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Elastic properties of three-dimensional lattices are usually anisotropic. This fact
limits the range of applicability of lattice models in solid mechanics problems. In the present
paper, we propose a simple three-dimensional lattice model with isotropic elastic properties. A
quasi-random lattice is generated by randomly displacing particles of the face-centered cubic
lattice. Then particles are connected by linear and angular springs such that initially forces in
all springs are equal to zero. It is shown numerically that the resulting quasi-random lattice has
isotropic elastic properties, provided that amplitudes of random displacements are sufficiently
large. Poisson's ratio of the lattice depends on number of angular springs per particle and
stiffnesses of these springs. In the present model, values of Poisson.s ratio belong to the
interval [0;0.41]. The model can be used, in particular, for simulation of deformation and brittle
fracture of rocks in hydraulic fracturing.
Keywords: particle dynamics; quasi-random lattice; face-centered cubic lattice; effective elastic properties; isotropy; molecular dynamics. |
full paper (pdf, 960 Kb)