@inbook{fc39206a426b4b359bf0c9426cda6285,
title = "Advances in multiscale modeling of granular materials",
abstract = "The paper reports recent advances in multiscale modeling of granular materials, particularly in the second-order computational homogenization method and corresponding global-local mixed FEM-DEM nested analysis scheme. The gradient Cosserat continuum and the classical Cosserat continuum are assumed for modelling granular media at the macro- and meso-scales, respectively. According to the generalized Hill{\textquoteright}s lemma formulated for the adopted meso-macro continuum modeling the non-uniform macroscopic strain field with macroscopic strain gradients is downscaled to each representative volume element (RVE), while satisfaction of the generalized Hill-Mandel condition is ensured. The advantage of the gradient Cosserat continuum model in capturing the meso-structural size effect and the performance of the proposed second-order computational homogenization in the simulation of strain softening and localization phenomena are demonstrated, without need to specify macroscopic phenomenological constitutive relationship and material failure model.",
author = "Xikui Li and Yuanbo Liang and Youyao Du and Bernhard Schrefler",
note = "Funding Information: The authors are pleased to acknowledge the support for this work by the National Natural Science Foundation of China through contract/grant numbers 11372066, 11072046 and the National Key Basic Research and Development Program (973 Program) through contract number 2010CB731502. Publisher Copyright: {\textcopyright} 2016 Springer International Publishing Switzerland. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.",
year = "2016",
month = jan,
day = "1",
doi = "10.1007/978-3-319-21494-8_5",
language = "English (US)",
series = "Springer Tracts in Mechanical Engineering",
publisher = "Springer International Publishing",
pages = "63--73",
booktitle = "Springer Tracts in Mechanical Engineering",
}