ABSTRACT
Much of our understanding of soil response has been developed within a continuum mechanics framework. Continuum-based analyses tools are dominant in geotechnical engineering practice. Use of a continuum mechanics framework requires knowledge of the stresses and strains in the material. In a slightly provocative tone, Cundall et al. (1982) suggest that for a granular material these stresses and strains are \ctitious" parameters. The deformation and strength responses that distinguish granular materials from other materials arise from their particulate nature and special, highly complex constitutive models are needed to apply continuum mechanics to granular materials. Continuum mechanics cannot capture many important mechanisms that operate at the particle scale. Geomechanics cannot exclusively adopt either a continuum or a discrete approach, leading Muir Wood (2007) to state that there is a \particulate-continuum duality" in geomechanics. From a geomechanics perspective, DEM micro-scale analyses serve little purpose, and will have little impact on research or practice, if the particulate measurements are not interpreted or translated into
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continuum mechanics terminology. The need to relate discrete and continuum parameters has been recognized since the early work of Cundall and Strack (1978) who presented formulae for the average stress tensor, the average moment tensor and the average displacement gradient tensor within an assembly of disks. In this Chapter approaches that have been proposed to \translate" the results of DEM simulations into the language of continuum mechanics are discussed, considering rstly stress and then strain.
