饱和多孔介质中的混合有限元法和有限应变下应变局部化分析

对基于Biot理论的饱和多孔介质中动力-渗流耦合分析提出了一个耦合场混合元．固相位移、应变和有效应力以及流相压力、压力梯度和Darcy速度在单元内均处理为独立变量分别插值．基于胡海昌-Washizu三变量广义变分原理给出的饱和多孔介质动力-渗流耦合问题控制方程的单元弱形式，导出了单元公式．进一步导出了考虑压力相关非关联塑性的非线性单元公式和发展了相应的一致性算法．对几何非线性分析，采用了共旋公式途径．数值结果例题显示所发展耦合场混合元模拟大应变下由应变软化引起以应变局部化为特征的渐进破坏现象的性能．

Mixed finite element method for saturated porous media and application to starin localization at finite strain

A mixed finite element for dynamic-seepage analysis in saturated porous media in the frame of the Biot theory is proposed. Displacements, effective stresses, strains for the solid phase and pressure, pressure gradients, Darcy velocities for the fluid phase are interpolated as independent variables. The weak form of the governing equations of coupled dynamic-seepage problems in saturated porous media within the element are given on the basis of the Hu-Washizu three-filed variational principle. The proposed mixed finite element formulation is derived. The nonlinear version of the element formulation is further derived with particular consideration of the pressure dependent non-associated plasticity. The return mapping algorithm for the integration of the rate constitutive equation, the consistent elasto-plastic tangent modulus matrix and the element stiffness matrix are developed. For geometrical non-linearity, the co-rotational formulation approach is utilized. Numerical results demonstrate the capability and the performance of the proposed element in modelling progressive failure characterized by strain localization due to strain softening in dynamic conditions at large strain.