Constitutive equations and finite element implementation ofstrain localization in sand deformation

来源期刊：中南大学学报(英文版)2009年第3期

论文作者：黄林冲 徐志胜 王立川

文章页码：482 - 487

Key words：constitutive equations; deformation band; finite elements; hydraulic conductivity; sand

Abstract: 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.

基金信息：the Foundation of the Science and Technology Section of Ministry of Railway of China
the Excellent PhD Thesis Innovation Foundation of Central South University, China