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Application of Discrete Element Method for Continuum Dynamic Problems

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Abstract

A new method based on the principle of minimum potential energy is presented, aiming to overcome some weakness of the present discrete element method (DEM). Our primary research is to put forward the DEM with a tight theory base and a fit technique for treating continuum dynamic problems. By using this method, we can not only extend the existing seven-disc model, but also establish a new nine-disc model in a general way. Moreover, the equivalences of two kinds of models have been verified. In addition, three numerical examples of stress wave propagation problems are given in order to validate accuracy and efficiency of the present DEM models and their algorithms. Finally, the dynamic stress concentration problem of a square plate with a circular hole is analyzed.

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References

  1. Liu K., Gao L., TANIMURA S. (2004). Application of discrete element method in impact problems. JSME Int J Ser A 47:138–145

    Article  Google Scholar 

  2. Cundall P.A. (1971). A computer model for simulating progressive large scale movement in block rock system. Symp ISRM Proc 2:129–136

    Google Scholar 

  3. Herrmann H.J., Luding S. (1998). Modeling granular media on the computer. Continuum Mech Thermodyn 10:189–231

    Article  MATH  MathSciNet  Google Scholar 

  4. Tsuji Y. (2000). Activities in discrete particle simulation in Japan. Powder Technol 113:278–286

    Article  Google Scholar 

  5. Liu K., Gao L. (2003). A review on the discrete element method (in Chinese). Adv mech 33:483–49

    Google Scholar 

  6. Onate E., Rojek J. (2004). Combination of discrete element and finite element methods for dynamic analysis of geomechanics problems. Comput Methods Appl Mech Eng 193:3087–3128

    Article  MATH  Google Scholar 

  7. Mohammadi S., Owen D.R.J., Peric D. (1998). A combined finite/discrete element algorithm for delamination analysis of composites. Fin Elem Anal Des 28:321–336

    Article  MATH  Google Scholar 

  8. Sawamoto Y., Tsubota H., Kasai Y., Koshika N., Morikawa H. (1998). Analytical studies on local damage to reinforced concrete structures under impact loading by discrete element method. Nucl Eng Des 179:157–177

    Article  Google Scholar 

  9. Liu K., Gao L. (2003). The application of discrete element method in solving three dimensional impact dynamics problems. Acta Mech Sol 16:256–261

    Article  Google Scholar 

  10. Liu, K., Li, X.: Numerical simulation of stress wave propagation in an orthotropic plate. In: Proceedings of the 2nd international symposium on impact engineering, pp. 19–24 (1996)

  11. Berezovski, A., Maugin, G.A.: Simulation of thermoelastic wave propagation by means of a composite wave-propagation algorithm. J Comput Phys 168, 249–264 (2001)

    Google Scholar 

  12. LeVeque R.J. (1997). Wave Propagation algorithms for multiple hyperbolic systems. J Comput Phys 131:327–353

    Article  MATH  Google Scholar 

  13. Berezovski A., Engelbrecht J., Maugin G.A. (2003). Numerical simulation of two-dimensional wave propagation in functionally graded materials. Eur J Mech A Solids 22:257–265

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. LTCS and Department of Mechanics and Engineering Science, Peking University, Beijing, 100871, People’s Republic of China

    K. Liu & W. Liu

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  1. K. Liu
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  2. W. Liu
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Correspondence to K. Liu.

Additional information

This work was supported by Nation Natural Science Foundation of China (nos. 10232040 and 10572002).

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Liu, K., Liu, W. Application of Discrete Element Method for Continuum Dynamic Problems. Arch Appl Mech 76, 229–243 (2006). https://doi.org/10.1007/s00419-006-0018-8

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  • DOI: https://doi.org/10.1007/s00419-006-0018-8

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