Abstract
In this section, we discuss the role of numerical simulations in studying the response of materials and structures to large deformation or shock loading. The methods we consider here are based on solving discrete approximations to the continuum equations of mass, momentum, and energy balance. Such computational techniques have found widespread use for research and engineering applications in government, industry, and academia.
This work was performed at sandia National Laboratories and supportad by the U.S. Departmant of Energy under Contract DE-AC04-76DP00789.
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References
J.M. McGlaun and S.L. Thompson, CTH: A Three-Dimensional Shock Wave Physics Code, Internat. J. Impact Engrg. 10 (1990)
J.M. McGlaun, Personal communication
A.C. Robinson, C.T. Vaughan, H.E. Fang, C.F. Diegert, and K. Cho, Hydrocode Development on the nCUBE and the Connection Machine Hypercubes, Proceedings of the 1991 APS Topical Conference on Shock Compression of Condensed Matter, Williamsburg, VA, 1991
H.E. Fang, A. C. Ribinson, and K. Cho, Hydrocode Development on the Connection Machine, Minutes of the Fifth SIAM Conference on Parallel Processing for Scientific Computing, Houston, TX, 1991
C.T. Vaughan, Structural Analysis on Massively Parallel Computers, SAND90-1706C, Sandia National Laboratories Report, Albuquerque, NM 87185, 1991
J. Hopson, Personal communication
C.E. Anderson, An Overview of the Theory of Hydrocodes, Internat. J. Impact Engrg. 5 (1987)
W.E. Johnson and C.E. Anderson, History and Application of Hydrocodes in Hypervelocity Impact, Internat. J. Impact Engrg. 5 (1987)
C. Truesdell and R.A. Toupin, The Classical Field Theories, Encyclopedia of Physics, Volume III/l, Springer-Verlag, New York, 1960
W.F. Noh, CEL: A Time-Dependent, Two-Space-Dimensional, Coupled Eulerian-Lagrangian Code, in Methods in Computational Physics, Volume 3 (edited by B. Alder, S. Fernbach and M. Rotenberg), Academic Press, New York, 1964
J.F. Thompson, Z.U.A. Warsi, and C.W. Mastin, Numerical Grid Generation, North-Holland, Amsterdam, 1985
M.J. Frits, Two-Dimensional Lagrangian Fluid Dynamics Using Triangular Grids, in Finite-Difference Techniques for Vectorized Fluid Dynamics Calculations (edited by D.L. Book), Springer-Verlag, New York, 1981
H.E. Trease, Three-Dimensional Free Lagrangian Hydrodynamics, in The Free-Lagrange Method (edited by M.J. Fritts, W.P. Crowley and H.E. Trease), Lecture Notes in Physics, Number 238, Springer-Verlag, New York, 1985
R.B. deBar, Fundamentals of the KRAKEN Code, UCIR-760, Lawrence Livermore Laboratory, Livermore, CA, 1974
M.J. Berger and J. Olinger, Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations, J. Comput. Phys. 53 (1984)
M.J. Berger and P. Colella, Local Adaptive Mesh Refinement for Shock Hydrodynamics, UCRL-97196, Lawrence Livermore National Laboratory, Livermore, CA, 1987
P.A. Hookham, D. Hatfield, and M. Rosenblatt, Calculation of the Interaction of Three Spherical Blast Waves Over a Planar Surface with an Adaptive-Grid TVD Code, California Research and Technology Report, Chats worth, CA, 1991
R.D. Richtmyer and K.W. Morton, Difference Methods for Initial-Value Problems, Interscience, New York, 1967
D.L. Hicks, von Neumann Stability of the Wondy Wavecode for Thermodynamic Equations of State, SAND77-0934, Sandia National Laboratories, Albuquerque, NM, 1977
J.M. McGlaun, CTH Reference Manual: Lagrangian Step for Hydrodynamic Materials, SAND90-2645, Sandia National Laboratories, Albuquerque, NM, December 1990
