On the basis of Hill＇s lemma for classical Cauchy continuum, a version of Hill＇s lemma for micro-macro homogenization modeling of heterogeneous Cosserat continuum is presented in the flame of average-field theory. T...On the basis of Hill＇s lemma for classical Cauchy continuum, a version of Hill＇s lemma for micro-macro homogenization modeling of heterogeneous Cosserat continuum is presented in the flame of average-field theory. The admissible boundary conditions required to prescribe on the representative volume element for the modeling are extracted and discussed to ensure the satisfaction of Hill-Mandel energy condition and the first-order average field theory.展开更多
Displacement fluctuation is the difference between the real displacement and the affine displacement in deforming granular materials. The discrete element method （DEM） is widely used along with experimental approach...Displacement fluctuation is the difference between the real displacement and the affine displacement in deforming granular materials. The discrete element method （DEM） is widely used along with experimental approaches to investigate whether the displacement fluctuation represents the vortex structure. Current research suggests that the vortex structure is caused by the cooperative motion of particle groups on meso-scales, which results in strain localization in granular materials. In this brief article, we investigate the vortex structure using the finite element method （FEM） based on the Cosserat cor[tinuum model. The numerical example focuses on the relationship between the vortex structure and the shear bands under two conditions： （a） uniform granular materials; （b） granular materials with inclusions. When compared with distributions of the effective strain and the vortex structure, we find that the vortex structure coexists with the strain localization and originates from the stiffness cooperation of different locations in granular materials at the macro level.展开更多
基金supported by the National Natural Science Foundation of China (90715011, 10672033 and 10590354) the National Key Basic Research and Development Program (2002CB412709) the Australia Research Council through the ARC International Fellowship Offered at University of Newcastle (LX0666274)
文摘On the basis of Hill＇s lemma for classical Cauchy continuum, a version of Hill＇s lemma for micro-macro homogenization modeling of heterogeneous Cosserat continuum is presented in the flame of average-field theory. The admissible boundary conditions required to prescribe on the representative volume element for the modeling are extracted and discussed to ensure the satisfaction of Hill-Mandel energy condition and the first-order average field theory.
基金supported by the National Natural Science Foundation of China(Nos.11172216 and 11472196)the Natural Key Basic Research and Development Program of China(973 Program)(Nos.2010CB731502 and 2010CB732005)
文摘Displacement fluctuation is the difference between the real displacement and the affine displacement in deforming granular materials. The discrete element method （DEM） is widely used along with experimental approaches to investigate whether the displacement fluctuation represents the vortex structure. Current research suggests that the vortex structure is caused by the cooperative motion of particle groups on meso-scales, which results in strain localization in granular materials. In this brief article, we investigate the vortex structure using the finite element method （FEM） based on the Cosserat cor[tinuum model. The numerical example focuses on the relationship between the vortex structure and the shear bands under two conditions： （a） uniform granular materials; （b） granular materials with inclusions. When compared with distributions of the effective strain and the vortex structure, we find that the vortex structure coexists with the strain localization and originates from the stiffness cooperation of different locations in granular materials at the macro level.
