• HWANG HYUN-CHEOL (Department of Mathematics and Information Kyungwon University)
  • Published : 2005.07.01


We present the numerical algorithm for the model for high-strain rate deformation in hyperelastic-viscoplastic materials based on a fully conservative Eulerian formulation by Plohr and Sharp. We use a hyperelastic equation of state and the modified Steinberg and Lund's rate dependent plasticity model for plasticity. A two-dimensional approximate Riemann solver is constructed in an unsplit manner to resolve the complex wave structure and combined with the second order TVD flux. Numerical results are also presented.


  1. E. Bonnetier, H. Jourdren, and P. Veysseyre, Un Modele Hyperelastique-Plastique Eulerieti Applicable aux Grandee Deformations: Quelques Resuliais I-D, Tech. Report preprint, Centre d'Etudes de Limeil-Valenton, 1991
  2. X. Garaizar, The Small Anisotropy Formulation of Elastic Deformation, Acta Appl, Math. 14 (1989), 259-268
  3. P. Germain and E. Lee, On Shock Waves in Elastic-Plastic Solids, J. Meeh. Phys. Solids, 21 (1973), 359-382
  4. P. LeFloch and F. Olsson, A second-order Godunov method for the conservation laws of nonlinear elastodynamics, Impact Comput. Sci. Engrg. 2 (1990), 318-354
  5. X. Lin and J. Ballmann, A Numerical Scheme for axisymmetric elastic waves in solids, Wave Motion 21 (1995), 115-126
  6. R. Menikoff and B. Plohr, The Riemann Problem for Fluid Flow of Real Materials, Rev. Mod. Phys. 61 (1989), 75-130
  7. B. Plohr, Mathematical Modeling of Plasticity in Metals, Mat. Contemp. 11 (1996), 95-120
  8. B. Plohr and D. Sharp, A Conservative Eulerian Formulation of the Equations for Elastic Flow, Adv. Appl. Math. 9 (1988), 481-499
  9. B. Plohr and D. Sharp, A Conservative Formulation for Plasticity, Adv. Appl. Math. 13 (1992), 462-493
  10. M. Scheidler, On the Coupling of Pressure and Deoiatoric Stress in Hyperelastic Materials, Proceedings of the 13th Army Symposium on Solid Mechanics (S.-C. Chou, and F. Bartlett. T. Wright. and K. Iyer, EDS.), 1994
  11. J. Simo and M. Ortiz, A Unified Approach to Finite Deformation Elastoplastic Analysis Based on the Use of Hyperelastic Constitutive Relations, Comput. Methods Appl. Mech. Engrg. 49 (1985), 221-245
  12. D. Steinberg, S. Cochran, and M. Guinan, A Constitutive Model for Metals Applicable at High Strain-Rate, J. Appl. Phys. 51 (1980), 1498-1504rm
  13. E. F. Toro, The weighted average flux method applied to the Euler equations, Phil. Trans. Royal Soc. London, A (1992), no. 341, 499-530
  14. E. F. Toro, The weighted average flux method for hyperbolic conservation laws, Phil. Trans. Royal Soc. London, A (1989), no. 423, 401-418
  15. J. Trangenstein and P. Colella, A Higher-Order Godunov Method for Modeling Finite Deformation in Elastic-Plastic Solids, Comm. Pure Appl. Math. XLIV (1991), 41-100
  16. D. Wagner, Conservation Laws, Coordinate Transformations, and Differential Forms, Proceedings of the Fifth International Conference on Hyperbolic Problems Theory, Numerics, and Applications (j. Glimm, M. J. Graham, J. W. Grove, and B. J. Plohr, eds.), World Scientific Publishers, Singapore, 1996, 471-477
  17. D. Wallace, Thermoelasticity Theory of Stressed Crystals and Higher-Order Elastic Constants, Solid State Physics (H. Ehrenreich, F. Seitz, and D. Turnbull, eds.), Academic Press, New York 25 (1970), 301-403
  18. F. Wang, J. Glimm, J. Grove, B. Plohr, and D. Sharp, A Conservative Eulerian Numerical Scheme for Elasto-Plasticity and Application to Plate Impact Problems, Impact Comput. Sci. Engrg. 5 (1993), 285-308