Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Numerical computations for antiplane shear in a granular flow model

Author: Xabier Garaizar
Journal: Quart. Appl. Math. 52 (1994), 289-309
MSC: Primary 73G20; Secondary 35L65, 35Q72, 65C20, 73E50, 73N20, 73V20, 76A99
DOI: https://doi.org/10.1090/qam/1276239
MathSciNet review: MR1276239
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Abstract | References | Similar Articles | Additional Information

Abstract: We describe an algorithm for the numerical resolution of elasto-plastic deformations in the context of antiplane shear models. The algorithm is a second-order Godunov method. For these models the eigenvalues associated to the hyperbolic system are discontinuous. We test the algorithm on several examples.

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  • [1] S. S. Antman and W. G. Szymczak, Nonlinear elasto-plastic waves, Contemp. Math. 100, 27-54 (1989)
  • [2] I.-L. Chern, J. Glimm, O. McBryan, B. Plohr, and S. Yaniv, Front tracking for gas dynamics, J. Comp. Phys. 62, 83-110 (1986)
  • [3] A. Chorin, Random choice solutions of hyperbolic systems, J. Comp. Phys. 22, 517-533 (1976)
  • [4] X. Garaizar and D. Schaeffer, Numerical computations for shear bands in an antiplane shear model, J. Mech. Phys. Solids, Pergamon, Oxford-Elmsford, NY, in press, 1993
  • [5] J. Glimm, E. Isaacson, D. Marchesin, and O. McBryan, Front tracking for hyperbolic systems, Adv. Appl. Math. 2, 91-119 (1985)
  • [6] K. Godunov, Finite-difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics, Mat. Sbornik 47, 271-306 (1959)
  • [7] E. H. Lee, A boundary value problem in the theory of plastic wave propagation, Quart. Appl. Math. 10, 335-346 (1952)
  • [8] C. Moler and J. Smoller, Elementary interactions in quasilinear hyperbolic systems, Arch. Rat. Mech. Anal. 37, 309-322 (1970)
  • [9] D. Schaeffer, A mathematical model for localization in granular flow: Postcritical behavior, preprint, 1991
  • [10] D. G. Schaeffer and Michael Shearer, Scale-invariant initial value problems in one dimensional dynamic elasto-plasticity, with consequences for multidimensional nonassociative plasticity, European Journal of Applied Mathematics (3), 225-254 (1992)
  • [11] D. G. Schaeffer and Michael Shearer, Private communications, 1992
  • [12] J. Smoller, Shock-Waves and Reaction-Diffusion Equations Springer-Verlag, New York and Berlin, 1983
  • [13] T. C. T. Ting, In Propagation of shock waves in solids, E. Varley, editor, pages 41-64, Amer. Soc. Mech. Eng. AMD vol. 17, 1986
  • [14] John A. Trangenstein and R. B. Pember, Numerical algorithms for strong discontinuities in elastic-plastic solids, Journal of Computational Physics, 1991
  • [15] B. van Leer, Towards the ultimate conservative difference scheme. V. A. second-order sequel to Godunov's method, J. Comp. Phys. 32, 101-136 (1979)
  • [16] B. van Leer, On the relation between the upwind-difference schemes of Godunov, Engquist-Osher and Roe, SIAM J. Sci. Stat. Comp. 5 (1), 1-20 (1984)
  • [17] H. C. Yee, On the implementations of a class of upwind schemes for systems of hyperbolic conservation laws, Technical Report TM-86839, NASA, September 1987
  • [18] H. C. Yee, A class of high-resolution explicit and implicit shock-capturing methods, Technical Report TM 101088, NASA, February 1989

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DOI: https://doi.org/10.1090/qam/1276239
Article copyright: © Copyright 1994 American Mathematical Society

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