DOI QR코드

DOI QR Code

A NUMERICAL ALGORITHM FOR ELASTO-PLASTIC MATERIAL DEFORMATION

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

Abstract

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.

Keywords

References

  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 https://doi.org/10.1007/BF01307216
  3. P. Germain and E. Lee, On Shock Waves in Elastic-Plastic Solids, J. Meeh. Phys. Solids, 21 (1973), 359-382 https://doi.org/10.1016/0022-5096(73)90006-9
  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 https://doi.org/10.1016/0899-8248(90)90017-5
  5. X. Lin and J. Ballmann, A Numerical Scheme for axisymmetric elastic waves in solids, Wave Motion 21 (1995), 115-126 https://doi.org/10.1016/0165-2125(94)00046-8
  6. R. Menikoff and B. Plohr, The Riemann Problem for Fluid Flow of Real Materials, Rev. Mod. Phys. 61 (1989), 75-130 https://doi.org/10.1103/RevModPhys.61.75
  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 https://doi.org/10.1016/0196-8858(88)90025-5
  9. B. Plohr and D. Sharp, A Conservative Formulation for Plasticity, Adv. Appl. Math. 13 (1992), 462-493 https://doi.org/10.1016/0196-8858(92)90022-O
  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 https://doi.org/10.1016/0045-7825(85)90061-1
  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 https://doi.org/10.1063/1.327799
  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 https://doi.org/10.1006/icse.1993.1013