Modeling of granular materials with intrinsic length

Abstract
This paper addresses the continuum modeling of a discrete system such as granular media. Depending on the postulated form of the continuous deformation field, we have classified the continua into five model types. For higher-order models, the derived constitutive equations contain one or more material constants that have a dimension of length, which can be regarded as the intrinsic length of the material. In order to illustrate the influence of the intrinsic length, a high-gradient continuum model is applied for analysis of the behavior of a granular rod that is subjected to a forced vibration. The derived solution shows some salient behavior of the granular rod that can not be captured when using the classical continuum model. A discussion is given on the effect of the ratio between the intrinsic length and the sample size.