrossRefGoogle Scholar
- Yu, T.X., Symonds, P.S., and Johnson, W. (1985), A Quadrental Circular Beam Subjected to Radial Impact in its own Plane at its Tip by a Rigid Mass, Proc. Roy. Soc. London Ser. A, 400, 19.CrossRefMATHGoogle Scholar
- Zaid, M. and Paul, B. (1958), Normal Perforation of a Thin Plate by Truncated Projectiles, J. Franklin Inst., 265, 317.CrossRefGoogle Scholar
- Zhu, L. (1996), Transient Deformation Modes of Square Plates Subjected to Explosive Loading, Int. J. Solids Struct., 33, 301.CrossRefMATHGoogle Scholar
- Zukas, J.A. (1982), Penetration and Perforation of Solids, in Impact Dynamics (eds., J.A. Zukas et al.), Wiley, New York, p. 155.Google Scholar
- Zukas, J.A. and Gaskill, B. (1996), Ricochet of Deforming Projectiles from Deforming Plates, Int. J. Impact Engng., 18, 601.CrossRefGoogle Scholar