Abstract
We conduct two-dimensional molecular dynamics simulations to study the statistical distribution of the force-moment (defined as stress multiplied by volume) of static granular packings under external isotropic compression. To that end, we generate packings by compressing initially ordered lattices using irregular, randomly generated, walls. Velocity-Verlet algorithm and linear spring-dashpot interactions are employed. With this specific method, the obtained statistical distributions of the force-moment are similar for different initial packings. However they depend on the timestep selection within a range of values. This shows that inadequate molecular dynamic simulations may provide different classes of solutions for the same physical process, and this could cause problems to validate theoretical approaches based on statistical mechanics.
Graphical abstract
Similar content being viewed by others
References
H.M. Jaeger, S.R. Nagel, Rev. Mod. Phys. 68, 1259 (1996).
P.G. de Gennes, Physica A 261, 267 (1998).
H.J. Herrmann, Physica A 313, 188 (2002).
J.D. Bernal, J. Mason, Nature 188, 910 (1960).
S. Torquato, F.H. Stillinger, Rev. Mod. Phys. 82, 2633 (2010).
C.H. Liu, S.R. Nagel, D.A. Schecter, S.N. Coppersmith, S. Majumdar, O. Narayan, T.A. Witten, Science 269, 513 (1995).
T.S. Majmudar, R.P. Behringer, Nature 435, 1079 (2005).
D.M. Mueth, H.M. Jaeger, S.R. Nagel, Phys. Rev. E 57, 3164 (1998).
F. Radjai, M. Jean, J.-J. Moreau, S. Roux, Phys. Rev. Let. 77, 274 (1996).
S. Luding, Phys. Rev. E 55, 4720 (1997).
J.H. Snoeijer, T.J.H. Vlugt, M. van Hecke, J. van Saarloos, Phys. Rev. Lett. 92, 054302 (2004).
J.H. Snoeijer, T.J.H. Vlugt, W.G. Ellenbroek, M. van Hecke, J.M.J. van Leeuwen, Phys. Rev. E 70, 061306 (2004).
J.H. Snoeijer, W.G. Ellenbroek, T.J.H. Vlugt, M. van Hecke, Phys. Rev. Lett. 96, 098001 (2006).
B.P. Tighe, A.R.T. van Eerd, T.J.H. Vlugt, Phys. Rev. Lett. 100, 238001 (2008).
S. Henkes, C.S.O. Hern, B. Chakraborty, Phys. Rev. Lett. 99, 038002 (2007).
S. Henkes, B. Chakraborty, Phys. Rev. E 79, 061301 (2009).
S. Edwards, R. Oakeshott, Physica A 157, 1080 (1989).
S. Edwards, Physica A 353, 114 (2005).
M.P. Ciamarra, P. Richard, M. Schroter, B.P. Tighe, Soft Matter 8, 9731 (2012).
D. Frenkel, Eur. Phys. J. Plus 128, 1 (2013).
I.G. Tejada, R. Jimenez, Engin. Comput. 30, 301 (2013).
D.C. Rapaport, The Art of Molecular Dynamics Simulation, 2nd edition (Cambridge University Press, 2004).
B.J. Alder, T.E. Wainwright, J. Chem. Phys. 31, 459 (1959).
A. Rahman, Phys. Rev. 136, A405 (1964).
P.A. Cundall, O.D.L. Strack, Geotechnique 29, 47 (1979).
L. Verlet, Phys. Rev. 159, 98 (1967).
W.C. Swope, H.C. Andersen, P.H. Berens, K.R. Wilson, J. Chem. Phys. 76, 637 (1982).
C. O’Sullivan, J.D. Bray, Engin. Comput. 21, 278 (2007).
A. Peña, P. Lind, S. McNamara, H. Herrmann, Acta Mech. 205, 171 (2009).
C.S. Campbell, J. Fluid Mech. 465, 261 (2002).
L. Aarons, S. Sundaresan, Powder Technol. 169, 10 (2006).
S.J. Plimpton, J. Comput. Phys. 117, 1 (1995).
S. Luding, in Physics of Dry Granular Media, edited by H. Herrmann, J.-P. Hovi, S. Luding, Vol. 350 of NATO ASI Series (Springer, The Netherlands, 1998) pp. 285--304.
L.E. Silbert, D. Ertaş, G.S. Grest, T.C. Halsey, D. Levine, S.J. Plimpton, Phys. Rev. E 64, 051302 (2001).
J.W. Landry, G.S. Grest, L.E. Silbert, S.J. Plimpton, Phys. Rev. E 67, 041303 (2003).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tejada, I.G., Jimenez, R. Impact of the timestep in some molecular dynamics simulations on compression of granular systems. Eur. Phys. J. E 37, 15 (2014). https://doi.org/10.1140/epje/i2014-14015-4
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/i2014-14015-4