In this paper, a mixed two-scale numerical manifold computational homogenization model is presented for dynamic analysis and wave propagation of the discontinuous heterogeneous porous media based on the first-order homogenization theory. Instead of the conventional version which neglects microscopic dynamics, the extended Hill–Mandel lemma is employed to incorporate the microscale dynamic effects. Microscale and macroscale Initial Boundary Value Problems (IBVPs) are solved simultaneously using the Numerical Manifold Method (NMM) with the information conveyed between different scales. The microscale IBVP is solved under Linear Boundary Conditions (LBCs) and Periodic Boundary Conditions (PBCs) that are defined with macroscale solid displacement, fluid pressure and their first-order gradients. The discontinuous macroscale IBVP is solved iteratively using the Newton method with the macroscale internal forces and Jacobian determined by solving the microscale IBVPs. A stick–slip contact model is implemented using an augmented Lagrange multiplier method to impose frictional contact conditions along the macroscale discontinuities. Through various numerical simulations, the presented two-scale NMM is shown to be able to effectively and accurately capture the fully dynamic and wave propagation responses of the discontinuous heterogeneous porous media under the fluid injection and impact loading condition.

在本文中，基于一阶均质化理论，提出了一种混合两尺度数值流形计算均质化模型，用于不连续非均质多孔介质的动力学分析和波传播。与忽略微观动力学的传统版本不同，采用扩展的 Hill-Mandel 引理来合并微观动态效应。微观和宏观初始边界值问题 (IBVP) 使用数值流形方法 (NMM) 与不同尺度之间传递的信息同时解决。微尺度 IBVP 在线性边界条件 (LBC) 和周期边界条件 (PBC) 下求解，这些条件由宏观固体位移、流体压力及其一阶梯度定义。不连续的宏观 IBVP 使用牛顿法迭代求解，宏观内力和雅可比通过求解微观 IBVP 确定。粘滑接触模型是使用增强拉格朗日乘子方法实现的，以沿宏观不连续性施加摩擦接触条件。通过各种数值模拟，表明所提出的两尺度 NMM 能够有效、准确地捕捉流体注入和冲击载荷条件下不连续非均质多孔介质的全动态和波传播响应。粘滑接触模型是使用增强拉格朗日乘子方法实现的，以沿宏观不连续性施加摩擦接触条件。通过各种数值模拟，表明所提出的两尺度 NMM 能够有效、准确地捕捉流体注入和冲击载荷条件下不连续非均质多孔介质的全动态和波传播响应。粘滑接触模型是使用增强拉格朗日乘子方法实现的，以沿宏观不连续性施加摩擦接触条件。通过各种数值模拟，表明所提出的两尺度 NMM 能够有效、准确地捕捉流体注入和冲击载荷条件下不连续非均质多孔介质的全动态和波传播响应。