A particle method for history-dependent materials. (English) Zbl 0851.73078

We propose a particle-in-cell method in which particles are interpreted as material points that are followed through the complete loading process. A fixed Eulerian grid provides the means for determining a spatial gradient. Because the grid can also be interpreted as an updated Lagrangian frame, the usual convection term in the acceleration associated with Eulerian formulations does not appear. With the use of maps between material points and the grid, the advantages of both Eulerian and Lagrangian schemes are utilized, so that mesh tangling is avoided while material variables are tracked through the complete deformation history. Example solutions in two dimensions are given to illustrate the robustness of the algorithm.


74S30 Other numerical methods in solid mechanics (MSC2010)
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[1] Harlow, F. H.: The particle-in-cell computing method for fluid dynamics. Methods for computational physics 3, 319-343 (1964)
[2] Brackbill, J. U.; Ruppel, H. M.: FLIP: a method for adaptively zoned, particle-in-cell calculations of fluid flows in two dimensions. J. comput. Phys. 65, 314-343 (1986) · Zbl 0592.76090
[3] Brackbill, J. U.; Kothe, D. B.; Ruppel, H. M.: FLIP: a low-dissipation, particle-in-cell method for fluid flow. Comput. phys. Comm. 48, 25-38 (1988)
[4] Burgess, D.; Sulsky, D.; Brackbill, J. U.: Mass matrix formulation of the FLIP particle-in-cell method. J. comput. Phys. 103, 1-15 (1992) · Zbl 0761.73117
[5] Sulsky, D.; Brackbill, J. U.: A numerical method for suspension flow. J. comput. Phys. 96, 339-368 (1991) · Zbl 0727.76082
[6] Hirt, C. W.; Amsden, A. A.; Cook, J. L.: An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J. comput. Phys. 14, 227-293 (1974) · Zbl 0292.76018
[7] Belytschko, T. B.; Kennedy, J. M.; Schoeberle, D. F.: Quasi-Eulerian finite element formulation for fluid-structure interaction. J. pressure vessel technol. 102, 62-69 (1980)
[8] Bensen, D. J.: Computational methods in Lagrangian and Eulerian hydrocodes. Comput. methods appl. Mech. engng. 99, 235-394 (1992) · Zbl 0763.73052
[9] Smolarkiewicz, P. K.: A fully multidimensional positive definite advection transport algorithm with small implicit diffusion. Comput. phys. 54, 325-362 (1984)
[10] Libersky, L. D.; Petschek, A. G.; Carney, T. C.; Hipp, J. R.; Allahdadi, F. A.: High strain Lagrangian hydrodynamics: a three-dimensional SPH code for dynamic material response. J. comput. Phys. 109, 67-75 (1993) · Zbl 0791.76065
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