Simulation of strain localization with discrete element-Cosserat continuum finite element two scale method for granular materials

• Published in: Journal of the mechanics and physics of solids 2019-01, Vol.122, p.450-471
• Main Authors: Tang, Hongxiang, Dong, Yan, Wang, Ting, Dong, Yifeng
• Format: Article
• Language: English
• Subjects: Algorithms; Computer simulation; Consistent algorithm; Constitutive equations; Constitutive relationships; Continuum modeling; Cosserat continuum; Deformation mechanisms; Digital imaging; Discrete element; Discrete element method; Edge dislocations; Elastoplasticity; Experiments; Failure analysis; Failure modes; Finite element; Finite element analysis; Finite element method; Friction resistance; Granular materials; Mapping; Matrix; Multiscale analysis; Multiscale method; Performance prediction; Physical properties; Plane strain; Regularization; Rolling resistance; Shear bands; Simulation; Sliding friction; Strain localization
• ISSN: 0022-5096; 1873-4782
• DOI: 10.1016/j.jmps.2018.09.029

•The multi-scale approach combines Cosserat FEM and DEM with rolling resistances.•The kinematic consistency of physical parameters in micro-macro models is ensured.•The Cosserat continuum preserves the well-posedness of the localization problem.•A consistent algorithm for generalized elastoplastic Cosserat model is presented.•The rotational deformation and shear band failure modes are effectively reproduced. A multiscale method is proposed based on an individual particle provided with rotational freedom, which considers the kinematic connections and transformation consistency of physical parameters in micro-macro models, as well as the need for a regularization mechanism in the classical macroscopic continuum model to preserve the well-posedness of the localization problem. This method uses the discrete element method to incorporate both rolling resistances (rolling friction tangential force and rolling resistance moment) and the sliding friction tangential force between particles in the contact model on a microscopic scale, while the Cosserat continuum is used to describe the granular materials on a macroscopic scale. In addition, a consistent return mapping algorithm for the integration of the rate constitutive equation and the closed form of the consistent elastoplastic tangent modulus matrix for the generalized elastoplastic Cosserat continuum model are presented. The effectiveness of the developed multiscale method is demonstrated with two cases: one comparing discrete element computations with the Cosserat finite element analysis, and the other comparing a plane strain compression experiment using digital imaging measurements with the Cosserat finite element analysis. The rotational deformation and shear band failure modes are well reproduced in both cases. It also demonstrates that the present model has better performance in predicting the phenomena of shear bands than previous ones.