A three-dimensional (3D) numerical manifold formulation with continuous nodal gradients (H8-CNS) is presented for dynamic analysis of saturated elasto-plastic porous media based on the three-variable ($u-w-p$) formulation. Using meshes of 8-node hexahedra as mathematical patches, the skeleton displacement ($u$) and fluid velocity ($w$) interpolations are constructed with a constrained and ortho-normalized least-squares (CO-LS) scheme and a piecewise constant interpolation for fluid pressure field is employed. One feature of H8-CNS is to overcome locking in both limiting cases of low permeability and rigid skeleton. Another feature of H8-CNS is to achieve higher accuracy in stress results for porous media problems involving both elastic and elasto-plastic skeleton behaviors. H8-CNS is also able to fully capture dynamic responses of porous media under high-frequency loading. The accuracy and stability of H8-CNS are verified by performing a variety of numerical simulations. Time integration of H8-CNS is shown to be stable and accurate using the energy balance condition.

提出了一种具有连续节点梯度 (H8-CNS) 的三维 (3D) 数值流形公式，用于基于三变量 ($你-瓦-磷$） 公式。使用 8 节点六面体的网格作为数学补丁，骨架位移 ($你$) 和流体速度 ($瓦$) 插值是用约束和正交归一化最小二乘 (CO-LS) 方案构造的，并采用流体压力场的分段常数插值。H8-CNS 的一个特点是在低渗透性和刚性骨架两种极限情况下克服锁定。H8-CNS 的另一个特点是在涉及弹性和弹塑性骨架行为的多孔介质问题中获得更高的应力结果精度。H8-CNS 还能够完全捕获高频载荷下多孔介质的动态响应。H8-CNS 的准确性和稳定性通过执行各种数值模拟得到验证。使用能量平衡条件显示 H8-CNS 的时间积分是稳定和准确的。