饱和多孔介质中动力渗流耦合分析的Biot-Cosserat连续体模型与应变局部化有限元模拟

提出了适用于饱和多孔介质中应变局部化分析及动力渗流耦合分析的Biot-Cosserat连续体模型。基于饱和多孔介质动力渗流耦合分析的Biot理论,将固体骨架看作Cosserat连续体,并考虑旋转惯性,建立了饱和多孔介质动力渗流耦合分析的Biot-Cosserat连续体模型。基于Galerkin加权余量法,对所发展的模型推导了以固体骨架广义位移(包含旋转)及孔隙水压力为基本未知量的有限元公式。利用所发展的数值模型,对包含压力相关弹塑性固体骨架材料的饱和多孔介质进行了动力渗流耦合分析与应变局部化有限元模拟,结果表明,所发展的两相饱和多孔介质动力渗流耦合分析的Biot-Cosserat连续体模型能保持饱和两相介质应变局部化问题的适定性及模拟饱和多孔介质中由应变软化引起的应变局部化现象的有效性。

THE BIOT-COSSERAT CONTINUUM MODEL FOR COUPLED HYDRO-DYNAMIC ANALYSIS IN SATURATED POROUS MEDIA AND FINITE ELEMENT SIMULATION OF STRAIN LOCALIZATION

The Biot-Cosserat continuum model for coupled hydro-dynamic processes in saturated porous media is proposed by means of the combination of both Biot theory and Cosserat continuum theory to simulate the strain localization phenomena due to the strain softening. In the present contribution, the Biot formulation of the skeleton material is extended with the rotational degree of freedom and associated coupled stresses defined in the Cosserat continuum. The finite element formulations governing the coupled hydro-dynamic behavior with the primary variables of the displacements and the microrotation for the solid phase and pressure for the fluid phase are derived on the basis of the Galerkin-weighted residual method. The strain localization phenomena in saturated porous media due to the strain softening are numerically simulated by using the developed model with corresponding fmite element method and the non-associated Drucker-Prager yield criterion particularly considered for the pressure-dependent elasto-plastic Cosserat skeleton. Numerical results of the plane strain slope illustrate the capability of the developed model in keeping the well-posedness of the boundary value problems with strain softening behavior incorporated, and the availability of modeling the strain localization phenomena in saturated media.