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Title: Finite element implementation and application of a sand model in micropolar theory
Authors: Liu, J
Yin, ZY 
Wu, L
Hicher, PY
Issue Date: Aug-2021
Source: SN applied sciences, Aug. 2021, v. 3, no. 8, 725
Abstract: Abstract: In traditional finite element failure analyses of geotechnical structures, the micro grain rotations cannot be modelled and numerical solutions are mesh dependent. In this study, a user element including rotational degree of freedom has been developed based on micropolar theory (Cosserat theory), then an enhanced non-associated sand model is calibrated with laboratory data and used to model the plane strain tests. The simulated results demonstrate the polarized model is able to model reasonably the sand behavior as well as the grain rotations in the localized region. What’s more, with this enhanced model, the mesh independent numerical solutions in terms of mechanical responses, shear bands thickness and orientations have been obtained.
Article highlights: (1)In failure analysis of geostructures, significant rotations of soil grains have been observed to occur in the strain localized regions, but the current commercial Finite Element tools cannot model the micro rotations. Therefore, a user defined element must be developed to include the rotational degree of freedom. The micropolar approach is proven to be effective to model the grain rations in present paper. (2)More suitable than other classical soil or sand constitutive models, the selected non-associated sand model in present paper is capable of describing well the contraction and shear dilatancy behaviors of sand. Then the model has been enhanced by means of micropolar technique, in this way, the reasonable strain localization phenomena in laboratory tests could be predicted well.(3)There are always the mesh dependent problems for traditional simulations of the strain localization phenomena in finite element analysis. It can be found in present paper that the mesh independent numerical solutions are obtained by means of micropolar technique. Furthermore, the micropolar approach can obviously improve convergence difficulties in finite element analyses.
Keywords: Granular material
Mesh independency
Micropolar technique
Numerical simulations
Strain localization
Publisher: Springer
Journal: SN applied sciences 
ISSN: 2523-3963
EISSN: 2523-3971
DOI: 10.1007/s42452-021-04708-z
Rights: © The Author(s) 2021
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit
The following publication Liu, J., Yin, ZY., Wu, L. et al. Finite element implementation and application of a sand model in micropolar theory. SN Appl. Sci. 3, 725 (2021) is available at
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