A mixed finite element procedure of gradient Cosserat continuum for second-order computational homogenisation of granular materials

Xikui Li, Yuanbo Liang, Qinglin Duan, B. A. Schrefler, Youyao Du

Research output: Contribution to journalArticle

20 Scopus citations

Abstract

A mixed finite element (FE) procedure of the gradient Cosserat continuum for the second-order computational homogenisation of granular materials is presented. The proposed mixed FE is developed based on the Hu–Washizu variational principle. Translational displacements, microrotations, and displacement gradients with Lagrange multipliers are taken as the independent nodal variables. The tangent stiffness matrix of the mixed FE is formulated. The advantage of the gradient Cosserat continuum model in capturing the meso-structural size effect is numerically demonstrated. Patch tests are specially designed and performed to validate the mixed FE formulations. A numerical example is presented to demonstrate the performance of the mixed FE procedure in the simulation of strain softening and localisation phenomena, while without the need to specify the macroscopic phenomenological constitutive relationship and material failure model. The meso-structural mechanisms of the macroscopic failure of granular materials are detected, i.e. significant development of dissipative sliding and rolling frictions among particles in contacts, resulting in the loss of contacts.

Original languageEnglish (US)
Pages (from-to)1331-1356
Number of pages26
JournalComputational Mechanics
Volume54
Issue number5
DOIs
StatePublished - Oct 8 2014

Keywords

  • Computational homogenisation
  • Discrete particle assembly
  • Gradient Cosserat continuum
  • Granular material
  • Mixed finite element

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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