Constitutive equations and finite element implementation of strain localization in sand deformation

  • Lin-chong Huang (黄林冲)Email author
  • Zhi-sheng Xu (徐志胜)
  • Li-chuan Wang (王立川)


A recently proposed model coupling with the solid-fluid of the saturated sand was utilized to study the deformation band. Based on the critical state plasticity model by Borja and Andrade, the hydraulic conductivity tensor was naturally treated as a function of the spatial discretization matrix about the displacement and the stress field, allowing a more realistic representation of the physical phenomenon. The fully Lagrangian form of the Darcy law was resolved by Piola algorithm, and then the flow law was gained, leading to the implementation of a modified model of the saturated sand. Then the criterion for the onset of localization was derived and utilized to detect instability. The constitutive model was implemented in a finite element program coded by FORTRAN, which was used to predict the formation and development of shear bands in plane strain compression of saturated sand. At last, the formation mechanism of the shear band was discussed. It is shown that the model works well, and the simulation sample bifurcates at 1.18% axial strain, which is in a good qualitative agreement with the experiment. The pore pressure greatly affects the onset and development of the deformation band, and it obviously increases around the localization-prone regions with the direction toward the outer side of the normal of the shear band, while the pore stress flows nearly horizontally and is distributed equally far away the shear band region.

Key words

constitutive equations deformation band finite elements hydraulic conductivity sand 


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Copyright information

© Central South University Press and Springer-Verlag GmbH 2009

Authors and Affiliations

  • Lin-chong Huang (黄林冲)
    • 1
    • 2
    Email author
  • Zhi-sheng Xu (徐志胜)
    • 1
  • Li-chuan Wang (王立川)
    • 1
  1. 1.School of Civil and Architectural EngineeringCentral South UniversityChangshaChina
  2. 2.Department of Civil and Environmental EngineeringNorthwestern UniversityEvanstonUSA

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