Macroscopic elastic properties of regular lattices

Wang, Yucang and Mora, Peter (2008) Macroscopic elastic properties of regular lattices. Journal of the Mechanics and Physics of Solids, 56 12: 3459-3474. doi:10.1016/j.jmps.2008.08.011

Author Wang, Yucang
Mora, Peter
Title Macroscopic elastic properties of regular lattices
Journal name Journal of the Mechanics and Physics of Solids   Check publisher's open access policy
ISSN 0022-5096
Publication date 2008-12
Sub-type Article (original research)
DOI 10.1016/j.jmps.2008.08.011
Volume 56
Issue 12
Start page 3459
End page 3474
Total pages 16
Place of publication Oxford, United Kingdom
Publisher Pergamon
Language eng
Abstract In this paper we study analytically the elastic properties of the 2-D and 3-D regular lattices consisting of bonded particles. The particle-scale stiffnesses are derived from the given macroscopic elastic constants (i.e. Young's modulus and Poisson's ratio). Firstly a bonded lattice model is presented. This model permits six kinds of relative motion and corresponding forces between each bonded particle pair. By comparing the strain energy distributions between the discrete lattices and the continuum, the explicit relationship between the microscopic and macroscopic elastic parameters can be obtained for the 2-D hexagonal lattice and the 3-D hexagonal close-packed and face-centered cubic structures. The results suggest that the normal stiffness is determined by Young's modulus and the particle size (in 3-D), and that the ratio of the shear to normal stiffness is related to Poisson's ratio. Rotational stiffness depends on the normal stiffness, shear stiffness and particle sizes. Numerical tests are carried out to validate the analytical results. The results in this paper have theoretical implications for the calibration of the spring stiffnesses in the Discrete Element Method.
Keyword Lattice elasticity
Hexagonal closed packing(HCP)
Face-centered cubic(FCC)
Spring stiffness
Discrete Element Model(DEM)
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: Earth Systems Science Computational Centre Publications
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Created: Thu, 03 Sep 2009, 09:09:56 EST by Mr Andrew Martlew on behalf of Earth Systems Science Computational Centre