Elastomers and Composites

The Rubber Society of Korea (한국고무학회)
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Particle-based Numerical Modeling of Linear Viscoelastic Materials using MPM based on FEM for Taylor Impact Simulations

  • Kim, See Jo (Department of Mechanical Design Engineering, Andong National University)
  • Received : 2018.11.06
  • Accepted : 2018.11.14
  • Published : 2018.12.31
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Abstract

Taylor rod impact tests have been the subject of many theoretical and experimental investigations. This paper discusses the numerical methods for simulating the Taylor impact test, which is widely used to obtain constitutive equations and failure conditions under high-velocity collisions of materials. With this in mind, a particle-based MPM (material point method) for linear viscoelastic solid materials was implemented, and MPM simulations for viscoelastic deformation behavior were numerically verified and confirmed by comparing the MPM and FEM results. In addition, this modeling and numerical approach could be extended to more complex viscoelastic models for basic understanding and to analyze the deformation and fracture behavior of more complicated viscoelastic material systems.

Keywords

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Figure 1. Linear viscoelastic solid model.

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Figure 2. (a) Element meshes for FEM and (b) material particles for MPM.

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Figure 3. (a) Time = 5.0(μs) (b) Time = 10.0(μs) (c) Time = 20.0 (μs) for FEM.

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Figure 4. (a) Time = 5.0(μs) (b) Time = 10.0(μs) (c) Time = 20.0 (μs) for MPM.

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Figure 5. Decay constant = 6.5$(\frac{1}{{\mu}s})$ , 65$(\frac{1}{{\mu}s})$ , and 650$(\frac{1}{{\mu}s})$ from left to right at time = 20.0 (μs) (a) for FEM and (b) for MPM.

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Figure 6. (a) β = 6.5(1/μs) (b) β = 65(1/μs) (c) β = 650(1/μs) at time = 20.0(μs) for MPM at time = 20(μs).

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Figure 7. (a) β = 6.5(1/μs) (b) β = 65.0(1/μs) (c) β = 650.0(1/μs) for FEM (left) and MPM (right), respectively.

References

  1. R. A. Gingold and J. J. Monaghan, "Smoothed particle hydrodynamics: theory and application to non-spherical stars", Mon. Not. R. Astron. Soc., 181, 375 (1977). https://doi.org/10.1093/mnras/181.3.375
  2. D. T. Gethin, X. S. Yang, and R. W. Lewis, "A two dimensional combined discrete and finite element scheme for simulating the flow and compaction of systems comprising irregular particulates", Computer Methods in Applied Mechanics and Engineering, 195, 5552 (2006). https://doi.org/10.1016/j.cma.2005.10.025
  3. J. A. Nairn, "Material Point Method Calculations with Explicit Cracks", Computer Modeling in Engineering & Science, 4, 649 (2003).
  4. K. J. Son and E. P. Fahrenthold, "Hybrid particle-element simulation of composite material impact physics", 18th International Conference on Composite Materials, (2011).
  5. Z. Chen, S. Jiang, Y. Gan, H. Liu, and T. D. Sewell, "A Particle-Based Multiscale Simulation Procedure within the Material Point Method Framework", Computational Particle Mechanics, 1, 147 (2014). https://doi.org/10.1007/s40571-014-0016-5
  6. S. E. Jones, A. D., and L. L. Wilson, "An elementary theory for the Taylor impact test", International Journal of Impact Engineering, 21, 1 (1998). https://doi.org/10.1016/S0734-743X(97)00036-5
  7. H. S. Shin, S. T. Park, S. J. Kim, J. H. Choi, and J. T. Kim, "Deformation behavior of polymeric materials by Taylor impact", International Journal of Modern Physics B, 22, 1235 (2008). https://doi.org/10.1142/S0217979208046591
  8. S. J. Kim, K. H. Lim, H. S. Shin, J. T. Kim, and J. H. Choi, "Numerical simulation of viscoelastic effects on the rod deformation of Taylor impact test", International Journal of Modern Physics B, 22, 1297 (2008). https://doi.org/10.1142/S0217979208046682
  9. Zhang, Z. Chen, and Y. Liu, "The Material Point Method : A Continuum-Based Particle Method for Extreme Loading Cases (Tsinghua University Press Computational Mechanics Series)", Elsevier Science. Kindle Edition, (2016).
  10. 류민영, 조광수, 주상우, 권영돈, 정인재, "이론유변학", 한국유변학회, (2009).
  11. J. I. Lin, "Dyna3D: A explicit three-dimensional finite element code for solid structural mechanics, User manual", UCRL-MA-107254, (2005).
  12. J. O. Hallquist, LS-DYNA Theory manual, (2006).