S.L. Thompson, CSQII—An Eulerian Finite Difference Program for Two-Dimensional Material Response—Part 1, Material Sections, SAND77-1339, Sandia National Laboratories, Albuquerque, NM, January 1979
A.R. Mitchell and R. Wait, The Finite Element Method in Partial Differential Equations, Wiley, New York, 1977
D.E. Burton, Exact Conservation of Energy and Momentum in Staggered-Grid Hydrodynamics with Arbitrary Connectivity, UCRL-JC-104258, Lawrence Livermore National Laboratory, Livermore, CA, 1990
W. Herrmann and L.D. Bertholf, Explicit Lagrangian Finite-Difference Methods, in Computational Methods for Transient Analysis (edited by J.D. Achenbach), North-Holland, Amsterdam, 1983
D.E. Burton, Conservation of Energy, Momentum, and Angular Momentum in Lagrangian Staggered-Grid Hydrodynamics, UCRL-JC-105926, Lawrence Livermore National Laboratory, Livermore, CA, 1990
W.D. Schultz, A Tensor Artificial Viscosity for Numerical Hydrodynamics, J. Math. Phys. 5, Na. 1 (1964)
L.G. Margolin, A Centered Artificial Viscosity for Cells with Large Aspect Ratio, UCRL-53882, Lawrence Livermore National Laboratory, Livermore, CA, 1988
W.F. Noh, Errors for Calculations of Strong Shocks Using an Artificial Viscosity and an Artificial Heat Flux, J. Comput. Phys. 72 (1978)
29. P.R. Woodward, PPM: Piecewise-Parabolic Methods for Astrophysical Fluid Dynamics, in Astrophysical Radiation Hydrodynamics (edited by K.A. Winkler and M.L. Norman), D. Reidel, Dordrecht, 1982
J.B. Bell, P. Colella, and J.A. Trangenstein, Higher Order Godunov Methods for General Systems of Hyperbolic Conservation Laws, J. Comput. Phys. 82 (1989)
J.K. Dukowicz, A General, Non-Iterative Riemann Solver for Godunov’s Method, J. Comput. Phys. 61 (1985)
P. Colella and H.M. Glaz, Efficient Solution Algorithms for the Riemann Problem for Real Gasses, J. Comput. Phys. 59 (1985)
L.M. Taylor and D.P. Flanagan, PRONTO 2D: A Two-Dimensional Transient Solid Dynamics Program, SAND86-0594, Sandia National Laboratories, Albuquerque, NM, 87185, 1987
S.A. Silling, Stability and Accuracy of Differencing Schemes for Viscoplastic Models in Wavecodes, SAND91-0141, Sandia National Laboratories, Albuquerque, NM, 1991
S.L. Thompson Private communication
B. Engquist and A. Majda, Absorbing Boundary Conditions for the Numerical Simulation of Waves, Math. Comput. 31, No. 139 (1977)
D. Givoli, Non-reflecting Boundary Conditions, J. Comput. Phys. 94, No. 1, (1991)
J.M. McGlaun, Improvements in CSQII: A Transmitting Boundary Condition, SAND82-1248, Sandia National Laboratories, Albuquerque, NM, 87185, 1982
M. Cohen and P.C. Jenning, Silent Boundary Methods for Transient Analysis, Computational Methods for Transient Analysis (edited by J.D. Achenbach), North-Holland, Amsterdam, 1983
R. Vichnevetsky and J.B. Bowles, Fourier Analysis of Numerical Approximations of Hyperbolic Equations, SIAM Studies in Applied Mathematics, 1982
B. van Leer, Towards the Ultimate Conservative Difference Scheme. V.A. Second-Order Sequel to Godunov’s Method, J. Comput. Phys. 32 (1979)
S.T. Zalesak, Fully Multidimensional Flux-Corrected Transport Algorithms for Fluids, J. Comput. Phys. 31 (1979)
G. Luttwak and R.L. Rabie, The Multimaterial Arbitrary Lagrangian–Eulerian Code MMALE and its Application to Some Problems of Penetration and Impact, LA-UR-2311, Los Alamos National Laboratory, Los Alamos, NM, 1985
J.M. McGlaun, CTH Reference Manual: Cell Thermodynamics, SAND91-0002, Sandia National Laboratories, Albuquerque, NM, 1991
C.W. Hirt and B.D. Nichols, Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, J. Comput. Phys. 39 (1981)
J.M. Hyman, Numerical Methods for Tracking Interfaces, Physica 12D (1984)
