J. Phys. IV France
Volume 105, March 2003
Page(s) 373 - 380

J. Phys. IV France
105 (2003) 373
DOI: 10.1051/jp4:20030209

Finite deformation of random elastic networks: A molecular dynamics study

A. Alaoui1 and K. Sab2

1  Laboratoire d'Analyse des Matériaux et Identification, ENPC/LCPC, 6 & 8 avenue Blaise Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée cedex 2, France
2  Laboratoire des Matériaux et des Structures du Génie Civil, LCPC/ENPC/CNRS, 2 allée Kepler, 77420 Champs-sur-Marne, France

In this paper, we apply the Molecular Dynamics method [7] to the determination of the stable elastic equilibrium of a strut structure compressed beyond its critical buckling loading. In order to illustrate our approach, we consider a square network of elastic beams. The elastic energy of each beam is expressed in terms of the generalised displacements of its ends. Therefore, the total energy can be expressed in terms of the displacements of the lattice nodes : $\underline{U}$. The idea is to compute the solution as follows : each node is endowed with a virtual mass. Starting from arbitrary nodal displacements with zero velocity, we use Molecular Dynamics to compute the oscillations of the system during a prescribed period of time T. Then, we determine the moment $0 < t_0 \le T$ when the potential is minimum and we iterate the algorithm with initial nodal displacements $\underline{U} (t_0)$, and so on.

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