Abstract
Concentrated research over the last decade has led to rapid development of an understanding of the response of solid materials to high amplitude dynamic loads. Constitutive equations have been developed for such real materials as engineering alloys, fiber composites, porous earth materials, and polymers. Together with the conservation laws, these equations have been incorporated into numerical solution methods which have allowed analysis of such problems as ballistic penetration, high velocity impacts, explosive devices and components, and many others which were intractable only a few years ago. Stress wave codes have also become an indispensable tool in further research on the dynamic behavior of materials.
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References
R. Courant and D. Hilbert Methods of Mathematical Physics, Vol. 2 Interscience Publishers, New York (1962)
P. R. Garabedian Partial Differential Equations John Wiley & Sons, Inc., New York (1964)
J. von Neumann and R. D. Richtmyer A Method for the Numerical Calculation of Hydrodynamic Shocks J. Appl. Phys., 21; 232 (1950)
R. N. Brodie and J. E. Hormuth The PUFF 66 and P PUFF 66 Computer Programs Air Force Weapons Laboratory, AFWL-TR-66-48, May 1966
W. Herrmann, P. Holzhauser and R. J. Thompson WONDY A Computer Program for Calculating Problems of Motion in One Dimension Sandia Laboratories, SC-RR-66-601, Feb. 1967
R. Courant and K. O. Friedrichs Supersonic Flow and Shock Waves Interscience Publishers, New York (l948)
R. Courant, K. O. Friedrichs and H. Lewy Über die Partiellen Differenzengeichungen der Mathematischen Physik Math. Ann, 100; 13 (1928)
R. D. Richtmyer and K. W. Morton Difference Methods for Initial-Value Problems Interscience Publishers, New York (1967)
W. G. Strang Accurate Partial Difference Methods II: Non-linear Problems Numer. Math, 6; 37 (l964)
W. Herrmann and J. W. Nunziato Nonlinear Constitutive Equations in “Dynamic Behavior of Materials under Impulsive Loading” ed. P. C. Chou (in press)
D. L. Hicks and D. B. Holdridge The CONCHAS Wavecode Sandia Laboratories, SC-RR-72-0451, Sept. 1972
R. Landshoff A Numerical Method for Treating Fluid Flow in the Presence of Shocks Los Alamos Scientific Laboratory, LA-1930, Jan. (l955)
P. D. Lax and B. Wendroff Systems of Conservation Laws Comm. Pure Appl. Math, 13; 217 (1960)
R. Courant. M. Isaacson and M. Rees On the Solution of Nonlinear Hyperbolic Differential Equations by Finite Differences Comm. Pure Appl. Math, 5; 243 (l952)
D. R. Hartree Some Practical Methods of Using Characteristics in the Calculation of Non-Steady Compressible Flow Atomic Energy Commission, AECU-2713, Sept. 1953
D. L. Hicks Analysis of CAVIL, A Conservative Artificial Viscosity Implicit and Lagrangean Wavecode Sandia Laboratories, SC-RR-71 0863, July 1972
B. J. Thorne and D. A. Dahlgren A Comparison of Numerical Techniques for Wave Propagation Problems in Solids Sandia Laboratories, SC-RR-70-571, Nov. 1971
L. M. Barker SWAP-9: An Improved Stress Wave Analyzing Program Sandia Laboratories, SC-RR-69-233, Aug. 1969
D. S. Mason and B. J. Thorne A Preliminary Report Describing the Rezoning Features of the WONDY IV Program Sandia Laboratories, SC-DR-70-146, March 1970
W. Herrmann Nonlinear Stress Waves in Metals in “Wave Propagation in Solids” ed. J. Miklowitz The American Society of Mechanical Engineers (1969)
W. Herrmann Constitutive Equations for Compaction of Porous Materials in “Applied Mechanics Aspects of Nuclear Effects in Materials” ed. C. C. Wan The American Society of Mechanical Engineers (l97l)
W. Herrmann, D. L. Hicks and E. G. Young Attenuation of Elastic-Plastic Stress Waves in “Shock Waves and the Mechanical Properties of Solids” ed. J. J. Burke and V. Weiss Syracuse University Press (l97l)
W. Herrmann, R. J. Lawrence and D. S. Mason Strain Hardening and Strain Rate in One-Dimensional Wave Propagation Calculations Sandia Laboratories, SC-RR-70-471, Nov. 1970
M. L. Wilkins Calculation of Elastic Plastic Flow in “Methods in Computational Physics, Vol. 3 Fundamental Methods in Hydrodynamics” ed. B. Alder, S. Fernbach and M. Rotenberg Academic Press, New York (l964)
B. J. Thorne and W. Herrmann TOODY, A Computer Program for Calculating Problems of Motion in Two Dimensions Sandia Laboratories, SC-RR-66-6o2, July 1967
S. K. Gudunov and K. A. Bagrinovskii Difference Schemes for Multidimensional Problems Doklady Akad Nauk, 115; 431 (l957)
D. Gottlieg Strang-type Difference Schemes for Multidimensional Problems Siam J. Numer. Anal., 9; 650 (l972)
L. D. Bertholf and S. E. Benzley TOODY II--A Computer Program for Two-Dimensional Wave Propagation Sandia Laboratories, SC-RR-68-41, Nov. 1968
B. J. Thorne and D. Holdridge The TOOREZ Lagrangian Rezone Code Sandia Laboratories, SC-RR, in press
R. T. Walsh Finite Difference Methods in “Dynamic Response of Materials under Impulsive Loading” ed. P. C. Chou, in press
F. H. Harlow The Particle-in-cell Computing Method for Fluid Dynamics in “Methods in Computational Physics, Vol. 3, Fundamental Methods in Hydrodynamics” ed. B. Alder, S. Fernbach and M. Rotenberg Academic Press, New York (l964) p. 319
W. E. Johnson OIL — A Continuous Two-Dimensional Hydrodynamic Code General Atomic/General Dynamics, GAMD-5580, Oct. ?(l964)
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Herrmann, W., Hicks, D.L. (1973). Numerical Analysis Methods. In: Rohde, R.W., Butcher, B.M., Holland, J.R., Karnes, C.H. (eds) Metallurgical Effects at High Strain Rates. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-8696-8_4
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DOI: https://doi.org/10.1007/978-1-4615-8696-8_4
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