I.L. Chern and P. Colella, A Conservative Front Tracking Method for Hyperbolic Conservation Laws, UCRL-97200, Lawrence Livermore National Laboratory, Livermore, CA, 1987
N. Ashgriz and J.Y. Poo, FLAIR: Flux Line-Segment Model for Advection and Interface Reconstruction, J. Comput. Phys. 93 (1991)
W.F. Noh and P.R. Woodward, SLIC (Simple Line Interface Calculation), Lecture Notes in Physics, No. 59, Springer-Verlag, New York, 1977
P. Colella, Multidimensional Upwind Methods for Hyperbolic Conservation Laws, LBL-17023, Lawrence Berkley Laboratory, Berkley, CA, 1984
J. Saltzman and P. Colella, Second-Order Corner Coupled Upwind Transport Methods for Lagrangian Hydrodynamics, LA-UR-85-678, Los Alamos National Laboratory, Los Alamos, NM, 1987
J.B. Bell, C.N. Dawson, and G.R. Shubin, An Unsplit, Higher-Order Godunov Method for Scalar Conservation Laws in Multiple Dimensions, J. Comput. Phys. 74 No. 1 (1988)
J.M. McGlaun, Improvements on CSQII: An Improved Numerical Convection Algorithm, SAND82-0051, Sandia National Laboratories, Albuquerque, NM, 1982
R.J. LeVeque and J.B. Goodman, TVD Schemes in One and Two Space Dimensions, Lectures in Applied Mathematics, Vol. 22, 1985
P.K. Sweby, High Resolution TVD Schemes Using Flux Limiters, Lectures in Applied Mathematics, Vol. 22, 1985
A. Harten, ENO Schemes with Subcell Resolution, J. Comput. Phys. 83 (1989)
D.J. Benson, An Efficient, Accurate, Simple ALE Method for Nonlinear Finite Element Programs, Comput. Methods Appl. Mech. 79 (1989)
D.F. Hawken, JJ. Gottlieb, and J.S. Hansen, Review of Some Adaptive Node-Movement Techniques in Finite-Element and Finite-Difference Solutions of Partial Differential Equations, J. Comput. Phys. 95 (1991)
J. Donea, Arbitrary Lagrangian–Eulerian Finite Element Methods, Computational Methods for Transient Analysis (edited by J.D. Achenbach), North-Holland, Amsterdam, 1983
M.E. Kipp and R.J. Lawrence, WONDY V—A One-Dimensional Finite-Difference Wave Propagation Code, SAND81-0930, Sandia National Laboratories, Albuquerque, NM, 1982
61. M.E. Kipp and D.E. Grady, Shock Compression and Release in High-Strength Ceramics, SAND89-1461, Sandia National Laboratories, Albuquerque, NM, 1989
M.L. Wilkins, Mechanics of Penetration and Perforation, Internat. J. Engrg. Sci., 16, 793–807 (1978)
M.L. Wilkins, Lawrence Livermore National Laboratory Report, UCRL-7322, Rev. 1, 1969
J.W. Swegle, TOODY IV—A Computer Program for Two-Dimensional Wave Propagation, SAND78-0552, Sandia National Laboratories, Albuquerque, NM, 1978
65. L.D. Bertholf et al., Kinetic Energy Projectile Impact on Multi-Layered Targets: Two-Dimensional Stress Wave Calculations, Prepared by Sandia National Laboratories, Contract Report ARBRL-CR-00391, Ballistic Research Laboratory, 1979
G.R. Johnson, R.A. Stryk, and M.E. Nixon, Two-and Three-Dimensional Computational Approaches for Steel Projectiles Impacting Concrete Targets, Proc. Post-SMIRT Seminar on Impact, Lausanne, Switzerland, 1987
L.N. Kmetyk and P. Yarrington, Cavity Dimensions for High Velocity Penetration Events— A Comparison of Calculational Results with Data, SAND88-2693, Sandia National Laboratories, Albuquerque, NM, 1989
C.K. Hwee and A.C.J. Ong, Simulation of Penetration into Armor Using VEC/ DYNA3D, Engrg. Technol. 1, No. 3 (1991)
M.E. Kipp, Private communication
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McGlaun, J.M., Yarrington, P. (1993). Large Deformation Wave Codes. In: Asay, J.R., Shahinpoor, M. (eds) High-Pressure Shock Compression of Solids. High-Pressure Shock Compression of Condensed Matter. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0911-9_9
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