Enhanced continua and discrete lattices for modelling granular assemblies

This article discusses the derivation of continuum models that can be used for modelling the inhomogeneous mechanical behaviour of granular assemblies. These so-called kinematically enhanced models are of the strain-gradient type and of the strain-gradient micro-polar type, and are derived by means...

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Bibliographic Details
Published in:Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 2005-11, Vol.363 (1836), p.2543-2580
Main Authors: Suiker, Akke S. J., de Borst, René
Format: Article
Language:English
Subjects:
Continuum modeling
Discrete Lattice Models
Enhanced Continuum Models
Granular Material
Granular materials
Harmonics
Homogenization
Kinematics
Mathematical expressions
Micro-Structure
Rotation
Stiffness
Wave dispersion
Wave Propagation
Wavelengths
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Summary:This article discusses the derivation of continuum models that can be used for modelling the inhomogeneous mechanical behaviour of granular assemblies. These so-called kinematically enhanced models are of the strain-gradient type and of the strain-gradient micro-polar type, and are derived by means of homogenizing the micro-structural interactions between discrete particles. By analysis of the body wave dispersion curves, the enhanced continuum models are compared to corresponding discrete lattice models. Accordingly, it can be examined up to which deformation level the continuum models are able to accurately describe the discrete particle behaviour. Further, the boundary conditions for the enhanced continuum models are formulated, and their stability is considered. It is demonstrated how to use the body wave dispersion relations for the assessment of stability.
ISSN:1364-503X
1471-2962
DOI:10.1098/rsta.2005.1586