颗粒土中剪切带临界状态数学描述及其完全解OA北大核心CSTPCD

High-order continuum models are needed for properly capturing the post-failure mechanical respon-ses of soils involving shear bands.Through analysis on the evolution of shear band in granular soils based on a previously proposed micropolar hypoplastic model,a governing equation for the shear band in the critical state was obtained,which is a special nonlinear ordinary differential equation satisfied by the Cosserat angular veloc-ity.A concise derivation of the governing equation was conducted.The properties of the governing equation,the range of the chief parameter and the approach to the solution were mainly discussed.An energy balance equa-tion was formulated as a complementary condition for the determinant of the problem through analysis on the mechanical properties of the shear band.Then,the complete solutions,including the shear-band thickness fac-tor,the stress distribution,the strain rate components,and the shear velocity,were obtained through numeri-cal integration.The shear band thickness factor is particularly useful in determination of the micro-strength pa-rameter of the constitutive model.